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\title{Microfluidics \\ Bootcamp 2011}
\author{Saurabh Vyawahare}
\publisher{Princeton Physical Sciences-Oncology Center \\ Princeton, UCSF, John Hopkins, UCSC, Salk }

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%Acknowledgement section
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We gratefully acknowledge support from the National Cancer Institute Award Number U54CA143803. The author would like to specially thank Temple Douglas, Megan McClean, and Jason Puchalla for assisting in running the course. Further thanks to Robert Austin (senior PI, PPS-OC), James Sturm (PI, PPS-OC), Amy Wu, Joseph Desilva (silicon devices), Kevin Loutherback (bump array), Airon Wills (C.Elegans), Robert Cooper (dicty-ostelium), Rafael Gomez-Sjoberg, Benjamin Arar (control system). Melissa Aranzamendes, Sandra Lam and Kim Hagelbach provided superb administrative help; Claude Champaign, Barbara Grunwerg, Lauren Callahan, and Darryl Johnson helped with purchasing supplies.  Michelle Khine (UC Irvine), Scott Strayer (Nanoshrink), Elias Horn (Ibidi), Megan Nicolson (Ibidi), Ilse Geller (Fluidigm), Pedja Sekaric (Fluidigm), Peter M. Ignelzi (3M),RJ Taylor provided valuable input for parts of the course. Any errors are solely the responsibility of the author.  The information presented here does not necessarily represent the official views of the National Cancer Institute or the National Institutes of Health.
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Copyright \copyright\ \the\year\ \thanklessauthor \\
This work is licensed under a Creative Commons Attribution - Non-Commercial - ShareAlike 3.0 Unported License. 
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\par\smallcaps{Published by \thanklesspublisher}

\par These notes were produced using the Tufte book Latex code \smallcaps{tufte-latex.googlecode.com}which is licensed under the Apache License, Version 2.0.

Images were obtained from Wikipedia commons (public domain) or the author's personal collection, unless otherwise specified.  

\par The information in this course is provided "as-is" without any explicit or implied warranties as to its accuracy, safety, and applicability to any specific purpose. The author does not bear any responsibility for any use given by third parties to this information, and to the devices herein described. The users of this information shall assume all risks and full responsibility for all aspects of their assembly and use.


\par\textit{First printing, August 2011}
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\tableofcontents

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\part{Lecture Notes}

\chapter{1: Microfluidics, Fluid Mechanics and Scaling}
\section{Introduction}
Have you used a microfluidic device before? \\

For almost all readers - the answer is yes.  If you have used an ink-jet printer, you have used a microfludic device. The ink-jet nozzle shoots picoliter (\(10^{-12}\) liter) volume drops of ink onto a page.  Volumes this small, fall within the ambit of microfludics; we can define microfluidics as the science and technology of controlling fluids (gases, liquids) at the micro-scale.  

\marginnote[-2cm]{ Conversion units: \\  \(1000 \mu m^3 = 1 \) picoliter = Volume of a \(10 \mu m\) side cube \\
\(10^6 \mu m^3 = 1\) nanoliter = Volume of a \(100 \mu m\) side cube}

\par Here, in this course, we are primarily interested in the bio-chemical applications of microfluidics, rather than physical applications like printing\sidenote[][-1cm]{Although it worth noting that micro-arrays can be printed using ink-jet techniques}. And while picoliter volumes may seem small, they are still large in comparison to  microbiological volumes. For example, consider a bacteria like \emph{Esherichia Coliform} (E.Coli) - nearly 10,000 E.Coli would fit in one picoliter.  Other volumes are more comparable: about 10 red blood cells would fit into \(1\) picoliter. Scaling down into the world of proteins and atoms, we find over a million molecules of a large protein like a ribozyme can fit in one picoliter. And a $1$ picoliter drop of water contains nearly \(10^{13}\) molecules. 

\begin{marginfigure}
\includegraphics[height=50mm]{./pic/volume.png}
\caption{Volume of cells and proteins: 10000 E.coli = 10 RBC = $10^6$ ribozymes = $10^{13}$ water molecules}
\label{fig:volume}
\end{marginfigure}

\par This leads us confronting the \emph{central problem of microfluidics}: how to make machines and devices that manipulate cells, proteins and other biological materials, bridging the gap between everyday volumes we are familiar with to the micro-scale volumes common in biology.  If successful, this type of plumbing could be used to miniaturize and automate sequencing, protein crystallization, immunoassays, cell cultures and many, many other applications.  And, this is not all: perhaps we may find that physical laws at the micro-scale will allow machines and techniques that would that would be impossible at a larger scale.

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%\begin{center} 
%Microfluidic Chip
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\section{A Tour of Fluid Mechanics}
We will attempt a whirlwind tour of fluid mechanics in this section, proceeding in an approximately historic order.   Of course, the reader will understand, that this is not a real history, just a pedagogic tool to quickly come to grasp with the fantastic field of fluids.

It is remarkable that despite several centuries of active work on fluids - far from being a sterile field where everything is understood, surprises seem to hide at every corner.  Still a formidable amount \emph{is} known; fluid mechanics is a large field, rich and deep, and we have occasion only to 'wet our feet'.

One way to think of fluid-mechanics is that it is a series of approximation to what a fluid is. We build mathematical models that capture essential elements, while ignoring seemingly inconsequential or confounding complexities - hoping that they won't matter.  Sooner or later, however, experiments will reveal the model fails against reality, and we need to add to our approximation as understanding increases with time.  This process has been going on for a long time and continues today.  To start with there are three basic concepts that should be clearly understood - buoyancy, pressure and viscosity.

\begin{marginfigure}
\includegraphics[width=2in]{./pic/FieldsMedalFront.jpg}
\caption{Archimedes' face on the Fields Medal in Mathematics}
\label{fig:Arch}
\end{marginfigure}

\subsection{Buoyancy}
Our starting point is the law of buoyancy discovered by Archimedes (280 to 212 BC, Syracuses, Sicily), supposedly while trying to solve the problem given to him by the king of finding out if a crown was made of real gold (it wasn't if we believe a few accounts).  Archimedes principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces with its submerged volume.   If an object was fully submerged, its apparent weight is given by:

\begin{equation}
W_{\mbox{fluid}}=W\left(1-\frac{\rho_{\mbox{fluid}}}{\rho}\right)
\end{equation}

At this point in time our ancestors have only a vague notion of what flow is, or for that matter what forces are, but the laws of buoyancy are sufficient to design many ships and go sailing.   After this there was a long hiatus in scientific achievement in western Europe, though progress was being made elsewhere. 

\begin{marginfigure}
\includegraphics{./pic/Blaise_Pascal.PNG}
\caption{Blaise Pascal (1623-1662)}
\label{fig:Pascal}
\end{marginfigure}

\subsection{Pressure}
Several hundred years later, with renaissance blossoming in Europe, Blaise Pascal made a leap by understanding the nature of pressure (hence founding the science of hydrostatics). Imagine that you put an small object in water - pressure is simply the force needed per unit area to keep  water out. At a given point, pressure in a fluid is the same in any direction - it is what physicists call a \emph{scalar} quantity.  The SI unit of pressure is now called the Pascal (Pa) in Blaise Pascal's honor \sidenote[][]{ A wonderful set of educational videos on fluid dynamics by prominent scientists can be found here \url{http://web.mit.edu/hml/ncfmf.html} for free (needs Real media player)}. 

Consider a water tank standing undisturbed by itself.  If you took a pressure sensor and measured the pressure you would find that the pressure depended linearly on height given by:  

\begin{equation}
p - p_{0} = \rho g h
\end{equation}

\begin{figure}
\includegraphics{./pic/pressure.png}
\caption{Pressure at a point A in a stationary fluid is the same in all directions and depends on the height of the column above it.}
\label{fig:pressure}
\end{figure}

where \(p_{0}\) is the atmospheric pressure (or reference pressure), \(\rho\) the density of the liquid and h the height of liquid column.  This equation can be derived from elementary considerations of force balances: the column of water is not accelerating, so from Newton's law its weight must be balanced by the pressure exerted over any surface area chosen.  

Pressure is measures in units of \unitfrac{N}{$m^2$} also called a Pascal(Pa). In practice, a variety of units are used and it is worth remembering the conversion factors between them. Atmospheric pressure is about $10^5$ Pa.  This being the US, we will make things harder for ourselves by using psi as our measuring unit in experiments, and it may be worth remembering that about 14.7 psi is equal to one atmospheric pressure as a point of reference.

\begin{margintable}
\emph{Atmospeheric Presure} \\
$1.01325 x 10^5$ Pascal (Pa)  \\
$1.01325$ bar \\
$1$ atmosphere (atm) \\
$760$ torr \\
 $14.696$ pound-force per square inch (psi) \\
\end{margintable}

A fluid has, at any given point, several physical properties - each point is associated with a pressure, temperature, a velocity etc. The job of a fluid mechanist is to try to predict, knowing some initial conditions and the geometry, what these values will be at a future time.  As one knows from weather prediction, most of the time, this is a miserable endeavor!  Only in certain simple cases can complete prediction be made.  Still, much information can be gleaned about the behavior in general, even if we cannot calculate everything.  Let's continue to explore fluid properties:

\subsection{Viscosity}
Next in the line of illustrious scientists is Issac Newton. Newton being rather perspicacious, grasped that fluids have a special property called viscosity. 

\begin{marginfigure}
\includegraphics[width=2in,height=2in]{./pic/Newton.jpg}
\caption{Issac Newton (1642-1727)}
\label{fig:Newton}
\end{marginfigure}

He describes an experiment: imagine two parallel plates separated by a distance d, and with a liquid in between.  If one were to move the top plate forward, while keeping the bottom plate fixed- how much force is required?  The force it turns out depends on the area of the plate, the velocity you want to move it, and the distance between the plates and a characteristic number for each fluid called the viscosity. We can write for the force.

\begin{equation}
\frac{F}{A} = \mu \frac{v}{d}
\end{equation}

\begin{figure}
\includegraphics[width=3in]{./pic/viscosity.png}
\caption{Viscosity determines the force needed to move the plate}
\label{fig:viscosity}
\end{figure}

Here F is the force, v the velocity of the plate, A the area of the plate and d the distance between the plates.  Newton realized that in contrast to solids,where the force to shear them depends on the distortion, in fluids the force depends on the \emph{rate of distortion}. This is a fundamental difference between liquids and solids.

\begin{margintable}
\caption{Viscosity}
\begin{tabular}{lll}
\toprule
\multicolumn{3}{c}{Viscosity values at $20^0$ C}\\
\cmidrule(r){1-3}
Type &amp; Viscosity ($\eta$) &amp; Specific Viscosity ($\nu$)\\
 &amp;  $Ns/m^2$ &amp; $m^2/s$ \\
\midrule
air &amp; $10^{-3}$&amp;  $10^{-6}$   \\
water &amp; $10^{-5}$ &amp;  $15 \times 10^{-6}$  \\
\bottomrule
\end{tabular}
\end{margintable}

For many fluids the coefficient of viscosity is nearly independent of velocity. These are called Newtonian fluids.  For some fluids, this is not the case and the viscosity can vary in many interesting ways depending on the velocity or past history. A classical example of this is silly putty. Silly putty will move freely if you push on it slowly, but try impinging on it with a fast motion (like a hammer) and it will resist like a solid.  This behavior is called viscoelastic - in-between what you could expect from a solid and a liquid.  Figure \ref{fig:non-newtonian} below shows other kinds of behavior - dilatant (paints) and thickening (toothpaste).  This is a large field or research in material science called rheology. Newton's equation is followed by many liquids - water, glycerin, alcohol, honey etc., but not all liquids.   Fluids can be shear thinning or shear thickening, and can have complicated time (i.e history) dependent effects, many of which are not completely understood.
 
\begin{figure}
\includegraphics[width=4in]{./pic/non-newtonian.png}
\caption{A variety of viscoelastic behaviors}
\label{fig:non-newtonian}
\end{figure}

The units of viscosity are $kg\cdot m^{-1} \cdot s^{-1}$ or equivalently $Pa\cdot s$. Often other units are used: $1 Pa \cdot s$ is equal to 10 Poise (P), and 1 Poise is equal to a 100 centi-Poise (cP).  Occasionally, viscosity is divided by the density and this is called the kinematic viscosity or specific viscosity. Viscosity has a strong dependence on temperature. 

\subsection{Surface and Body Forces}
For any given object in a fluid two types of forces may act on it - surface forces that are localized to surfaces and body forces like gravity and electromagnetic forces that act at a distance and influence the whole body.  The forces that act on a surface can take on two forms - either the force can be normal to the surface or tangential to it.  These result in different consequences. The normal force per unit area - simply the pressure can compress or dilate the fluid, the tangential force called shear - tends to deform the fluid.  

\begin{marginfigure}
\includegraphics{./pic/shearstress.pdf}
\caption{Shear Stress and Strain}
\label{fig:stressstrain}
\end{marginfigure}

In comparison to most solids, fluids are far more deformable. A element of fluid, as it moves in a stream, can be deformed in many ways. First, it translates - moves from one place to another. It can dilate or compress. And finally it can rotate.  To visualize flows in a fluid experimentally we have to add tracers of some sort - bubbles, dyes, small particles etc.  We have many possible visualization possibilities: we could follow a small element of fluid as it flows, and draw the line that joins these points. Or we could draw a line that is tangential to the velocity of the fluid particle etc.  These possibilities are shown in Table \ref{table:streamline}.

\begin{table}

\label{table:streamline}
\begin{tabular}{lp{3.5cm}p{3.5cm}}
\toprule
Type &amp; Description &amp; Comment \\
\midrule
Path-line  &amp; Draw the path a small fluid element follows &amp; \\
Streak-line  &amp; Draw the (instantaneous) line that joins all fluid elements that have passed through a given point  &amp; In steady flow path-lines and streak-lines are the same  \\
Time-line &amp; Draw a line joining a set of fluid elements and follow it with time &amp;  Generally, initially drawn perpendicular to the flow   \\
Streamline &amp; Draw the line joining the instantaneously tangent to the velocity vector of the flow &amp; This is more sophisticated concept. Vector mathematics guarantees that if we have a continuous field of velocities - i.e. a velocity associated with every point in the fluid, then such  streamlines exists and two of them don't intersect unless the velocity is zero\\
\bottomrule
\\
\end{tabular}
\caption{Visualizing fluid motion}
\end{table}

\begin{figure}
\includegraphics[width=4in,height=2in]{./pic/lines.pdf}
\caption{Pathline, Streakline, Timeline and Streamline}
\label{fig:lines}
\end{figure}

\begin{marginfigure}
\includegraphics[width=2in]{./pic/bernoulli_pipe.jpg}
\caption{Fluid moving through a pipe}
\label{fig:forces_bernoulli}
\end{marginfigure}

\subsection{Bernoulli's equation}
\par  Next consider the work of Venturi, Daniel Bernoulli and Giovanni Battista Venturi - the inventor of venturimeter used to measure velocities in aeroplanes etc.  First let us write the equation of continuity for incompressible fluids. If Q is the mass flow rate
\begin{equation}
v_1 A_1=v_2 A_2= \frac{Q}{\rho}
\end{equation}

Further, we have from Bernoulli's principle that

\begin{equation}
p_1+\rho g h_1 +\frac{1}{2}\rho {v_1}^2 = p_2+\rho g h_2 +\frac{1}{2}\rho {v_2}^2
\end{equation}

\begin{figure*}
  \centering
  \subfloat[Daniel Bernoulli (1700-1782)]{\label{fig:bernoulli}\includegraphics[width=0.3\textwidth]{./pic/bernoulli.jpg}}                
  \subfloat[Venturi  (1746-1822)]{\label{fig:venturi}\includegraphics[width=0.3\textwidth]{./pic/Venturi.jpg}}
  \subfloat[Hydrodynamica by Bernoulli]{\label{fig:book}\includegraphics[width=0.3\textwidth]{./pic/bennoullibook.png}}
  \label{fig:venturi}
\end{figure*}

Technically, Bernoulli equation is only valid along a streamline, for fluids of negligible viscosity. In certain types of flows know as irrotational (meaning that if you put a small particles in the flow it will not rotate) the equation is valid for all streamlines at once. It is safe to say that this is the most famous equation of fluid mechanics. Based on the Bernoulli's principle, a venturi-meter shown in Figure \ref{fig:venturimeter} can be used to determine flow speeds.

\begin{marginfigure}
\centering
\includegraphics[width=2in]{./pic/VenturiFlow.png}
\caption{An venturimeter}
\label{fig:venturimeter}
\end{marginfigure}



\subsection{Euler's equation}
In the 18th century Leonard Euler (who was Bernoulli's student) wrote down equations for frictionless and non-compressible fluids - essentially "dry" water.  Imagine a crowd of people moving: To follow what is going on we have two choices: either we can pick an individual and follow that person as she weaves through the crowd - ignoring everything else.  The other possibility is to pick a location and study the people who pass through it.  The first approach is called the Lagrangian method and the second Eulerian.   In fluid mechanics we can do the same thing - concentrate of a small mass as watch as it moves or choose a point and watch the fluid whizzing by.  The second approach is more mathematically tractable.  When Euler wrote down his equation, the idea of viscosity had still not caught on and so he missed a fundamental property.   Nevertheless, he did get part of the idea right.  In one dimension we can write:

\begin{equation}
\rho \frac{ \partial v}{\partial t} + \rho v \frac{\partial u}{\partial x} = - \frac{\partial P}{\partial x}
\end{equation}

\begin{marginfigure}
\includegraphics[width=3in,height=1.5in]{./pic/path.pdf}
\caption{Velocity varies in time and space}
\label{fig:path}
\end{marginfigure}

The u and v are the x and y components of velocity. The complicated form of the derivatives on the left side of the equation is necessary to account for the Eulerian co-ordinate system. 

\subsection{Navier-Stokes equation}
\begin{figure}
  \centering
  \subfloat[Leonhard Euler (1707-1783)]{\label{fig:Euler}\includegraphics[width=0.4\textwidth, height=2in]{./pic/Euler.jpg}}                
  \subfloat[George Gabriel Stokes (1819-1903)]{\label{fig:stokes}\includegraphics[width=0.4\textwidth,height=2in]{./pic/SS-stokes.jpg}}
  \subfloat[Claude-Louis Navier(1785-1836)]{\label{fig:book}\includegraphics[width=0.4\textwidth,height=2in]{./pic/Navier.jpg}}
  \label{fig:navier}
\end{figure}


Including viscosity and getting the complete and correct form of the equation right took the efforts of Navier and Stokes - two giants of fluid mechanics.   The Navier-Strokes equation for fluid mechanics in the fundamental equation we use today to model fluidic behavior.  However, it must be admitted that it is a nasty, nonlinear equation that defies complete understanding\sidenote{Need a million dollars in a hurry? Find out if the Navier Strokes equations have "nice" solutions (in a certain mathematical sense):\\ \url{ http://www.claymath.org/millennium}}. Here it is in it's full three dimesional g(l)ory

\begin{equation}
\rho ( \frac{\partial v}{\partial t} + v \cdot \nabla v) = -  \nabla p + \mu \nabla^2 v + f
\end{equation}

(the equation written here is for the case of a non-compressible fluid). This equation is complicated but it is only a mathematical statement of force or momentum balance.

\begin{equation}
\overrightarrow{\mbox{Net Inertial Forces}}=\overrightarrow{ \mbox{Net Pressure Force}} + \overrightarrow{\mbox{Net Viscous Force}} 
\end{equation}

In fluids one or more terms may become negligible simplifying the analysis.  In particular for most microfluidic devices the net inertial force term is negligibly small.

\begin{figure}
\includegraphics[width=4in,height=3in]{./pic/forces.pdf}
\caption{Force Balance on a Fluid Element}
\label{fig:forces}
\end{figure}


\section{Scaling laws}
Let us try to understand what happens as things become smaller. Consider a cube of lengthy \(L\). The volume of this cube is \(L^3\) and the surface area is \(6L^2\). Assume that that it shrinks in size in each dimension by half.  The volume of the cube shrinks by \(1/8\) to \(L^3/8\) and the surface area by \(1/4\) to \(1.5L^2\).  Hence, the ratio of surface to volume has increased (from \(6/L\) to \(12/L\)). The change is inversely proportional to the change in length.  A smaller body has a much greater surface area to volume compared to a larger body.  These sort of scaling arguments are extremely valuable when thinking about microfluidics.  In many cases the scaling arguments can provide insight into whether something is feasible or impossible without having to go into a detailed analysis. For instance questions like can magnetic forces be used to actuate devices at the nanoscale? What kind of pressures would be needed to push liquids though nanoscale channel? can be answered. 

Scaling is widely used in fluid mechanics in the form of dimensionless numbers. Let's get to our first dimensionless number.

\begin{marginfigure}
\includegraphics[width=2in]{./pic/./cubes.png}
\caption{Scaling of Area and Volume}
\label{fig:scaling}
\end{marginfigure}

\subsection{Reynolds' Number}
As the full Navier Stokes equations are hard to solve in nearly every practical instance, engineers have to resort to other methods. The method of dimensionless number has been found to be extraordinarily useful.  These number compare the ratio of two quantities  two of quantities of interest in a system. If in two experiments the the ratio is the same the experiments are dynamically similar, and will show similar behavior.  To avoid complicating things with measurement units the ratio is usually created so that all the dimensions cancel out and it is dimensionless.  

\begin{marginfigure}
\includegraphics[width=2in]{./pic/OsborneReynolds.jpg}
\caption{Osborne Reynolds(1842-1912)}
\label{fig:OReynolds}
\end{marginfigure}

These handful of number can be defined in standard ways in different systems.  Often engineers build smaller (or larger) scale models to perform experiments that would behave in the same way as the system we are interested in.  The first dimensionless number we will consider is Reynolds number:

\begin{equation}
Re=\frac{\rho v L}{\mu}
\end{equation}

We can gain some insight into $Re$ by writing the equation in a slightly modified way; Think of a body of characteristic length L in a flowing fluid.  The inertial forces are simply (mass $\times$ acceleration). The mass is (density $\times$ volume), which is $\rho L^3$. Since a fluid particle abruptly comes to zero velocity at the surface, and the time it takes to do so is approximately $L/v$   and the acceleration therefore is $v^2L$. The viscous forces are proportional to the (area $\times$ viscous stress). Area can be approximated as $L^2$ and the viscous stress as $\mu v/L$. Putting this all together we have

\begin{equation}
\nicefrac{\mbox{Inertial Forces}}{\mbox{Viscous Forces}}= \frac{\rho L^2 v^2}{\mu v L} = \frac{\rho v L}{\mu}=Re
\end{equation}

The Reynolds number is really the ratio of inertial to viscous forces.  The reader may wonder about what happens to bodies that have a complicated shape - how can one define L. In this case the answer is convention: We define L in some standard way for each geometry so that comparisons can be made.  Comparing Re in two different systems requires two similar geometries - it is meaningless to compare Re in systems that are not geometrically similar.

\section{Laminar and Turbulent flow}
Reynolds' number can be used to mark the change from laminar to turbulent flow in a particular geometry.  Osborne Reynolds was the first to bring attention to this phenomena\cite{1883Reynolds}. It's easy to observe turbulence - just turn on the tap.  Near the top, the fluid flows out smoothly, but beyond a certain height depending on the flow rate you can see a transition to another kind or flow regime - here the water flows in an irregular, chaotic way.    In pipes with a circular cross section - at Re&gt;4000 the flow is turbulent whereas below 2100 it is laminar. In between there is a transition regime.  One consequence of turbulence is that mixing is much more efficient. Another consequence which we shall see in the next lecture is that the force opposing motion through a fluid actually drops leading to some seemingly counter intuitive phenomena.

Most microfluidic devices operate at Re well below 5.  This is easy to show with a calculation. \\

\noindent {\sf Example: Reynolds Number}\\
Consider fluid flow through a circular channel or diameter  \unit[100]{$\mu m$}. Assume the flow is moving a \unitfrac[5]{mm}{s} and the fluid is water (density \unitfrac[1000]{kg}/{$m^3$}, viscosity \unitfrac[$10^{-3}$]{Ns}{$m^2$}\\
{\sf Solution:}\\
Plugging in the number with appropriate dimensional conversions we have
\begin{equation}
Re=\frac{(100 \mu m) (1 m/1000000 \mu m) (1000 kg/m^3 )(5mm/s) (1m/1000mm)}{(10^{-3} Nsm^{-2})} = 0.5 
\end{equation}

\begin{figure}
\centering
\includegraphics{./pic/parabolic.pdf}
\caption{Parabolic and Plug Profiles}
\label{fig:parabolic}
\end{figure}
Re is much less than the transition number and flows are therefore laminar. In fact the flow in almost all microfluidic devices is laminar. Let us examine a few geometries and evaluate the flow there. For the case of a circular tube, at low Re the flow regime is known as \emph{Hagen-Poisuelle flow}.  The Navier Stokes equations can be solved in this case to reveal that the flow profile is parabolic with the velocity at the center being the highest and the velocity at the boundary being zero.  This type of flow is called parabolic flow.  Its counterpart is plug flow where the profile is flatter and this is seen in the turbulent regime and in certain electrical force driven flows. For a given mass flow rate $Q$, the pressure drop is inversely proportional to the fourth power of the radius.

\begin{equation}
\Delta P = \frac{8 \mu L Q}{\pi r^4}
\end{equation}

This kind of flow is the most common type in microfluidic devices.

\section{A Very Brief History of Microfluidics}

\begin{marginfigure}
\includegraphics[width=2in]{./pic/manz.png}
\caption{A channel in a capillary electrophoresis device built in early 90s}
\label{fig:manz}
\end{marginfigure}

Historically, microfluidic devices in the form they can be recognized today started being developed in the 80's. Prior to that in the 50's and 60's there was an extensive effort to make fluidic circuits for defense application in the US as fluidic circuits would be able to outlast the impact of the electromagnetic pulse of a nuclear detonation.  During that time while miniaturization for making electronics and circuits had tremendous success, fluidic devices had long been used in control systems proved problematic to miniaturize and this effort largely petered out.  A prescient and much beloved talk by Richard Feynman from that era (\url{http://calteches.library.caltech.edu/archive/47/02/1960Bottom.pdf}) including speculation about machines for biological applications is worth reading even today \cite{Feynman59}.

A few decades later the increasing needs of small volumes for chemical analysis lead to work on miniaturizing sensors.  Perhaps the first microfluidic devices were gas sensors made in the 70s.  But another starting point can be taken to be the particularly noteworthy work done by Andreas Mann and co-workers at Imperial College, London miniaturizing devices to perform chemical analysis\cite{Manz1990}. They called their devices Micro-Total Analysis Systems. These  are the precursors to modern capillary electrophoresis equipment that you may use in a biological laboratory today.  More researchers making devices borrowing lithography and etching techniques from electronics (this field is called Micro Electro Mechanical Systems (MEMS) today) became involved and several innovative devices made out of silicon and other hard materials were demonstrated in the 80's and 90's and indeed new devices continue to be designed even today.  Robert Austin, the senior PI of the Princeton PS-OC and his collaborators designed a number of innovative nano-scale sorting devices in the early 90's.  This work is summarized in a review in 1997 \cite{AustinBrodyYager}, which also recounts the challenges and opportunities for small scale fluidic biotechnology.  A few MEMS foundries have now over 30+ years experience in making microfluidic devices for customers for both biological (eg. loading reagents into a machine) and physical applications (pressure sensors used in cars)

\begin{margintable}
\emph{Related Names:} \\
Lab-on-a-chip (LOC) \\
Micro-Total Analysis Systems (\(\mu\)TAS)\\
Micro-Electro-Mechanical-Systems (MEMS) \\
Bio-microfluidics \\
Bio-mimetics \\
\end{margintable}

In the late 90's Duffy, Whitesides and co-workers invented soft-lithography\cite{Duffy_softlitho1998} and demonstrated the technique with an transparent elastomer PDMS (poly dimethyl siloxane) and this finally brought microfluidics to the masses. The ease of fabrication and low overhead made PDMS a very popular material. Within a few years complicated multi-layer devices with hundred of valves per square inch became feasible and a shift towards softer elastomeric materials caught steam\cite{Scherer2000} that continues today. 

In the last few years, the push for faster sequencing machines and single cell analysis has resulted in a host of new highly parallel fludic devices and integrated detectors and this seems to be the driving force moving the density of fluidic components further.  Several new startup companies in the last decade have focused on making microfluidic products including Ibidi, Dolomite, Fludigm, Raindance, Bio-nanomatrix among many others.  And over 2000+ papers are published in the field every year. Microfluidics is no more a obscure topic of research, but a thriving field with dedicated journals and conferences, and nearly every large research university in the US has multiple groups working in the field. 

A recounting of the factors that lead to the development of microfluidics can be found in a (somewhat sober) review by Whitesides \cite{Whitesides2006}. This particular issue of Nature contains a special supplement to microfluidics which has many broad review articles \url{http://www.nature.com/nature/journal/v442/n7101/} and a good starting point if you want to start research in the field.

\section{Microfluidics and Cancer Research}
Microfluidics application to cancer research are very recent.  A few areas of interest are noted, with one example paper of each type.

\begin{table*}
\caption{Examples of Microfluidics and Cancer Research applications}
\begin{tabular}[c]{lp{5cm}p{5cm}}
\toprule
Type &amp; Comment &amp; Representative Example\\
\midrule
Diagnostic Screening &amp; Devices take advantage of small volume handling. Also relevant for drug testing. &amp; Rong Fan, Ophir Vermesh, Alok Srivastava et. al. Integrated barcode chips for rapid, multiplexed analysis of proteins in microliter quantities of blood. Nature biotechnology, 26(12):1373â€“1378, December 2008p\\
Extracting Circulating tumor cells &amp; Replacement for biopsies? Testing therapies? &amp;  Sunitha Nagrath, Lecia V. Sequist, Shyamala Maheswaran, et al Isolation of rare circulating tumour cells in cancer patients by microchip technology. Nature, 450(7173):1235â€“1239, December 2007. \\
Chemotaxis and Motility Assays &amp; These assays tells us more about the mechanism of metastasis. Microfluidic devices can be used to generate a variety of gradients. Sizes of channels can mimic blood capillaries &amp; Liu, Liyu, Bo Sun, Jonas N. Pedersen, Koh-Meng, Robert H. Getzenberg, Howard A. Stone, and Robert H. Austin. "Probing the invasiveness of prostate cancer cells in a {3D} microfabricated landscape." Proceedings of the National Academy of Sciences (2011)  \\ 
Mechanical Signaling &amp; Cancers cells may have altered mechanical responses &amp;"Matrix Crosslinking Forces Tumor Progression by Enhancing Integrin Signaling" Kandice R. Levental, Hongmei Yu, Laura Kass, Johnathon N. Lakins, Mikala Egeblad, Janine T. Erler, Sheri F.T. Fong, Katalin Csiszar, Amato Giaccia, Wolfgang Weninger, Mitsuo Yamauchi, David L. Gasser, Valerie M. Weaver Cell - 25 November 2009 (Vol. 139, Issue 5, pp. 891-906) \\
\bottomrule
\end{tabular}
\end{table*}

\clearpage
\subsection{Suggested Exercises}
1) If I had a helium balloon in a car and the car suddenly stopped - would the balloon move forward or backward? Why?
(to watch this (and many other) demonstrations see Walter Lewin perform in inimitable style(shortened url):\\
 \url{http://goo.gl/GEKLN}\\

2) Do you think a fluid without any viscosity can exist in nature? Why or why not?\\

3) Reading Material (papers will be available in a zip file that you can access)
"Life at low Reynold's numbers" by Edward Purcell. \\
Osborne Reynold's paper \\

4) Watch videos from the National Committee for Fluid Mechanics films \\
\url{http://web.mit.edu/hml/ncfmf.html}\\
a) Eulerian Lagrangian Description\\
b) Deformation of Continuous Media	
c) Flow Visualization \\		
d) Low Reynolds Number Flow 	\\
e) Rheology and Fluid Mechanics\\

5) Try this experiment: tie a string across a cup of water. Tilt the cup and start to pour while holding the the string over the top of the cup and at an angle. The water will seem to stick to the string! You can also see the same effect if you brought the round side of a spoon near a water stream pouring from a faucet - the water stream will be attracted to the spoon. The spoon itself will seem stuck to the stream.  Why? \\

6) For your entertainment: \url{http://news.bbc.co.uk/2/hi/science/nature/227572.stm}\\

7) How does a siphon work? (Hint:Bernoulli's Principle). See figure \ref{fig:siphon}

\begin{marginfigure}
\includegraphics[width=3in]{./pic/siphon.pdf}
\caption{Siphon}
\label{fig:siphon}
\end{marginfigure}

\chapter{2: Drag, Diffusion, Gradients, and Mixing}
If we had a cube of sugar in tea and there was no other mixing process but diffusion - how long would it take the sugar to dissolve? Could you drink this tea? This chapter will allow use to answer this and other similar questions.

\begin{marginfigure}[-8pt]
\includegraphics{./pic/Robert_Brown.jpg}
\caption{Robert Brown (1773-1858)}
\label{fig:RBrown}
\end{marginfigure}
Diffusion is the process of random mass transport at the molecular scale.  The first clue that this process can move things was the discovery of Brownian motion - observed by Robert Brown in 1827, incidentally a botanist. It is typically assumed that Brown found pollen grains seem to move around randomly in a drop of water observed under a microscope, but in fact pollen grains that Brown used were too big to show an effect and what he observed seems to be smaller particles shed by the pollen grains.  (Indeed, Brown may not have even been the first to observe diffusion, but in any case his name is forever associated with it). A fascinating modern reconstruction of this experiment can be found here:\\

\url{http://physerver.hamilton.edu/Research/Brownian/index.html}\\[0.1in]

\begin{marginfigure}[-4pt]
\includegraphics{./pic/einstein.jpeg}
\caption{Albert Einstein (1879-1954) in front of his house in Princeton}
\label{fig:einstein}
\end{marginfigure}
We can hardly talk about diffusion without mentioning the name of the most famous person who ever lived at Princeton: Albert Einstein. As a 26 year old, Einstein published a paper in 1905 which connected viscosity, diffusion and temperature. His equation (Einstein-Stokes equation)\cite{einstein_brownian}

\begin{equation}
D = \frac{k_B T}{6 \pi \mu r}
\end{equation}

Here $k_B$ is the Boltzman constant, $T$ the temperature, $\mu$ the viscosity and $r$ the radius of the particles under consideration. a similar equation had been derived a little earlier by Smoluchowski using a different method.  



In the same paper Einstein showed that the average (root mean square) distance L, a particle would move in time t, is simply:

\begin{equation}
L = \sqrt{2Dt}
\end{equation}

D is the diffusion coefficient. Note that the size dependence, viscosity and temperature is hidden here in the diffusion constant.  The units of the diffusion constant are $[{Length}^2][{Time}^{-1}]$ and can be given in $cm^2/s$ or in $m^2/s$.

The most important observation about this equation is that the length scales as the square root of time.  To really understand where this relationship comes from we have to understand what a random walk is.   Imagine you play a game - which involves tossing a coin - if heads you move a step d forward, if tails you move a step backwards. After $n$ steps the distance traveled will be written as $L(n)$. Now L(n) is reached from L(n-1) and this could be one step ahead or back, so we may write

\begin{equation}
L(n)=L(n-1) \pm d
\end{equation}

Now imagine that you did this many many times and took the average (or alternatively there were many people playing the same game and you take their average) represented by the symbol $\langle \rangle$
\begin{equation}
\langle L(n) \rangle =\langle L(n-1) \rangle \pm \langle d \rangle
\end{equation}

Since the probability of a forward or backward step is the same, on average you get zero - the forward steps cancel out the backward steps.  So
\begin{gather}
\langle L(n) \rangle =\langle L(n-1) \rangle  \\
\langle L(n-1) \rangle =\langle L(n-2) \rangle  \\
\dotso \\
\Rightarrow \langle L(n) \rangle = \langle L(0) \rangle = 0
\end{gather}

This also means we can work backwards all the way to the initial position and find that the average distance moved is zero! The forward and backward steps cancel out and you get nowhere! Or do you? Well, while in the long run you get nowhere, the walking does spread out if you take more steps.  And if there are many walks, the average may be zero but they will be more spread out.  How can we characterize this? The trick is to consider the root-mean square, which gives a way to measure how spread out the path was.  Here we average not $&lt;L(n)&gt;$ but the $&lt;L(n)^2&gt;$ and then take its square root.  We can write:
\begin{equation}
L(n)^2 = L(n-1)^2 \pm 2dL(n-1)+d^2
\end{equation}
Again taking averages, we find that the middle term on the right averages to zero, and since $d$ is constant we can remove the average symbols to get:
\begin{equation}
\langle L(n)^2 \rangle =\langle L(n-1)^2 \rangle + d^2 
\end{equation}
Now you can see the germ of the reason why the square root dependence comes from.  As $L(0)=0$, $\langle L(1)^2 \rangle = d^2$ and $\langle L(2)^2 \rangle = 2d^2$ and in general,
\begin{equation}
\langle L(n)^2\rangle = nd^2
\end{equation}
But $n$ is simply the number of steps and if the movement is steady (equal number of steps per unit time), then $n$ is proportional to $t$. But this means that on average the root mean square average distance is proportional to the square root of time as Einstein had noted:

\begin{equation}
\sqrt{\langle L^2 \rangle} = \sqrt{2Dt}=L_{RMS}
\end{equation}

This length is a useful quantity to know in many situations and is called the diffusion length. It can be used as ruler to compare other length scales and deduce the importance of diffusion to other processes.
\begin{margintable}
\caption{Diffusion constants}
\begin{tabular}{p{2cm}ll}
\toprule
\multicolumn{3}{c}{Diffusion constants} \\
\cmidrule(r){1-3}
Type &amp; D (at $20^0$ C)&amp; $\sqrt{2Dt}$ (cm) \\
\midrule
1 $\mu m$ sphere &amp; $2.5 X 10^{-9} cm^2/s $&amp;  $7 x 10^{-5} \sqrt{t}$   \\
Protein (Haemoglobin) &amp; $7 X 10^{-7} cm^2/s$ &amp;  $1.2 x 10^{-3} \sqrt{t}$  \\
Small Molecule (Fluorescein)&amp; $5 X 10^{-6} cm^2/s$ &amp;   $3.2 x 10^{-3}\sqrt{t}$ \\
\bottomrule
\end{tabular}
\end{margintable}

Now with this information at hand we can answer the question posed at the beginning - sugar which is made of sucrose a small molecule like fluoresein. If you cup is approximately 10 cm , then nearly $10^6$ seconds are needed to mix completely by diffusion - about 12 days!

\section{Laws of diffusion}
In 1855, Adolf Fick derived the laws of diffusion that are still applied today.  It is interesting to note that Fick was a physiologist, not a physicist. There are two basic laws. To understand them first consider a situation where are are two reservoirs connected by a channel. Let us assume that one reservoir has a chemical at a concentration $c_1$ and another at $c_2$. If we take a cross-section of the channel and ask how many molecules are diffusing through per unit area per unit time? This is called the flux (mass flux, or molecule flux, or molar flux depending on what you are working with)  usually designated by the letter $J$. We have for the flux:

\begin{equation}
J = - D  \frac{c_2 - c_1}{x_2 - x_1} = -D  \frac{dc}{dx}
\end{equation}

The flux depends on the change in concentration with distance and the negative sign indicates that transport occurs from a higher concentration to a lower one, in line with our intuition. Molecules diffuse from a region of higher to lower concentration. Note that there is no time dependence in this equation - it is just a static one-time picture. Fick's second law gives the full time dependent equation. 

\begin{equation}
\frac{dc}{dt} = - D  \frac{d^2c}{dx^2}
\end{equation}

This is a partial differential equation of second order in the co-ordinate. Of course, we have only written it in one dimension x, and we can also write the same for y and z directions. We can derive it easily by combining the first law with the law of conservation of mass (try it!)
\begin{marginfigure}
\includegraphics[width=2in,height=2in]{./pic/Adolf_Fick.jpg}
\caption{Adolf Fick (1829-1901)}
\label{fig:Fick}
\end{marginfigure}
As for all differential equation, given  boundary conditions and initial conditions we can solve this to get the concentrations profiles with time. For the simple case where a tracer dye is released at a point instantaneously and spreads in one dimension from there the solution looks like a Gaussian. If instead it is released over a period of time the solution takes the form of a curve called the error function.  For example if we had an interface with two different concentrations of a chemical - after a while the concentration profile appropriately scaled would look like Figure \ref{fig:error}

\begin{figure}
\centering
\includegraphics[width=3in]{./pic/error.png}
\caption{The error function}
\label{fig:error}
\end{figure}


\subsection*{Peclet number}
In microfluidic devices there is competition between convectional flow and diffusion - two mass transport processes. Convectional flow tends to move matter in the direction of flow and diffusion tends to move matter to equalize concentration gradients.  We can write a dimensionless number called Peclet number, that compares the two tendencies 

\begin{equation}
Pe = \frac{vL}{D}
\end{equation}

where L is a characteristic length scale of the system, v the velocity of flow and D the diffusion constant. If Pe is large gradients can exist, otherwise diffusion will smoothen any gradient out out




\section{Drag}
Drag is the force that any body moving through a fluid experiences acting against the direction of motion.  It is the result of a kind of fluid friction.  The drag is dependent only on the relative velocity - the body could be moving in a fluid or the fluid could be moving across it - only the relative velocity counts not the absolute velocity.  

What does drag depend on? It seems like drag is complicated function of flow and body parameters and takes on different forms in different flow regimes.  In the low reynolds number regime Strokes found that drag is directly proportional to the the viscosity, the relative velocity and size of body (BUT not the density of the fluid!) 

\begin{equation}
Drag= C_d L \mu v
\end{equation}

were $C_d$ is a constant, the drag coefficient or friction factor.  If you were an engineer and needed to calculate the friction factor you would use the Moody diagram for a pipe and add a geometric factor for other shapes.  In the laminar regime the friction factor is a straight line of slope $64/Re$.   

\begin{figure}
\centering
\includegraphics[width=5in]{./pic/Moody_diagram.jpg}
\caption{Moody Diagram to estimate friction factor}
\label{fig:Moody}
\end{figure}

From the figure it is clear that behavior in the turbulent regime is complicated - in fact in that regime drag is a different function of velocity etc and depends on the density of the fluid unlike the laminar case.

\begin{equation}
Drag_{turbulent}=C_d v^2 \rho L^2
\end{equation}

It is interesting to note the non-intuitive fact that in either case the absolute pressure plays no role in determining the drag force.  For a solid,  frictional forces do depend on the normal component of force and hence on the pressure exerted by the solid on the surface.  This is not the case in liquids. You would experience the same drag deep in the ocean or near the surface if the body shape and other parameters like density of water and size remain the same despite the higher pressure and similarly the drag experienced at higher altitudes is not different from that at lower altitudes if other parameters don't change.  



\section{Mixing and Sorting}
Depending on experimental needs we may need to mix two ingredients or sort them. Microfluidics designs offer a number of ways to do so. Often pure diffusional mixing is fast enough.    

\subsection{Taylor-Aris dispersion}
\begin{figure}
\includegraphics[width=5in,height=3in]{./pic/taylor.pdf}
\caption{Taylor-Aris Dispersion (adapted from Squires and Quake, 2005)}
\label{fig:taylor}
\end{figure}

\begin{marginfigure}
\includegraphics[width=2in,height=2in]{./pic/G_I_Taylor.jpg}
\caption{GI Taylor (1886-1975)}
\label{fig:Taylor}
\end{marginfigure}

In laminar flow the effect of flow is to increase the apparent diffusion constant in certain flow regimes leading to faster dispersion of a chemical. This phenomena is called Taylor-Aris dispersion after the discoverers \cite{Taylor,Aris}. In flow through a circular tube at low Reynolds number diffusion is occurring axially and radially.



\section{Creating Gradients}
Microfluidic devices excel at creating two dimensional spatial gradients.  These spatial gradients can be generated either passively (with no flow) or dynamically (with flow)

\subsection{Passive Gradients}
A simple way to generate gradients is to have a source and sink reservoir connected by a smaller tube. Once all the pressure driven flows are balanced - diffusion creates more or less linear gradients that can last from a few minutes to several days.  Cells can be put in the connecting chamber either by themselves (adherent cells) or in a gel.

\begin{figure*}
\caption{Cells in gradients (from Ibidi Gmbh}
  \subfloat[Cell in a gel]{\label{fig:gels}\includegraphics[width=0.4\textwidth,height=2in]{./pic/chemotaxis02.jpg}}                
  \subfloat[Adherent cells]{\label{fig:nogel}\includegraphics[width=0.4\textwidth,height=2in]{./pic/chemotaxis03.jpg}}
  \label{fig:static_gradient}
\end{figure*}

\subsection{Dynamic Gradients}
In this case flow is used to create the gradient allowing gradients to be kept for as long as flow is possible and also changing them on the fly.  The first such gradient generator was described by Jeon et al \cite{jeon2000}. We will make a similar mixer in our experiments.

\begin{figure}
\caption{Dynamic Gradient Generator (from Noo Li Jeon et al)}
\includegraphics[width=4in,height=4in]{./pic/gradientjeon.jpg}
\label{fig:dynamicgradient}
\end{figure}

Recently a arbitrary gradient mixer was described that uses a gel and channels in PDMS.  these devices are suitable for bacterial studies \cite{roman} - for mammalian cells the conditions to maintain gradients, while also keeping cell happy are much more stringent.  At the Princeton PS-OC we have several students working on Silicon devices for gradients. The idea here is to use a set of posts to separate out the growth chamber from the source and sink channels. The separation between the posts is small enough that most cells don't escape.  The posts protect the cells from direct flow and hence preserve cell growth factors and other chemicals inside the growth chamber for longer.  We will have occasion to see such a device in our final experiment.

\begin{figure}
\includegraphics[width=4in,height=4in]{./pic/arb_gradients.jpg}
\caption[][2in]{Arbitrary Gradient Generator(from Tanvir Ahmed et al 2010)}
\label{fig:arb}
\end{figure}

This kind of gradient control can be used to make micro-habitats or ecological niches where food concentration are varied. An Example of this device is the micro-habitat patch developed at Princeton University Figure \ref{fig:MHP}.  In the figure each square alternates with posts or no posts creating regions of food and starvation. These devices are unique in the sense that they are neither batch cultures nor chemostats, instead cells stay in place but nutrients diffuse in and out.

\begin{figure*}
\includegraphics[width=5in,height=1in]{./pic/habitats.jpg}
\caption{Microhabitat Patch (from Princeton PSOC)}
\label{fig:MHP}
\end{figure*}

\section{Suggested Exercises}
Here are a few things to do:\\

1) What does it mean when we say a body is streamlined? Will streamlining increase or decrease drag in micro-fluidic devices?\\

2) Read Einstein's original 1906 paper on diffusion.\\

3) Read the article titled: Half a century of Diffusion by Jean Philibert  and/or the Physics Todat 2006 historical article by T. N Narsimhan\\

4) Watch videos from the National Committee for Fluid Mechanics films \\
\url{http://web.mit.edu/hml/ncfmf.html}\\
a) Fluid Dynamics of Drag Part I \\	
b) Fluid Dynamics of Drag Part II \\	
c) Fluid Dynamics of Drag Part III \\	
d) Fluid Dynamics of Drag Part IV \\	


  

\chapter{3: Micro/Nano Fabrication Technology, Fluidic Circuit Components}
In this lecture we will learn about various manufacturing processes, materials used and their advantages and disadvantages and finally various fluidic components that can be used in a design.


\section{Microfluidic Rules of Thumb}

\section{Basics of Micro/Nano Technology}
\subsection*{Wafers}
Much of the processing capability we have in electronics is dependent on having high quality crystalline silicon wafers that range in size from 1" to 18" in diameter.  These wafers which are the substrates on which all processing is usually done are sold by several manufacturers and come in different qualities. Since in the work in this course we care only in surface smoothness we use test wafers.  Typically, prime wafers are used in many MEMS processes. Even higher grade wafers are available for specialized manufacturing.   

\begin{marginfigure}
		\includegraphics[width=1in,height=1in]{./pic/silicon.jpg}
		\caption{Silicon Wafer: The flat indicates crystalline orientation and doping}
                   \label{fig:wafer}  
\end{marginfigure}


\subsection{Photoresists}
Photoresists are UV sensitive chemicals. They are viscous enough to be spun on a wafer. The spin speed detemines the height of the features. When exposed through a mask to UV light a chemical reaction takes place that changes the solubility of the exposed region.  Then a solvent (called developer) can be used to remove the exposed (or unexposed area).  When the exposed area is more soluble we have a positive resist (e.g. SPR, AZ series). When the exposed area is less soluble, then we have a negative resist (eg SU8 series). The chemistry of the resists is optimized to ensure it has the right viscosity, adhesion and matches the exposure system.  Extensive development work has gone on to make suitable photoresist for the elctronics industry. In microfluidics it is common to use more viscous resists that give taller heights than those used in electronics.  

The dependence of spin speed on the height of resist is complicated and generally can only be detemined empirically.  Photoresists are examples of non-newtonian fluids.  

\subsection{Masks}
A mask is pattern on a transparent substrate. UV light passes through the mask to hit a wafer coated with photoresist allowing transfer of the pattern from the mask to the photo-resist coated wafer. A transparency mask, which as the name suggests is printed on a transparency, is suitable for designs that have patterns 15 micron or larger, whereas a chrome (or ferric oxide) mask is better for smaller patterns (upto 1 micron or so) For features smaller than 1 micron you would have to resort to e-beam lithography, steppers and other specialized equipment.

\begin{table}
\caption{List of companies making transparency masks}
\begin{tabular}{lp{5cm}}
\toprule
Name &amp; Location and Contact \\
\midrule
CAD/Art Services, Inc. &amp; 87509 Oberman Lane, Bandon, OR 97411  (541)-347-5315 (phone) (541)-347-6810 (fax) cas@outputcity.com \\
Fine Line Imaging &amp; 4733 Centennial Blvd., Colorado Springs, CO 80919  (719)-268-8319 (719)-359-5497 (fax) plotting@fineline-imaging.com \\
\bottomrule
\end{tabular}
\end{table}

Making transparency masks generally involve using a high quality laser printer (from 5000 to 40000 dots per inch) to print on a transparency. This is typically the most economic option for micro-fluidic designs with features over 15 microns. Chrome masks are the next step up - generally these masks have a coating of chrome on soda lime or quartz glass plates with a layer of photo-resist on top. A laser writer is used to write a pattern on the resist. Finally, developing the resist, etching the chrome and dissolving away the remaining resist gives the mask plate. For certain kinds of multi-layer designs having a more transparent mask helps in alignment - and this is often done by using a ferric oxide coating instead of chrome mask. Ferric oxide is more transparent in the visible light spectrum compared to chrome. Ideally, all kinds of masks should be made inside clean-rooms to avoid any errors due to dust particles.


\begin{table*}
\caption{List of companies making chrome masks}
\begin{tabular}{lp{5cm}}
\toprule
Name &amp; Location and Contact \\
\midrule
Photo Sciences, Inc. &amp; 2542 W 237th St. Torrance CA. 90505 (310)-634-1500 (phone) \\
HTA photomask Inc. &amp;1605 Remuda Lane San Jose, CA 95112 (408)-452-5500 (phone) (408)-452-5505 (fax) sales@htaphotomask.com (sales) kenc@htaphotomask.com (technical) \\
Advance Reproductions Corp. &amp;100 Flagship Dr. North Andover, MA 01845 (978)-685-2911 (phone) sales@advancerepro.com (sales) drobinson@advancerepro.com (technical)\\
Fine Line Imaging &amp;4733 Centennial Blvd. Colorado Springs, CO 80919 (719)-268-8319 (phone) (719)-359-5497 (fax) plotting@fineline-imaging.com, cust.service@fineline-imaging.com \\
\bottomrule
\end{tabular}
\end{table*}


\subsection{Mask Aligners}
Mask Aligners are machines that have a vapor lamp (mercury, xenon, deuterium) to expose photoresist through a mask with a pattern. They have precision stages and optics that allows control of alignment and contact.  A mask fits into the mask holder of such a aligner.  Usually vacuum is used to hold both the mask and the aligner.  Contact aligners involve direct contact between the mask and photoresist. Proximity aligners allow a small separation between the phototresist and mask (which can protect the mask from damage but could also reduce the resolution.  


\subsection{Soft-lithography}
Soft-lithography is techniques invented at Harvard by Duffy, Whitesides and co-workers. It involves pouring  uncured PDMS over a mold and curing it in an oven (or at room temperature). \sidenote{The two common types of PDMS used are RTV 615 made by GE and Sylgard 184 made by Dow Corning}

\begin{figure*}
\includegraphics[width=4in]{./pic/softlitho.jpg}
\caption{Soft-Lithography}
\label{fig:softlitho}
\end{figure*}

\section{Fluidic Components}
We have now seen a few ways to make fluidic devices. Just like in electronics, fluidic devices can be considered to be made of various components.  These can be put together to form a "fluidic circuit". Let us consider the elements one by one. Here, we will primarily concentrate on components made with soft-lithography because this is where the most progress in integrating components has been made.

\section{Channels}
\begin{marginfigure}
\centering
\includegraphics[width=2in,height=2in]{./pic/channel.pdf}
\caption{Connecting channels in parallel and serial}
\label{fig:channel}
\end{marginfigure}

The basic element of a circuit is a channel.  In microfluidics the channel depth is the order or few tens or microns, whereas the width is of the order or few hundreds of microns. The aspect ratio is typically limited by the materials use - PDMS need an aspect ration of 1:15 or less otherwise it will collapse under its own weight.

The channels can be connected in a variety of ways - in parallel or in series.  In recent years there have also been demonstrations of 3-D geometries.  Further the cross section may be square, rounded or some other shape.  The resistance of a such a channel to fluid flow depends on the the geometry, the roughness of walls, and the (strongly) on the size. For example we showed earlier in a round cross section the resistance scales inversely as the forth power of the radius.

\subsection{3D and cross over channels}

\section{Valves}
Two channels separated by a thin membrane can be used to create a pneumatic valve\cite{Unger}.  The deflection of the membrane when the control channel is pressurized closes the channel.  The geometry of the flow channel can be important in determining pressures needed to actuate - rounded channels help lowering pressures since the sharp edges are hard to close.  
\begin{figure}
\centering
\includegraphics[width=4in]{./pic/valveblue.png}
\caption{Pneumatic valve closing a channel}
\label{fig:valveblue}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=3in]{./pic/valvemany.jpg}
\caption{Many valves operated simultaneously. Note the crossover lines}
\label{fig:valvemany}
\end{figure}
The design for a valve can be push down or push up as shown in Figure \ref{fig:pushup}.  In a push up design generally lower actuation pressures are needed but the material is surrounded by PDMS.  In the push down case the material in a channel can have one side in contact with a cover glass - an advantage in cases where surface chemistry needs to be controlled.  Many valves can be connected to a single control pressure line and this feature is extremely useful when many valves need to be opened and closed at the same time(Figure \ref{fig:valvemany}. Note in this case the presence of {\it crossover lines} where the overlap area on top of the fluid membrane is too small to close the valve. This sort of cross-over geometry is essential for complex designs since otherwise it would be topologically impossible to route the control line.  Typically, for a 10 micron height flow channel with 100 micron width, a crossover line has a width of 30 microns or less. 

 \begin{figure}
\centering
\includegraphics[width=4in,height=3in]{./pic/pushuppushdown.jpg}
\caption{Two types of valves - push-up and push down}
\label{fig:pushup}
\end{figure}

A variety of attempts have been made to make electrical-on-chip valves - including the use of braille pins, electroactive polymers, capacitive and magnetic valves,  electrorheological valves, shape memory alloys , electrolysis, gels, torque screws (including by the author himself!). However, none of them match the versatility and ease of manufacturing of plain pneumatic ones as yet. Electronic valves are desirable because we can then miniaturize the control system and integrate it with the fluidics.

\begin{marginfigure}
\centering
\includegraphics[width=2in, height=2in]{./pic/sma.png}
\caption{Shape memory alloy valve}
\label{fig:SMA}
\end{marginfigure}

\subsection{Mixers and Pumps}
A simple on-chip peristaltic pump can be made using 3 valves in a row that operate in the perstaltic sequence  (101,100, 110,010,011,001) continuously. This pump operates in a sense by squeezing the liquid forward (or backward) like you would squeeze a toothpaste tube.  One nice feature is that the number of cycles precisely determines the amount of fluid dispensed.  This pump will only work with incompressible fluids (i.e. liquids).

\begin{figure*}

\includegraphics[width=5in]{./pic/pumpgreen.png}
\caption{Three valves can create a peristaltic pump}
\label{fig:pump}
\end{figure*}

In laminar flow based devices mixing by diffusion can be so slow that it is can often a problem and specialized mixers are needed. A rotary peristaltic mixer involves a closed off circle and a a peristaltic pump as shown in Figure \ref{fig:perimixer}

\begin{figure*}

\includegraphics[width=4in, height=4in]{./pic/perimixer.pdf}
\caption[][-1in]{Rotary Peristaltic Mixer}
\label{fig:perimixer}
\end{figure*}

Another kind of mixer is the herringbone mixer shown in Figure \ref{fig:herring}. This was first introduced in 2002 \cite{herringbone}

\begin{figure}
\centering
\includegraphics[width=4in, height=4in]{./pic/herring.jpg}
\caption[][1in]{Herring Bone mixer from reference Stroock et al 2002}
\label{fig:herring}
\end{figure}

\section{Filters, Sieves, Button valves}
In many fluidic devices having a way to trap particles or cell while having fluid flow by is useful.  There are multiple ways to do this - one could simply introduce a series of posts, separated by a distance smaller than the particles themselves.  

Alternatively one could design a pneumatic valve which would only partially close - usually done by simply not rounding the channel, but leaving it square.  This allows trapping of particles.
\begin{figure}
\centering
\includegraphics[width=3in, height=3in]{./pic/column.jpg}
\caption{Seive Valve with beads trapped}
\label{fig:column}
\end{figure}

We will use this design in one of our experimental chip designs -attempting to trap yeast cells while keeping the flow on. Another kind of specialized valve is the button valve. It allows isolation of a region on a surface with a valve - removing any material non-specifically bound.

\begin{figure}
\centering
\includegraphics[width=3in, height=2in]{./pic/button.pdf}
\caption{Button Valve}
\label{fig:button}
\end{figure}
 
\subsection{Multiplexers}
A multiplexer in electronics selects out one output from a several input lines.  It is mainly used to increase the amount of data transmitted. For instance a cell phone tower may have to send out the information from several calls in a given amount of time.  One way to do this is to divide that  time into smaller units and select one line for every small unit of time, switching very quickly to another call. If the system is fast enough you would never notice the difference -  this is simply a form of timesharing.   A demultiplexer does the opposite - it takes one input and splits it into many outputs

\begin{figure*}
\centering
\includegraphics[width=5in, height=4in]{./pic/multiplexer.jpg}
\caption{Logarithmic and Combinatorial Mulltiplexer}
\label{fig:multiplexer}
\end{figure*}

In fluidics, it is possible that there are several channel that supply chemicals and you need to switch from one to the other.  We can build a fluidic multiplexer to do this.  Two types of multiplexers have been described - logarithmic (or binary) and combinatorial - shown in Figure \ref{fig:multiplexer}.  In these multiplexers a set of control lines are used to select out one flow line from a larger set of flow lines.  This allows savings in number of control lines required.  If each flow line had it's own valve the number of control lines would be equal to the number of flow lines. If however, for the operation of the chip, only a single line needed to be used at a give time, we could save on control line by putting in a multiplexer.  In this case a number of control lines are activated and they select out a particular flow line - for instance in the combinatorial mixer - turning on lines A and D selects flow line 3.   Another example, selecting control lines F, D and A results in flow line 2 being activated in the logarithmic multiplexer.  

It must be understood that there is no free lunch - certain combinations of lines are impossible. For instance if I wanted BOTH 1 and 2 flow lines to be on, and all other lines closed - no combination of valves would do (in either type). Multiplexers are useful only if at a given time only one input line is needed.

The reader may wonder how these multiplexers are designed - the design is based on elementary principles of logic and comitbinatorics. Without going into too many details the binary (or logarithmic) multiplexer relies oit{Fn the representation of number in base 2 or binary.  In the case of a combinatorial multiplexer - the design is based on asking the question: how to maximize the number of flow lines controlled if a certain number of control lines have to be actuated to select a flow line. It turns out from combinatorial principles, this number is a maximum, if half the control lines (C) need to be selected to specify a flow line (F).  

\begin{equation*}
F=\binom{C}{\frac{C}{2}} \approx \sqrt{2 \over \pi} {2^C \over \sqrt{C+1}}
\end{equation*}


The scaling is incredibly fast. For instance 10 control lines can control 252 flow lines, 20 can control 184,756, 30  more than a 1.5 million! A combinatorial multiplexer is more efficient then a binary one (which scales as $2^{C/2}$), but binary multiplexer can also be used in a binary tree design which makes it more versatile in some situation where cross-contamination between lines has to be minimized.  A binary multiplexer can be improved upon by a ternary multiplexer (using base 3).  This happens because 3 is closer to Euler's constant $e$ than 2 and this is where the maximum lies for this kind of multiplexing.  In our class we will attempt to make a chip with each type of multiplexer so that you can see it in action.

\begin{figure*}
\includegraphics{./pic/binary.pdf}
\caption{Binary Tree multiplexer}
\label{fig:binary}
\end{figure*}

It's worth mentioning that even more sophisticated possibilities exist - valves may be of latching types - sending signal turns them on or off and lets them remain that way.  Further, vacuum may be used in conjunction with pressure to make three state systems.  The multiplexer can itself be used to run a set another set of channels that in turn control valves on a chip - so the multiplexer selects out an instruction or state of a chip rather than a simple line (this design called deconvolver was proposed by the author).  The possibilities for control are fairly sophisticated - but we are running ahead of things here - our fabrication technologies have not reached the level of reliability to routinely use these options and unless the process actually needs the type of control, there is no point in making a device with such complicated controls.  In fact, the limiting factor seems to be the space on the wafer.

One can dream (and the author certainly does) that in the future we will have the fluidic equivalent of an electronic microcontroller and this will open up all kinds of possibilities similar to what happened in electronics.  What could one use such devices for? Sequencing? High throughput assays? Genetic engineering? Who knows!

\begin{table*}
\caption{List of Microfluidic Foundries. These foundries will generally accept a design or a mask and provide you a PDMS chip for a fee.}
\begin{tabular}{lp{5cm}}
\toprule
Name &amp; Location and Contact \\
\midrule
Caltech Microfluidic Foundry,&amp; Kavli Nanoscience Institute 1200 E. California Blvd., California Institute of Technology, Pasadena, CA 91125, USA (e-mail) foundry@caltech.edu \\
Stanford Microfluidic Foundry &amp;Stanford University, Palo Alto, CA 94315, USA (e-mail) sufoundry@lists.stanford.edu \\
\bottomrule 
\end{tabular}
\end{table*}


All the component described can be combined to produce a device that has many capabilities - exactly in the same way as you would combine electronic components into a circuit. We shall see two such examples in our course.



\section{Comparison of materials for microfluidics}
A variety of materials have been used for microfluidics \sidenote[][]{A partial listing: silicon, elastomers (PDMS etc), plastics, metals, glass, ceramics, paper, gels, wax, adhesive tapes, epoxies, parylene, fabrics}. In this course we will see plastic films, PDMS, adhesive films and silicon being used in experiments.  

Every material used comes with its advantages and disadvantages - the most popular materials in academia nowadays seems to be PDMS. PDMS has several advantages -it is inexpensive, transparent, mostly inert, tolerates aqueous solutions well (aqueous acids, bases etc), and easy to work with, seals gaps very well (being elastomeric).  PDMS is air permeable which is helpful in dead-end filling and reduction in bubbles, but harmful for any kind of anaerobic culture and maintaining osmolarity.  PDMS does not age well - PDMS after a few years may have very different properties than what it started out with.  Most organic solvents tend to partition into PDMS and swell it - making chemical reactions that involve such solvents difficult.  This rules out DNA or peptide synthesis which need solvents like aceto-nitrile. A class of fluorinated elastomers - teflon-like have been developed (the author was involved with some of that work) to overcome these problems - however they are expensive and difficult to work with at the moment. 

Silicon and glass on the other hand are much more inert and resistant to chemical attack. However, working with them requires harsh chemical conditions making processes expensive. Bubbles can be a huge problem as they cannot diffuse through the material of the chip.  With silicon, due to the electronics industry, well developed processes allow careful control of etching - and very small features can be built - nanometers in size.  Silicon and glass tend to age well, unlike PDMS.  Due to their hardness, valving can be a difficult proposition - some sort or gaskets or diaphragms are needed.  Silicon and gals tend to withstand higher pressures than PDMS. For very high pressure applications, steel and other metal alloys are used.

Plastics (polythene, polycarbonate etc) are the most common materials in industry - injection molding is used to make inexpensive parts by the millions.  Currently, there no well developed processes to make very small features reliably, so plastics are used for larger parts and manifolds.  
    
%\clearpage
\section{Suggested Exercises}
1) How does a rotary mixer physically work? Can you explain it to someone else in a few sentences.\\[0.1in]

\noindent 2) Read Trimmer's paper "Microbots and Micromechanical Systems"\\[0.1in]

\noindent 3) Read "There is plenty of room at the bottom" (1960) - Richard Feynman

\chapter{4: Surface Tension, Two Phase flows, Cells in Devices}
Anyone who has played with soap bubbles will know that surface tension leads to many beautiful and unexpected results. In microfluidics,  as we go down to smaller and smaller size scales - surface tension keeps increasing relative to other forces since it only scales as the inverse power of length (as opposed to the inverse fourth power for pressure for instance). It can easily, overwhelming be the largest force.  In this lecture we will study some of these consequences.

\subsection*{Surface Tension}
Simply stated, surface tension is the energy needed to create more surface area.  
\begin{marginfigure}
\includegraphics[width=1in,height=1in]{./pic/surfaceenergy.jpg}
\caption{Surface and bulk energy}
\label{fig:surfaceenergy}
\end{marginfigure}
Why does creating a surface need more energy?  imagine a water molecule deep inside a water glass - it feels attractive forces from all sides. From elementary chemistry we are aware that these bonds allow it to rest in a energetically favorable state. Compare this with one at a surface. Approximately, half it's interactions are now missing and energetically it is an unhappy molecule.   Creating a surface requires energy. The energy is approximately half the average energy of a molecules $~kT$.  The table at the side shows some surface tension values for a number of liquids.  

\begin{margintable}
\caption{Surface Tension}
\begin{tabular}{p{2cm}l}
\toprule
\multicolumn{2}{c}{at $20^0 C$} \\
\cmidrule(r){1-2}
Type &amp; $\gamma (Nm^-1 \times 10^{-3})$ \\
\midrule
Water-air &amp; 73   \\
Mercury-air &amp; 485  \\
PDMS-air&amp; 19 \\
Ethanol-air &amp; 22 \\
\bottomrule
\end{tabular}
\end{margintable}

There is a another complementary way to think of surface tension - as a the force exerted along a boundary.  Since the molecules at a surface are energetically in a unfavorable position, they exert a force to reduce the surface area - to close a boundary if possible. 

\section{Laplace Pressure}
Fluid surfaces that are curved cause an increase in surface area - which must be balanced by a change in pressure to balance out the forces.   This excess pressure is given by the Young-Laplace equation written as:

\begin{equation}
\Delta P = \gamma (\frac{1}{R_1} + \frac{1}{R_2})
\end{equation}

\begin{figure}
  \centering
  \caption{}
  \subfloat[Thomas Young (1773-1829)]{\label{fig:Young}\includegraphics[width=0.4\textwidth,height=2in]{./pic/Young.jpg}}                
  \subfloat[Pierre-Simon Laplace (1789-1827]{\label{fig:Laplace}\includegraphics[width=0.4\textwidth,height=2in]{./pic/Laplace.jpg}}
  \label{fig:LaplaceYoung}
\end{figure}


Here $R_1$ and $R_2$ are the principle radii of curvature of a surface. Every every surface has two principle radii of curvature at every point - they are both equal to the radius for a sphere, for a cylinder one is infinity and the other - the radius of the cylinder

Capillary forces are responsible for the rising of liquids in small capillaries. An elementary force balance calculation shows that the meniscus of an liquid has an height given by:

\begin{marginfigure}
\includegraphics[width=2in, height=2in]{./pic/paper_microfluidics.jpg}
\caption{Paper Microfluidic Device}
\label{fig:paper}

\end{marginfigure}
\begin{equation}
h=\frac{2 \gamma cos \theta}{\rho g r}
\end{equation}

where $r$ is the radius, $\theta$ the contact angle. This height can be substantial - several inches for sub-millimeter bore capillaries.

Several diagnostic devices use capillary action to take in liquids - examples of this include diabetes test strips, and lateral flow kits for pregnancy testing.  Recently several groups developed methods to produce simple microfluidic devices with paper and photo-resist - creating hydrophilic and hydrophobic areas and using wicking to move liquids \cite{paper,yager_paper}. This technology is being commercialized by "Diagnostics for All" \url{www.dfa.org}. The main attraction for this technology is the low cost of fabrication.



\section{Rayleigh-Plateau Instability}
This is an instability that converts a stream of liquid into droplets.  It can be seen when turning on  a tap.  This phenomena which is exploited in in-jet nozzles.  It is analyzed in a mathematically sophisticated way, but some insight can be gained by considering Laplace's formula.  In a stream imagine a disturbance (wave) that goes through. This type of noise is always present.   

\begin{figure}
\centering
\includegraphics[width=2in,height=3in]{./pic/Rayplat.png}
\caption{Rayleigh Plateau Instability}
\label{fig:rayplat}
\end{figure}


A narrow portion of the stream has a smaller radius and therefore a higher pressure due to surface tension, while a larger radius results in a lower pressure.  Hence liquid should flow from the narrow part to the broader parts creating droplets. However, this is not all -  there are two radii of curvatures as shown in Figure \ref{fig:rayplat} and the combined effect must be considered. It turns out that only at certain wavelength can one expect the droplets to develop and it is this that determines the size of drops.

\section{Capillary Number}
The Capillary number is the dimensionless scaling number that governs the behavior of systems involving surface tension. It is given by:

\begin{equation}
Ca = \frac{\mu v}{\nu}
\end{equation}

The capillary number compares viscous forces to surface tension forces.  If Ca $&gt;&gt;1$ , viscous forces dominate.  The capillary number will show up in most microfluidic phenomena involving bubbles and emulsions.


\section{Wetting and De-wetting} 
If you own a waterproof raincoat you may have noticed that water droplets tend to ball up on the surface of the raincoat. The surface is hydrophobic or non-wetting.  When three phases of matter (solid, liquid and gases) meet at an interface they create an angle that is the most energetically favorable - this is known as the contact angle.

\begin{figure}
\centering
\includegraphics{./pic/contactangle.pdf}
\caption{Contact angle}
\label{fig:contact}
\end{figure}

Wetting and de-wetting properties of aqueous solution have been used to create microfluidic devices in a field called "digital microfluidics". In these devices the surface energy is changed using electrical fields and the difference in surface energy provides the force for droplets to be moved. While very promising at the moment this is very much a niche area with only a few groups working on it. A review is available for those interested \cite{digital}.  This technology was first developed at Duke University and is being commercialized at Advanced Liquid Logic \url{http://www.liquid-logic.com/}

\begin{figure}
\centering
\includegraphics[width=3in, height=2in]{./pic/electro.jpg}
\caption{Design of electrowetting devices}
\label{fig:electrowetting}
\end{figure}

\section{Two Phase Devices}
Up to now we have only considered single phase devices. Adding an extra phase makes things much more complicated and interesting.  There is greater interest in recent time in using water droplets in oil as tiny reaction chambers, with the idea of increasing throughput drastically.  In some sequencing techniques emulsion PCR - done in drops of aqueous reagents suspended in oil is used. In these cases droplets acts as independent compartments.  It is also possible to use air as the continuous phase, separating plugs of liquids.
 
\begin{figure}
\centering
\includegraphics[width=4in]{./pic/mixing.pdf}
\caption{Creating isolated picoliter compartments}
\label{fig:gas_oil}
\end{figure}

Another type of two phase flow involves solids inside liquids. In this case  a parameter called Stokes number is often used
\subsection{Stokes Number}
Stokes number is the ratio between the particle relaxation time to the fluid relaxation time. Let us assume that particles of diameter d are in a fluid and encounter an object of size L. The fluid velocity far away from the obstacle is taken to be $v$

\begin{equation}
St=\frac{\tau v}{L}
\end{equation}

where $\tau$ is the relaxation (also called response time) for the particle.   This can be calculated as

\begin{equation}
\tau = \frac{d^2\rho_p}{18 \mu}
\end{equation}

Putting these two together we have

\begin{equation}
St=\frac{ \rho_p d^2 v}{18 \mu D}
\end{equation}

A low Stokes number indicates particles that can easily follow the fluid flow. A high (&gt;&gt;1) indicates particles that cannot follow the flow and will tend to bump into obstacles. This principle can be used to make a separating device as shown in Figure \ref{fig:dld}\cite{dld} 
\begin{figure}
\includegraphics[width=3in, height=3in]{./pic/dld.jpg}
\caption[][2in]{A set of posts at an angle to the flow can sort particles by size}
\label{fig:dld}
\end{figure}



\section{Surfactants}
Surfactant are chemicals that are active at surfaces. They tend to lower the surface energy (hence surface tension).  Surfactants come in different types - neutral, anionic, cationic, amphoteric etc.  Several volumes can be written just about surfactants.  For microfluidic two-phase devices that involve droplets surfactants are critical get both appropriate physical and chemical properties and influence everything from the physical properties of emulsion to the denaturing of proteins at interfaces\cite{merten1,biocompatible,droplet_pnas}.

\begin{figure}
\centering
\includegraphics[width=2in, height=2in]{./pic/surfactant.png}
\caption{Neutral, Anionic, Cationic and Amphoteric surfactants}
\label{fig:surfactant}
\end{figure}

Sorbitan monooleate (Span 80) and Polysorbate 80 (Tween 80) are two common surfactants used in many microfluidic oil/water devices. One problem with these is that material tends to be exchanged between droplets which destroys the isolation needed for many applications; proteins can denature at the interface - damaging enzymatic capabilities and properties of droplets can change with time.  More recent devices tend to use perfluoro oils (e.g. Fluoinert FC-75, FC-40 etc) as the inert  carrier and fluoro-surfactants that have been chemically modified.  In the commercial space, RainDance Technologies is commercializing droplet based processes \url{http://www.raindancetechnologies.com/}

\section{Mixing}
Mixing in droplets occurs due to a process called chaotic advection and serpentine channels are good at inducing it. The process is best shown in picture format in Figure \ref{fig:clay}

\begin{figure*}
\includegraphics[width=4in, height=4in]{./pic/chaotic.pdf}
\caption{Clay model of chaotic advection}
\label{fig:clay}
\end{figure*}


\section{Cells in Chips}
We can subdivide the methods to put cells into devices into four possibilities as shown in the Table \ref{table:cellsinchip}.  

\begin{table*}
\label{table:cellsinchips}
\caption{Types of systems}
\begin{tabular}[]{lcc}
\toprule
Name &amp; Cells move in-out &amp; Nutrients move in-out \\
\midrule
Batch &amp; \ding{54} &amp; \ding{54}\\
Chemostat &amp;\ding{52} &amp;\ding{52} \\
Microhabitat patch &amp; \ding{54} &amp; \ding{52} \\
(no name -ecology?) &amp; \ding{52} &amp; \ding{54} \\
\bottomrule 
\end{tabular}
\end{table*}

A general rule is that working with bacterial cells in microfluidic chips is much easier than dealing with mammalian cells. Mammalian cells  need precise control of gas concentrations, surface chemistry and osmolarity and this can be challenging to achieve especially on longer time scales (days and weeks)

A large number of different ways have been designed to trap cells in microfluidic devices for imaging purposes.  A prison for cells can be created with valves - and here as little as a single cell or a millions of them could be trapped.   We will see such a device in our experiments.

\begin{figure*}
\caption{Capturing cells}
\subfloat[Tesla chemostat: using differencial height]{\label{fig:tesla}\includegraphics[width=0.5\textwidth,height=2in]{./pic/tesla.pdf}}                
\subfloat[Valvetrap: using valves]{\label{fig:valvetrap}\includegraphics[width=0.5\textwidth,height=2in]{./pic/valvetrap.pdf}}
\label{fig:capturingcells}
\end{figure*}

\begin{figure*}
 \caption{Capturing cells}
 \subfloat[Post trap: using posts]{\label{fig:post}\includegraphics[width=0.5\textwidth,height=2in]{./pic/celltrap.jpg}}
 \subfloat[Post trap: using posts in another way]{\label{fig:post2}\includegraphics[width=0.5\textwidth,height=2in]{./pic/posts.pdf}}
 \label{fig:capturingcells2}
\end{figure*}

\section{Small Organisms in Chips}
Besides cells it is also possible to work with small organisms like C. elegans, zebra fish, planaria. This kind of work is just beginning and is the next logical step up from working with cells. In particular in the case of C.elegans, microfluidic chips have proved very versatile and seem poised there to be used in a big way \cite{whitesides_worm}.  To take one such instance, C. elegans worms can be trapped in channels and its nose exposed to odorants, and the neural pathways that are activated studied.  This was shown in a paper a few years ago \cite{bargmann}. We will in the experimental part of the course attempt a simple and entertaining experiment with C.Elegans - getting it to move towards odors. 

\begin{figure}
\centering
\includegraphics[width=2in]{./pic/wormnose.jpg}
\caption{C.Elegans trapped in a device and exposed to odors}
\label{fig:wormnose}
\end{figure}

\section{Suggested Exercises}
1) The mixing time in droplets is often given a $log_e(Pe)$ Where do you think the log factor comes from?

2) Watch videos from the National Committee for Fluid Mechanics films \\
\url{http://web.mit.edu/hml/ncfmf.html}\\
Surface Tension in Fluid Mechanics \\

3) Pouring Salt water into salt water results in more bubbles than poring fresh water in fresh water. Why? (From Jearl Walker's The Flying Circus of Physics)\\

4) Read "Snow, Rain, and the Stokes Number", by Daniel Cromer and Lynn Pruisner\\

5) Read the Bump array paper

\chapter{5: What was left out, Conclusion}
When people with experience look at microfluidic device, they don't start solving Navier Stokes equation, they use some simple rules of thumb to guide whether something seems reasonable or not. Let us try to recall the rules of thumb we learned in the first chapter:

\subsection{Re number is small}
The Reynolds number in all microfluidics devices is below the turbulent limit. Flow is linear and laminar.

\subsection{Flow velocity at surfaces is zero}
The flow velocity at the surface is zero. This is peculiar, non-intuitive fluid phenomena. In almost everything we do this is the case and this is known as the no-slip boundary condition. For solids this is not true as you well know from motion of cars etc.  

\subsection{Density is constant for liquids}
Most liquids are not very compressible and their density remains constant inside our devices. This also means that waves, particularly of small wavelengths, cannot be sustained inside the liquid, because they require density changes.   Large wavelengths on the other hand can are needed and indeed this is the principle of submarine sonar and whale songs - however these are irrelevant for most microfluidic devices.

\subsection{Scaling principles}
Having an idea of how things scale provide insight into a situation. Here is partial list of how physical quantities scale 
\begin{table}

\label{table:scale_physical}
\begin{tabular}{lp{3.5cm}}
\toprule
Quantity &amp; Scaling law\\
\midrule
Time  &amp; $L^0$\\
Capillary force  &amp; $L^1$ \\
Length &amp; $L^1$  \\
Velocity &amp; $L^1$\\
Electrostatic Force &amp; $L^2$\\
Diffusion Time &amp; $L^2$\\
Area &amp; $L^2$\\
Volume &amp; $L^3$\\
Mass &amp; $L^3$\\
Force of gravity &amp; $L^3$\\
Electrical Motive Force &amp; $L^3$\\
Magnetic force (exterior field) &amp; $L^3$ \\
Magnetic Force (no exterior field) &amp; $L^4$\\
Centrifugal Force &amp; $L^4$ \\
Pressure (low Re, constant Q) &amp; $L^4$\\
\bottomrule
\\
\end{tabular}
\caption{Scaling Laws (adapted from Introduction to Microfluidics (Patrick Tabeling)}
\end{table}
\section{What was left out}
We have covered a lot of material in the last few sections. But microfluidics has grown so large that is impossible to cover or even do justice to many parts of it.  So the author apologizes in advance to anyone offended that their favorite technology was not included. This omission is not a judgment on the importance of a topic, but a reflection of the author's ignorance.In listing things left out there is a danger of committing the double error of not listing the missing things that were missed out in the first place -the unknown unknowns.   Nevertheless, in the spirit of E.B. White ("Why compound ignorance with incomprehensibility. Why run {\it and} hide?") a brief mention of some areas is in order.\\

We have barely scratched the surface of flows influenced by electrical and magnetic fields. This is a very important part of microfluidics with many applications.  Capillary electrophoresis is what in fact got microfluidics started. \\

We did not cover any kind of heat transfer microfluidics. In reactions like PCR, temperature cycling is required. A variety of new effects and scaling numbers are needed to understand thermal effects in fluids.\\

In recent years there has been increasing interest in combining light and fluids - the fusion being termed optofludics. We also left out several technologies - for instance hydrogels microfluidics and microfluidics on spinning disks \\

No mention was made of nanofluidics - the technology where we try to go down even further in size scale. \\

For most industrial application the most cost effective way to make devices is via injection molding which we have also not covered.   (We will cover in the experiments some methods of using thin sheets of plastic or adhesive films) \\

\section{Challenges in Microfluidics}
The idea behind microfluidics is to be a practical technology that can be used by a large number of people. There are several challenges that preclude the widespread adoption of microfluidics The first is the barrier to learning and doing things - and this course, and others like it are designed to reduce that threshold.  There are other problems that need solutions; we mention three:

\subsection{Standardization}
The connectors and designs for microfluidic devices are not standardized. In electronics we have many different standards - USB, serial ports, that allow easy interchangeability. Other than 96-well plates this kind of standards do not exists for fluidics at the micro scale, making it harder to use them as everything has to be done from scratch.

\subsection{Control and Detection}
Building smaller chips is not enough - the control and detection systems like microscopes and solenoids also need to be miniaturized.  This macro to micro problem was solved in electronics with techniques like wire-bonding and specialized packaging.

\begin{figure*}
  \caption{Chips may be small...tubing, control and microscopes are large}
\includegraphics[width=4in,height=2in]{./pic/medusa1.png}           
 \label{fig:medusa1}
\end{figure*}


\subsection{Lack of a platform}
Again unlike electronics where PCB boards and silicon wafers are industry wide standards, there are many competing platform technologies in microfluidics.  It is not clear which ones will become standards. In academics, the "it's no good, because it was not invented here" syndrome prevents quick adoption of technology. In industry, patents and trade secrets create a barrier to diffusion of know-how.  

PDMS devices in recent years have really taken off - but they are largely ignored by industry because of problems with gas diffusion, leaching of chemicals and poor aging characteristics. Silicon devices which were very popular in the 90s have waned because of the difficulties in getting simple devices made without access to clean-rooms. They may yet stage a comeback because of silicon's desirable chemical characteristics.

\section{Conclusion}
We have come to the end of this course - our hope is that you have now a broad understanding of the kind of fluidics possible and we have reduced the threshold for making and using these devices, and can now exercise scientific judgment on whether it makes sense to use the tools in your specific research problem or project.

Microfluidics is a young field, and there much scope for making new discoveries and we hope that some of you will do so.

\part{Experiment Manual}
\chapter{1: Honey, I shrunk the chips...}
In the first few experiments we will make inexpensive microfluidic devices and use them. If you want to make something quickly without being too worried about the exact dimensions, these techniques will work. Of course, there is a 'price' to pay in the tolerances, and hence the kinds of things possible. 

\section{About the experiment}
This experiment is based on 2007 paper by Michelle Khine ( \url{http://shrink.eng.uci.edu/}) and collaborators\cite{shrinky}.  The design we will make is a H-filter first conceived of by Brody et al\cite{brody1996}. More information on this design can be found here:\\[0.1in] \url{http://faculty.washington.edu/yagerp/microfluidicstutorial/hfilter/hfilterhome.htm}\\[0.1in]

We use a children's toy called shrinky-dink. Shrinky dinks are sheets of plastic (poly-olefins for the plastic-geeks) that shrink when heated. When you shrink a film with something drawn on them, the ink particles become raised and squished leading to intense colors.  You can buy these films from a hobby craft store or on-line\sidenote{Some places to get them \url{http://www.shrinkydinks.com}, \url{http://www.grafixplastics.com/shrink.asp}}. Our films were obtained directly from Professor Michelle Khine and a company called NanoShrink.  

The raised ink particles create a mold with the height of features depending on the particular shrink factor and the type of ink used (printing multiple times can help in getting taller features).  This is microfluidics at its simplest - just a printer, some shrink film, an oven and some PDMS is needed.

\begin{marginfigure}[0.5in]
\includegraphics[width=2in]{./pic/1_autocad.jpg}
\caption{H filter design}
\label{fig:H-filer}
\end{marginfigure}

\section{Procedure}
Follow these steps:\\

1 Open the Hfilter.dwg file on the computer. \\

2 Insert a laser transparency in the laser printer (manual tray 2) and plot the file on the printer.  We have set the printer to print on a laser transparency. Don't change this setting. If all goes well the design will show up in the middle of the transparency.  \\
\begin{marginfigure}
\includegraphics[width=2in]{./pic/1_shrinky.jpg}
\caption{Tape shrink film}
\label{fig:tapefilm}
\end{marginfigure}
3 Wearing gloves and using the printed design as a guide, place a 2 in x 2in shrinky film to cover the design and tape all 4 sides with scotch tape. \\
\begin{marginfigure}
\includegraphics[width=2in]{./pic/1_cutout.jpg}
\caption{Cut out the printed film}
\label{fig:cutout}
\end{marginfigure}
\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Note}} &amp;Tape on all 4 sides is necessary to prevent curling due to the toner heat  \\
\end{tabular}
}\\[0.2in]
\begin{marginfigure}
\includegraphics[width=2in]{./pic/1_IPA_wash.jpg}
\caption{Wash with water and isopropanol}
\label{fig:washshrinkfilm}
\end{marginfigure}

4 Reprint the design - this time it will be printed on the shrink film. \\

5  Now cut out the shrink films and discard the laser transparency \\

6 Take the film to our toaster oven.  Place the film on a large glass slide inside the oven. Press "CONVECTION BAKE". Press the temperature button and adjust the temperature to 225 F.  Press START. After a few minutes the oven will beep and say temperature ready. Now count down to 5 minutes.\\

\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Note}} &amp;The shrinky dink will first curl and then flatten - don't be alarmed!  \\
\end{tabular}
}\\[0.2in]

7 Press temperature  again and adjust to 275 F.  Again like the last step bake for 5 minutes.\\

8 Remove from oven carefully -it's hot. If not completely flat, you can carefully flatten it while it's hot  \\

9  Take this design to the white room and using a plastic dish wash with isopropanol and water\\

10 Now keep the chip apart. Let's make our PDMS mixture.  Take a white plastic 150 ml container and mix the PDMS A and B in a 1:10 ratio. Only about 25g is needed - so add about 2.5 g of curing agent and about 25g of main mixture.  Weigh the container. Add the weight of the holder and balance the machine. Run the standard program. \\
\begin{marginfigure}
\includegraphics[width=2in]{./pic/1_PDMS_make.jpg}
\caption{PDMS mixer}
\label{fig:PDMSmixer}
\end{marginfigure}
11 Put your shrink mold in a small petri dish. Pour the PDMS mixture on top of the shrinky dink and let it cure in the curing oven at $60^0$ centigrade for 30 minutes (until solid) \\
\begin{marginfigure}
\includegraphics[width=2in]{./pic/1_PDMS_add.jpg}
\caption{Pour PDMS}
\label{fig:pour_PDMS}
\end{marginfigure}

12 Remove the  PDMS carefully and cut out the design. \\

13 Take a cover glass and the PDMS to the plasma machine and treat with plasma for &lt;10 s.  Your TA will show you how to use this machine.  Bond the two. Put in the curing oven for 30 minutes. \\

\begin{figure}
  \caption{Microwave Plasma and Toaster Oven}
  \subfloat[Plasma]{\includegraphics[width=0.5\textwidth,height=2in]{./pic/plasma_system.jpg}}                
  \subfloat[Toaster Oven]{\includegraphics[width=0.5\textwidth,height=2in]{./pic/toaster.jpg}}
  \label{fig:PlasmaandToaster}
\end{figure}


14 Remove and insert bent hollow steel pins into ports (0.025 in OD and 0.017 ID, New England Small Tube, MA).  Using the syringe and tubing (Tygon microbore tubing, 0.020in ID x 0.060in OD, 100, Cole Parmer EW 06418-02) attached to it - suck a solution of micro-spheres in one and distilled water in another. \\
\begin{marginfigure}
\includegraphics[width=2in]{./pic/1_cut_PDMS.jpg}
\caption{Cut out PDMS design}
\label{fig:cutPDMS}
\end{marginfigure}

\begin{marginfigure}
\includegraphics[width=2in]{./pic/hfilterchip.jpg}
\caption{Insert pins into chips}
\label{fig:PinInChip}
\end{marginfigure}

15 Flow through you chip using the syringe pumps provided and observe the flow pattern. Start with a low pumping rate (in micro-liters per hour). \\

16 We will provide you with a solution of fluorescence micro-spheres and another solution of water. Flow them through the chip and collect the two solutions that emerge for the outlet ports. Device a protocol to count the number of micro-spheres in each. What do you observe? \\
\clearpage

\begin{figure*}
\includegraphics[width=4in,height=3in]{./pic/brody1996hh.jpg}
\caption{The original H filter design}
\label{fig:H filter}
\end{figure*}


\section{Further Followup:}
\noindent 1) Using Shrink film to Culture Embyroid Bodies -
\url{http://www.jove.com/details.php?id=692}\\

\noindent 2) Shrink-film microfluidic education modules: Complete devices within minutes, Diep Nguyen, Jolie McLane, Valerie Lew, Jonathan Pegan, and Michelle Khine Biomicrofluidics 5, 022209 (2011); doi:10.1063/1.3576930 \\

\noindent 3) Diffusion-based extraction in a microfabricated device J P Brody, P Yager Sensors and Actuators A: Physical (1997)
Volume: 58, Issue: 1, Pages: 13-18

\chapter{2: A-mazing Cutting Edge Worms}
This experiment uses a craft cutting printer to cut shapes in pressure sensitive adhesive films. For simple microfluidic devices, the method is attractive because cutting printers are inexpensive and a variety of materials can be used, including paper, adhesive tapes, plastic and PDMS films. 


\section{Introduction}
\begin{figure*}
\centering
\includegraphics[width=6in]{./pic/Adult_Caenorhabditis_elegans.jpg}
\caption{Adult C. elegans}
\label{fig:c_elegans1}
\end{figure*}

Besides working with cells and molecules, microfluidics is a versatile tool for working with small creatures like C. elegans, planaria, and zebra fish. The size scale of microfluidic deices is well suited to manipulating these animals. In particular, high throughput sorting of mutants is an area receiving much attention.  

\section{Cancer and C. Elegans}
C.Elegans is a small worm that was introduced as a biological model by Sydney Brenner in 1974.  Its genome and cell lineage are completely known.  Because it is so easy to handle and grow, and mutants can be frozen and kept for years, it is as close as possible to an ideal biological model. Recently, evidence emerged that starvation can prolong the life of these worms - this exciting finding seems to apply to many organisms and may also be relevant to humans.  Surprisingly, it was found that mutations that lead to longer life spans reduce tumor formation \cite{aging_tumor} which is am intriguing connection.  Many genes in C. Elegans share homologues with human genes, making genetic manipulation with C.elegans relevant to human disease. In fact, C.Elegans seems to have many genes related to to human oncogenes. Studies on this worm have reveled many insights into apoptosis (programmed cell death) and RNA interference mechanisms\cite{celeganscancer}.

\section{Mazes}
The experiment we will perform is a variant of that described by the Wheeler group at University of Toronto\cite{maze}.  The idea is to cut our mazes in pressure sensitive adhesive tape (9795R 3M Advanced Polyolefin Tape, donated by 3M company) and use these on agar plates.

\section{Worm Growth Protocol}
We will supply the C. Elegans wild type worms. The procedure to grow them is described below.  This experiment uses a simple maze to determine odor preference in wild-type Caenorhabditus elegans.  The odorants to be tested are pyrazine, 2,3 pentanedione, and 2-butanone; each of these is a chemoattractant sensed by a different neuron in the worm.  Here, we will use the maze to determine if worms can locate the \emph{combination spot} (all 3 attractive odors combined) in a field of attractive, competing smells. \\

We prepared the worms for you as follows:\\

1.	Using M9 buffer and a P-1000 pipette tip, wash day 1 adult worms off of a plate and place in a 15mL conical tube.\\

2.	Allow worms to settle by gravity.  Using a pipette or vacuum manifold, remove the buffer.  Wash with ~3mL of M9.\\

3.	Repeat step 2 twice.\\

4.	Starve worms in 3 mL of M9 in the conical tube for one hour.\\



\section{Cutting}
Our machine is a Craft Robo Pro CE-5000 machine, but any machine  that can cut films will do.\\

1) The exact cutting condition have been saved. We will only use them. Attach a film on the carrier sheet \\

\begin{figure}
\centering
\includegraphics[width=3in]{./pic/cutter.jpg}
\caption{Cutting printer}
\label{fig:cutter}
\end{figure}

2) Load the carrier sheet and let the cutting printer initialize. It will move the carrier sheet forward and backward and try to sense how long it is and then finally home the cutting blade \\

\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Caution}} &amp;The cutting blade is sharp - don't bring your fingers close to it while the machine is operating \\
\end{tabular}
}\\[0.2in]
\begin{marginfigure}
\centering
\includegraphics[width=6in, angle=90]{./pic/C_elegans_anatomy.png}
\caption{Anatomy of C.elegans worm}
\label{fig:c_elegans2}
\end{marginfigure}

3) Select the program Robo Cut Master Pro and select the maze.dwg file.  Cut the design out.\\

\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Caution}} &amp; Make sure you press origin and let the machine know where the origin is.  Otherwise unpredictable cuts can happen.  The machine can be stopped by using the "Pause" button \\
\end{tabular}
}\\[0.2in]
\HRule


\section{Running the worm through mazes}
5)	Meanwhile, prepare chemotaxis plates.  Using scissors, cut out the 3 worm mazes.  Make the mazes as small as possible, as this will make applying them to the plates easier.\\

6)	Carefully peel off the white backing and detach the inner portions of the maze.  Gently place the maze down on a 10cm, Normal Growth Media (NGM) agar plate.  \\

7)	Repeat for the other two mazes.\\

8)	Using scissors, cut the ends from some P-20 tips.  These will be used for transferring worms to the chemotaxis plates.\\

\begin{marginfigure}
\includegraphics[width=2in,height=2in]{./pic/SpokeMaze.pdf}
\caption{Design of Cut}
\label{fig:cutmaze}
\end{marginfigure}

9)	Turn over the chemotaxis plates.  In the middle of the endpoint of each spoke, use a lab marker to make a small dot on the bottom of the plate.  Label which spoke will be dotted with which odorant (2,3 pentanedione; 2-butanone; pyrazine; or all three).  The order doesnâ€™t matter, but being consistent between your plates will make the experiment easier.\\

10)	  When there are 10 minutes left in the worm's starvation period (not before), place 1uL of 1M Sodium Azide (NaN3) on the agar over each of the dots you made in step 9.  Allow the azide to absorb in the agar.  Azide will immobilize the worms, allowing you to distinguish their 'first choice' of odorant.  \\

\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Caution}} &amp; Azide is toxic. Use Gloves! \\
\end{tabular}
}\\[0.2in]

11)	 When there are 5 minutes left in the starvation period, place 1uL of each of the odorants on their appropriate spot.  The 'combo' spot receives 1uL of each odorant.  Odorants are volatile so keep the lid closed as much as possible.\\

12)	 When the starvation period ends, remove as much excess M9 buffer from the worms as possible.  Using the cut pipette tips, apply 3x 5uL of worms to the center of each maze for a total of 15uL of worms/plate (this helps prevent sticking to the sides of the tube).\\

13)	 Twist the corner of a KimWipe into a point.  Use this to remove the excess fluid from the 'puddle' of worms you have in your maze. \\

14)	 Allow worms to chemotax for 30 minutes.  Image using a stereomicroscope.\\

\subsection{Further Follow-up:}
\noindent 1) "Chemistry and the Worm: Caernorhabditis elegans as a Platform for Integrating Chemical and Biological Research", Hulme, S.E., and Whitesides.G.M., Angewandte Chemie International Edition, 2011, 50, 4774-4807\\

\noindent 2) Bargmann, C.I. Chemosensation in C. elegans, WormBook, ed. The C. elegans Research Community, WormBook, doi/10.1895/
wormbook.1.123.1, http://www.wormbook.org\\




\chapter{3: Move it, Move it, Move it}
In this experiment we will use an off-the-shelf device sold by Ibidi ( \url{www.ibidi.com} ) that generously donated the chips). These devices are made of plastic and are fairly inexpensive. The dimensions are shown in \ref{fig:ibidi}. The channels are $400 \mu m $ deep. Besides this design several other standard designs are available.

We will use the 3 in 1 design and do two types of experiments with them - first we will perform hydrodynamic focusing. Then we will look at motility of dictyostelium under gradients. 

\begin{figure}
\centering
\includegraphics[width=5in]{./pic/ibidi_dimensions.png}
\caption{Dimensions of Ibidi 3 in 1 chip}
\label{fig:ibidi}
\end{figure}

\section{Hydrodynamic Focusing}
We will learn about hydrodynamic focusing in the lectures - briefly it involves squeezing a flow stream using two adjacent streams.   This is the same process used in fluorescence activated cell sorting.  In 1998, Bob Austin (Princeton PS-OC senior PI) and collaborators showed that the same type of hydrodynamic focusing can be done in microfluidic devices\cite{austin1998}. 

We shall use hydrodynamic focusing as a way to create quick switching gradients that motile cells can react to. Our cells are the slime amoeba - which is convenient to use since it is safe, large and will move quickly in response to chemical signals.  First let us do some hydrodynamic focusing.  We will use the uncoated Ibidi 3 in 1 chip.

1) Attach the chip to tubing and syringe pumps using the tubing and elbow connectors. Fill the central tubing with food dye coloring

\begin{figure*}
  \caption{Using the chip}
  \subfloat[Pumps]{\label{fig:pump}\includegraphics[width=0.3\textwidth,height=2in]{./pic/pumps.jpg}}                
  \subfloat[Chip on microscope]{\label{fig:3in1}\includegraphics[width=0.3\textwidth,height=2in]{./pic/3in1.jpg}}
  \label{fig:focusmove}
\end{figure*}

2) By changing the flow rates you should be able to focus the food dye stream. 

3) By changing the flow rates of the two side streams it should be possible to move the central stream from one end to another.

4) How narrow can you get the stream in the middle? does the stream broaden as you move downstream?

\begin{figure*}
  \caption{Hydrodynamic Focusing}
  \subfloat[Focusing to a narrow stream]{\label{fig:austin01}\includegraphics[width=0.3\textwidth,height=2in]{./pic/austinfocus01.jpg}}                
  \subfloat[Confocal images]{\label{fig:austin02}\includegraphics[width=0.3\textwidth,height=2in]{./pic/austinfocus02.jpg}}
  \subfloat[Electrical Analogue model]{\label{fig:austin03}\includegraphics[width=0.3\textwidth,height=2in]{./pic/austinfocus03.jpg}}
  \label{fig:hydrodynamic}
\end{figure*}


\section{Metastasis and Social Amoeba}
Dictyostellium discoideum is a slime mold amoeba that is designated as a model organism by NIH\sidenote{\url{http://www.nih.gov/science/models/d_discoideum/}  and \url{http://dictybase.org/}}. They grow quickly, feed on E.coli and are easy to work with. If starved on a agar plate dicty tends to form multi-cellular fruiting bodies (asexual) or macrocysts (sexual). This form of aggregation has been the focus of intense study over the last few decades because it is an example of a switch from unicellular to multicellular behavior. From the point of view of cancer research dictyostellium shows many behaviors that are relevant including apoptosis (programmed cell death), DNA repair, cell movement.  There are several similar genes shared between humans and dicty.  Another amazing fact: this year a group showed that dicty can cultivate bacteria - i.e.\ they are farmers! \cite{farmers}
 
\begin{figure*}
\includegraphics[width=4.5in]{./pic/dicty_move.png}
\caption{Switching gradients in a microfluidic device}
\label{fig:dicty_move}
\end{figure*}

The type of experiment we would like to do is described in a recent paper by a German group \cite{dicty_switch}. We will modify this to make it simpler.\\
 
 1) In an ibitreat (physically treated surface) 3 in 1 slide put in dicty using a 200 $\mu l$ pipette, using the end with one output, rather than the end with 3 inputs. Wait for a 15-30 minutes. The dicty will settle down and spread out and start to explore the surroundings. (If they ball up then they are unhappy)\\
 
 2) Flow through the two side inlets, buffer at about 60 ul/hr\\
 
 3) Through the center channel flow a mixture of folic acid and fluorescein. Fluorescein allow visualization of the stream -use it to get a focused stream\\
 
 4) Now adjust the stream so that the folic acid stream is near one side wall. 
 
 5) Observe the motion of dicty - make a video if possible.
 
 6) Switch the folic acid stream to the other side wall and repeat.
 
 7) How fast do the dicty move? Can you track the paths and find out if they are moving randomly or with a bias of some sort?. For the experts in tracking of cells you could run an analysis on the image stack produced by the the imagining program. 
 
\section{Further Follow-up}
1) Millisecond Kinetics on a Microfluidic Chip Using Nanoliters of Reagents, Helen Song and Rustem F. IsmagilovJ Am Chem Soc. 2003 November 26; 125(47): 14613â€“14619.\\
2) Hydrodynamic Focusing on a Silicon Chip: Mixing Nanoliters in Microseconds, James B. Knight, Ashvin Vishwanath, James P. Brody, and Robert H. Austin Physics Review Letters, Volume 80, 17 (1998)


 
\begin{marginfigure}
\includegraphics[width=2in,height=3in]{./pic/Dictyostelia.jpg}
\caption{Fruiting body}
\label{fig:fruiting}
\end{marginfigure}

\chapter{4: Mix it up}
In this experiment we make a couple of molds - one for a gradient mixer and another for two phase devices. We use soft-lithography extensively. For these devices we can use any suitable resist.

\begin{marginfigure}
\includegraphics[width=2in,height=1.5in]{./pic/wash_water.jpg}
\caption{Wash your glass-plate with water}
\label{fig:wash}
\end{marginfigure}

\begin{marginfigure}
\includegraphics[width=2in,height=1.5in]{./pic/spin_resist.jpg}
\caption{Spinning resist}
\label{fig:spin}
\end{marginfigure}

\begin{marginfigure}
\includegraphics[width=2in,height=1.5in]{./pic/baking.jpg}
\caption{Baking wafer on hot-plate}
\label{fig:baking}
\end{marginfigure}

\begin{marginfigure}
\includegraphics[width=2in,height=1.5in]{./pic/mask_aligner1.jpg}
\caption{Using the Mask Aligner}
\label{fig:maskalign}
\end{marginfigure}

\section{Procedure}
Follow these steps:

1) Clean your glass plate if needed with deionized water (DI water) to remove any dust particles. Dry completely with air gun\\

2) Coat your wafers with HMDS (hexamethyldisilazane). One way to do this is to put a few drops of HMDS in a closed container and leave your wafer in there for &gt; 2 minutes.  Your TA will set this up for you. This step is optional for SU8 molds.\\[0.2in]

 \fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Note}} &amp; Silicon wafers are brittle and break easily. Handle with care   \\
\end{tabular}
}\\[0.2in]
   
3) Spread resists (flow mold) on the wafer, covering 1/4 to 1/2 the surface. Spin wafer at 2000 rpm to get a uniform coat.\\

4) Soft-bake on a hot-plate at $65^0$ C for 3 minutes followed by $95^0$ C for at least 5 minutes.\\

5) Expose the wafers in a mask aligner using a transparency or chrome mask. \\

\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Caution}} &amp; Wear protective glasses of look away when UV exposure is being done   \\
\end{tabular}
}\\[0.2in]

6) For SU8 a post expose bake is needed.\\

7) Develop SU8 and SPR molds in the appropriate developers (SU8 developer and CDK 351 diluted with DI water 1:3 respectively). \\

8) (optional) Round your SPR mold profile by baking on a hot plate at 95-105 degrees for about 30 minutes or Hard bake your SU8 mold by leaving wafer on a hot plate at 100-120 degrees for about an hour. 

\section{Soft-lithography}
We now take these molds to perform soft-lithography\\

9) Expose your molds to TMCS (Chlorotrimethyl silane). One way to do this is to put a few drops of TMCS in a closed container and leave your wafer in there for &gt; 2 minutes. This must be done inside a chemical safety fume-hood.\\

10) Mix PDMS in 1:10. De-gas in a centrifuge or a polymer mixer.\\
 
 \begin{figure*}
 \caption{Punching, Curing, Mixing}
 \subfloat[Puncer]{\label{fig:puncher}\includegraphics[width=0.3\textwidth,height=2in]{./pic/puncher.jpg}}                
 \subfloat[Mixer]{\label{fig:mixer}\includegraphics[width=0.3\textwidth,height=2in]{./pic/mixer.jpg}}
 \subfloat[Curing Oven]{\label{fig:oven}\includegraphics[width=0.3\textwidth,height=2in]{./pic/curing.jpg}}
 \label{fig:punch_mix_cure}
\end{figure*}  

11) Put in a 60-80 degree oven for 10-30 minutes until it is no more liquid.\\
  
12) Remove from oven, and using a razor blade cut around the chip and release it from the wafer. Punch through holes for the flow layer.\\

13) Bond the chip to a glass slide either using a plasma or by plopping on glass and baking for a day. \\

\begin{figure*}
\includegraphics[angle=90,width=4.5in]{./pic/diffmix.PDF}
\caption{A flow gradient maker}
\label{fig:mixer}
\end{figure*}

\section{Fluidic Mixer}
Once the devices are ready we will test them on a microscope. Our first device is a gradient generator developed by Jeon et al. \cite{jeon2000}


1) Set up your device on the microscope carefully.

2) Such in food dye coloring in tygon tubing you have used preciously and attach to a syringe pump at one end and the chip at the other end using hollow steel pin connectors.

3) Try to get flow rates to achieve the gradients shown in Figure \ref{fig:gradient}
\begin{figure}
\includegraphics[width=4in]{./pic/gradient.jpg}
\caption{Gradient generator (from the original mixer paper by Noo Li Jeon et al 2000)}
\label{fig:gradient}
\end{figure}

\section{Oil and water}
This experiment deals with two phase flows. Our experiments are based on a number of papers that have appeared in recent years that use droplets to speed up analysis \cite{songismagilov}. Using two phase flow - sorting objects embedded inside droplets -  provides one route to achieving very high throughput. However, before this is possible, a whole slew of  tools have to be developed that will allow manipulation of droplets - creating, combining, splitting them for instance.  Further, more work has to be done on surface chemistry and surfactants to ensure proteins don't get denatured at the oil water interface, which presents an enormous surface to volume ratio.  In recent years much progress has been made - techniques like emulsion PCR have been invented, sorting of cells and small organisms has been shown as proof of concept and methods have been developed to have precise control over droplets.

\begin{figure*}
\includegraphics[width=4in,height=4in]{./pic/twophase.pdf}
\caption{Two Phase Designs}
\label{fig:twophase}
\end{figure*}

\FloatBarrier

\section{Procedure}
Follow these steps:\\

1) As in the previous case set up your device on the microscope carefully. Suck oil and water into the tubing before you attach it to the chips.  You should now be familiar with this procedure from the previous experiments

2) First let us examine the three devices on the top left. They consists of focusing junction with varying angles (30, 60 and 90 degrees).  

2) Perform initial experiment without the addition of any surfactant and then try to add surfactants  (span 80, tween 80) about 0.5-2 \% by volume and observe the difference.  

3) Vary the flow rates (or the pressures) and observe the various phases that form - can you draw the phase diagram?

\begin{figure*}
  \caption{Oil and Water in a focusing geometry}
  \subfloat[No surfactant]{\includegraphics[width=0.4\textwidth,height=3in]{./pic/nosurf.jpg}}                
  \subfloat[Phase diagram with surfactant]{\includegraphics[width=0.4\textwidth,height=3in]{./pic/pearl.png}}
  \label{fig:surf}
\end{figure*}

4) Does the flow differ drastically depending on the angle of the channels?

5) The device on the bottom left is based on a paper published in 2001 \cite{thorsen} and some images from the paper are shown in Figure \ref{fig:thorsen3}.  Here we can try to dynamically generate different phases that depend on the pressure differential.  Try to produce the patterns that were seen in that experiment.

6) The other devices are based on a different paper \cite{pearl} with a modified geometry.  Try to flow oil and water (with surfactants or without) and see if you reproduce the phases seen in Figure \ref{fig:surf}. How much of a difference does device geometry make?

\begin{figure*}
 \caption{Oil and water}
 \subfloat[Device design]{\label{fig:thor1}\includegraphics[width=0.3\textwidth,height=2in]{./pic/Thorsen1.jpg}}                
 \subfloat[Oil/water phases]{\label{fig:thor2}\includegraphics[width=0.3\textwidth,height=2in]{./pic/Thorsen2.jpg}}
  \subfloat[Water/Oil phases]{\label{fig:thor3}\includegraphics[width=0.3\textwidth,height=2in]{./pic/Thorsen3.jpg}}
  \label{fig:thorsen3}
\end{figure*}

7) The final design on the bottom right of the wafer is a design that allows the creation of aqueous droplets with mixtures of different components \cite{ticesong}. Here, we will use food dyes to create droplets of different colors and observe the mixing as the drops snake down the channels. Repeat the same procedure as before, but this time flow in three different food dyes through the aqueous inlets (see Figure \ref{figgas_oil})

\clearpage
\section{Further Follow up}
1) Microfluidics Using Spatially Defined Arrays of Droplets in One, Two, and Three Dimensions Rebecca R. Pompano, Weishan Liu,Wenbin Du, and Rustem F. Ismagilov Annu. Rev. Anal. Chem. 2011. 4:59â€“81\\

\noindent 2) Generation of Solution and Surface Gradients Using Microfluidic Systems Noo Li Jeon, Stephan K. W. Dertinger, Daniel T. Chiu, Insung S. Choi, Abraham D. Stroock, and George M. Whitesides*, Langmuir 2000, 16, 8311-8316


\chapter{5: Plumber's Nightmare}
In this experiment we will make our most sophisticated multilayer devices. There are two designs that we shall make.  One is a simple design to test the various fluidic circuit components. The second is a sophisticated design meant for studying yeast cells based on a paper by Taylor CJ, Falconnet et al cite{mapk}. Here are the two designs:

\begin{figure*}
\includegraphics[height=4in]{./pic/two_layer_simple.pdf}
\caption{Simple two layer PDMS device with a rotary mixer and combinatorial multilexer}
\label{fig:two-layer}
\end{figure*}

Figure \ref{fig:two-layer} shows a design that contains a combinatorial multiplexer on the left bottom that allows multiplexing of 6 input lines. these line fill up an chamber that has a peristaltic pump backing allowing precise metering of fluids into a rotary mixer.


\begin{figure*}
\includegraphics[height=4in]{./pic/mapk.pdf}
\caption{Yeast Chip to study the dynamics of kinases in yeast mutants}
\label{fig:mapk}
\end{figure*}
 
Figure \ref{fig:mapk} shows the second design. At the bottom of this design are 8 input ports for eight yeast mutant. 4 input ports connected to a 16 line logarithmic multiplexer allows selection of conditions for each of the mutant yeast cells. The cells themselves are trapped in a square profile channel with a sieve valve.  In all simultaneous experiments can be performed on 8 X 16 array.

\section{Mold Making}
\subsection{Simple Two layer}
The fabrication procedure is similar to the previous experiment except that now two molds have to be made.  We will make the flow mold with SPR-220-7 positive resist and the negative mold with SU8 2025 resist. The positive mold features can be rounded like the last time. \\

\begin{tabular}{lp{2.5in}} 
\toprule
\multicolumn{2}{c}{Flow mold (SPR 220-7)} \\
\midrule
Spin speed &amp; 2000 rpm \\
Soft bake &amp;  1 minute at $65^0$C, 2 minutes at $95^0$C \\
Exposure time &amp; 15 s \\
Developer &amp;  CDK 351, dilute with DI water 1:3 \\
Developing time &amp;  few minutes \\
Rounding temperature &amp; $105^0$ C \\ 
Rounding time&amp; &gt;30 minutes \\
\bottomrule
\end{tabular}\\[0.2in]

\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Note}} &amp; SPR does not require a post expose bake, SU8 does! \\
\end{tabular}
}\\[0.2in]

\begin{tabular}{lp{2.5in}} 
\toprule
\multicolumn{2}{c}{Control mold (SU8 2025)} \\
\midrule
Spin speed &amp; 2000 rpm \\
Soft bake &amp; &gt;3 min at $65^0$C, &gt;5 minutes at $95^0$C\\
UV exposure time&amp; 15 s\\
Post expose bake&amp; &gt;3 min at $65^0$C, &gt;5 minutes at $95^0$C\\
Developer&amp; SU8 developer\\
Developing time&amp; few minutes\\
Hard Bake temperature&amp; $120^0$C for &gt;30 minutes\\
\bottomrule
\end{tabular}

\begin{figure}
\includegraphics[width=4in,height=6in]{./pic/twomolds.jpg}
\caption{The 4 molds made in the is experiment.  SPR resist is rounded by thermal reflow after the mold is made}
\end{figure}

\subsection{Yeast Chip}
The yeast mold is bit more sophisticated in that the flow mold contains two layers - there is a square channel segment made with SU8 2010, and the standard rounded section made with SPR. It is critical to do the SU8 part first - the SPR resist will not be able to handle the processing that SU8 requires, whereas SU8 is very resistant to chemical attack.\\

\begin{tabular}{lp{2.5in}} 
\toprule
\multicolumn{2}{c}{Flow mold square channel (SU8 2010)} \\
\midrule
Spin speed &amp; 2000 rpm \\
Soft bake &amp; &gt;1 min at $65^0$C, &gt;1 minutes at $95^0$C\\
UV exposure time&amp; 15 s\\
Post expose bake&amp; &gt;1 min at $65^0$C, &gt;1 minutes at $95^0$C\\
Developer&amp; SU8 developer\\
Developing time&amp; few minutes\\
Hard Bake temperature&amp; $120^0$C for &gt;30 minutes\\
\bottomrule
\end{tabular}\\[0.2in]

\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Note}} &amp; Align the SU8 to the SPR layer by first rotating the design so that lines are parallel to each other and the using the x and y adjustment to get the alignment right. this alignment can be hard the first time you do it!\\
\end{tabular}
}\\[0.2in]


\begin{tabular}{lp{2.5in}} 
\toprule
\multicolumn{2}{c}{Flow mold (SPR 220-7)} \\
\midrule
Spin speed &amp; 2000 rpm \\
Soft bake &amp;  1 minute at $65^0$C, 2 minutes at $95^0$C \\
Exposure time &amp; 15 s \\
Developer &amp;  CDK 351, dilute with DI water 1:3 \\
Developing time &amp;  few minutes \\
Rounding temperature &amp; $105^0$ C \\ 
Rounding time&amp; &gt;30 minutes \\
\bottomrule
\end{tabular}\\[0.2in]

\begin{tabular}{lp{2.5in}} 
\toprule
\multicolumn{2}{c}{Control mold (SU8 2025)} \\
\midrule
Spin speed &amp; 2000 rpm \\
Soft bake &amp; &gt;3 min at $65^0$C, &gt;5 minutes at $95^0$C\\
UV exposure time&amp; 15 s\\
Post expose bake&amp; &gt;3 min at $65^0$C, &gt;5 minutes at $95^0$C\\
Developer&amp; SU8 developer\\
Developing time&amp; few minutes\\
Hard Bake temperature&amp; $120^0$C for &gt;30 minutes\\
\bottomrule
\end{tabular}

\section{Soft Lithography}
In this experiment soft-lithography involves some extra spinning, alignment and punching steps that make it more challenging. Moreover timing can be critical if good bonding strength is required.  We will use the technique of multilayer soft-lithography. 
\begin{figure*}
\includegraphics[width=4in,height=4in]{./pic/msl.jpg}
\caption{Multi-layer Soft-lithography}
\label{fig:MSL}
\end{figure*}

\subsection{Procedure} 
Follow these steps: \\
1) Instead of using the standard 1:10 ratio of PDMS A and B parts we will use 1:20 for the flow layer and 1:5 for the control layer. Make two containers of PDMS with these ratio. You need about 35 g for each control layer and about 10g for each flow layer. \\

2) Treat the control and flow molds with TMCS for &gt;2 minutes in the fume-hood \\

\fbox{\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Note}} &amp; TMCS makes the wafer less sticky to PDMS allowing easier peel off. If even greater non-stick properties are needed - fluorinated silanes can be also used\\
\end{tabular}
}\\[0.2in]

3) Take a petri dish and smoothen a aluminum foil along its surface. Some people also like to put in a parafilm sheet before the foil. Place the control molds and pour PDMS at a steady pace trying to avoid excessive bubbles.\\

4) Place the (open) petri dish in the vacuum chamber. Degas the PDMS mixture for 10-20 minutes. If the PDMS starts to foam and overflow you can open the valve and quickly allow some air flow on top of the petri dish.\\

5) Remove the petri dish. If some bubbles remain - use a toothpick and move them away from the design.\\

6) Place inside the caring oven and wait until it is just solid (~15-30minutes). Now take it out and peel off the PDMS carefully.\\

7) Using the punching tool punch holes in the control layer.  Make certain that the design side faces the punch.\\

8) While punching spin the 1:20 PDMS on the flow layer at about 2000-2500 rpm and place in the curing oven.\\
\begin{marginfigure}
\includegraphics[width=2in,height=2in]{./pic/spinning_PDMS.jpg}
\caption{PDMS spinner}
\label{fig:PDMS_spinner}
\end{marginfigure}

9) Remove 1:20 layer and align the control layer to the flow layer using a stereoscope. It may be helpful to cut out the chip instead of doing them all at once.  Avoid touching the surface of the design as far as possible and use a new pair of gloves. Use scotch tape to remove any dust. The control layer pieces can be washed with ethanol if they are very dirty.  \\

\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Note}} &amp; PDMS stretches and compresses. You can use this to your advantage while aligning. Lift the PDMS from one end partially, while the rest is still stuck, and move the wafer slightly against it - so that it gets aligned - this can help getting elements on one part of the design aligned.\\
\end{tabular}
}\\[0.2in]


\fbox{
\\[0.2in]
\begin{tabular}[b]{cp{3in}}
{\ensuremath{\triangleright}{\sf Note}} &amp; The alignment and punching must be done as quickly as possible, the bond quality decreases with time - you have only about 30 minutes to 1 hour after you remove the thick layer from the oven.\\
\end{tabular}
}\\[0.2in]

\section{Building a Control System}
\begin{marginfigure}
\includegraphics[width=2in,height=2in]{./pic/controller.jpg}
\caption{Pneumatic Control Manifold}
\label{fig:control}
\end{marginfigure}

The valves and pumps on the chips are actuated with pneumatic solenoids connected to a pressure supply.  At least two pressures are needed - a low pressure for flow channels (1-3 psi) and  a higher one (10-25psi) for actuating valves.  We built our 24 valve controller based on a design from Raphael Gomez-Sjoberg. The printed circuit board for the controller was obtained from the Stanford Microfluidic foundry (for free!) and the matching for some of the fixtures was done at the Princeton Physics departmental workshop by Jason Puchalla. 

To make these you need a little familiarity with basic electronics.  You can find all the details on his website, with the latest designs for the controllers and the parts you will need:\\[0.1in]

\url{https://sites.google.com/a/lbl.gov/microfluidics-lab/valve-controllers}\\[0.1in]



The controller runs off a Labview program.  It looks complicated with all the wires and tubes! Don't panic!! all you need to know is that the program bootcamp\. vi operates the valves. You need to click on a button to actuate a valve and you can also create a pump with any three valves of your choice. A little red light indicates a valve is on.  



Test your valves and pumps by attaching the tubing and flowing in water or oil (dead-end filling). It is better to use liquids for control valve actuation because with air can diffuse through the membrane and enter the flow channels Using liquid in the flow lines can also help reduce problems with evaporation and maintaining salinity. Check if the valves work - it is possible to have collapses, de-laminations etc- and in that case you have to do triage to see what portions of the design are still usable.

\section{Simple Chip}
The simple chip design allows metered insertion of up to 6 different reagents (controlled by a combinatorial multiplexer) into a rotary mixer.  The reagents are flown in into the serpentine channel, Then this is isolated and the pump is used to push liquid (metering by using a known number of cycles) in the rotary mixer. Reagents can be mixed in the rotary mixer. This design gets you to test valves, pumps, mixers and multiplexers.

\section{MAPK yeast chip}
This chip is a modified version of that used by Taylor etc al in 2009\cite{taylormapk}. We won't try the full experiment - just a simple test of trapping single yeast cells and exposing them to reagents.The idea behind this design is to load yeast cell (from the 8 lines bottom of the design) and then trap them in a sieve valve. Reagents can then be flown in a controlled manner through the perpendicular channels and single yeast cells imaged responding to the chemicals. There is 32 line logarithmic multiplexer used to select the the channel. 

This is a sophisticated chip and is the cutting edge of what a single person could do in a lab - so don't be too disheartened if many things fail! 

\begin{figure*}
\includegraphics[width=3in,height=3in]{./pic/yeastMAPK.jpg}
\caption{Single cell imaging chip from Taylor et al}
\label{fig:yeastMAPK}
\end{figure*}

\subsection{Suggested Follow-up}
1) Melin J, Quake SR. "Microfluidic Large-Scale Integration: The Evolution of Design Rules for Biological Automation" Annu. Rev. Biophys. Biomol. Struct. 36:213-31\\

2) Dynamic analysis of MAPK signaling using a high-throughput microfluidic single-cell imaging platform. Taylor RJ, Falconnet D, NiemistÃ¶ A, Ramsey SA, Prinz S, Shmulevich I, Galitski T, Hansen CL. Proc Natl Acad Sci U S A. 2009 Mar 10;106(10):3758-63. Epub 2009 Feb 17.

\chapter{6: Silicon and Silicone}
This experiment, the last one in our course, is more in the nature of a demonstration than a full experiment.  Here we will understand how to use Silicon devices. The silicon devices has been etched and made ready for use. Because our lab has no silicon etching facilities we did the etching at the Micro Nano Fabrication laboratory (MNFL) at Princeton University which you will have a chance to visit. 

\section{Silicon Etching}
The etching is done using a plasma etcher.  The particular etcher used is the SAMCO-800 ICP-RIE (Inductively coupled Plasma Reactive Ion Etching). It uses fluorine gas chemistry to rapidly etch silicon structures.

\begin{marginfigure}
\includegraphics[width=2in,height=3in]{./pic/SAMCO-800.jpg}
\caption{Silicon etcher}
\label{fig:silicon}
\end{marginfigure}

The details of this machine are available here:\\[0.1in]
\url{http://www.princeton.edu/mnfl/the-tool-list/samco-rie800ipb/}\\[0.1in]
Briefly, the procedure involves coating a Silicon wafer with photo-resist, exposing the wafer (done on a MA6 mask aligner) and developing the design followed by silicon etching and removal of the any remaining resist.   

\begin{marginfigure}
\includegraphics[width=2in,height=3in]{./pic/MA6.jpg}
\caption{Karl Suess MA6 mask aligner}
\label{fig:MA6}
\end{marginfigure}

Silicon devices are different from PDMS in that they are more resistant to chemicals, allow for smaller size features and do not allow diffusion of gases through them.   However, they are harder to fabricate, generally more expensive to make and require access to a clean room and etching bays or tools, outside the range of an average biologists.  Nevertheless, for certain types of projects silicon is the only good option. Commercially, several foundries have decades of experience in silicon devices and processes, and will allow you to do process runs for large scale manufacturing.

\section{Making a manifold}
\begin{figure*}
\caption{Using a manifold}
\subfloat[Sandblasting Machine]{\label{fig:sandblast}\includegraphics[width=0.3\textwidth,height=2in]{./pic/sandblaster.jpg}}                
\subfloat[Protecting features with resist]{\label{fig:resistonchip}\includegraphics[width=0.3\textwidth,height=2in]{./pic/resistonchip.jpg}}
\label{fig:Jig}
\end{figure*}

To go with a silicon device we made a manifold out of acrylic and steel. This manifold was made at the Princeton Physics department workshop. The design is shown in the picture on the right. It consists of 6 ports to connect to the device. The silicon device itself had holes etched through it using a sand blasting machine. The procedure involves coving the sensitive portion of the design with thick photo-resist and baking on a hot plate. Then the wafer is taken to a sandblasting system which uses particles of alumina to drill through the ports. The resist is removed with iso-propanol and acetone, and the device is cleaned to dislodge any remaining particles. This process was also done for you by our  teaching assistants. 

\begin{marginfigure}
\includegraphics[width=2in,height=2in]{./pic/jig1.jpg}
\caption{Silicon chip inside jig}
\end{marginfigure}

The silicon chip is inserted into the jig and a thin film of PDMS is used to cover it. This PDMS cover is topped with a cover glass. The glass and PDMS provide a transparent barrier allowing the use of a microscope to take images of the channel.  O-rings are placed at the ports and the entire jig is tightened with screws.  Using luer stub fittings we can connect the chip to tubing of our choice.

\begin{figure*}
  \caption{Scanning electron microscope images of device}
  \subfloat[Silicon Chip - etched seives]{\label{fig:amy1}\includegraphics[width=0.3\textwidth,height=2in]{./pic/amy1.jpg}}                
  \subfloat[Silicon Chip - growth chamber]{\label{amy2}\includegraphics[width=0.3\textwidth,height=2in]{./pic/amy2.jpg}}
  \label{fig:amy}
\end{figure*}



\chapter{CAD self-guided tutorial}
This section teaches you how to make your own designs. We will get you to draw one of the designs we use in the class. This will be done in AutoCAD, but the procedure is similar for other types of CAD software, and you can quickly adapt to other software. 

%EPS figues are not compatible with pdflatex so I had to convert to PDF figure here
\begin{figure*}
\centering
\includegraphics[width=8in,angle=90]{./pic/two_layer_simple.pdf}
\caption{Two Layer PDMS chip design meant to fit a 3" wafer}
\label{fig:design}
\end{figure*}

\section{Design Dimensions}
The first thing to consider is the dimensions you need for your system.  Depending on the biology involved you may need the channels to be a certain height or width (for e.g. so that you cells won't get squished). {\it The CAD design only determines the width of a channel or feature}. The height will depend on the photo-lithography step of spinning the photoresist. However, the two are inter-related: if the aspect ratio (height to width ratio) of a channel in PDMS exceed 1:15, a sagging of of the PDMS can be expected to close off the channel.  In this case you may have to add pillars to support the channel.  Similarly, you must consider what kind of aspect ratios are achievable for silicon based devices and any other materials you will use to prevent structural failure.

The second thing to consider is the size of silicon wafer you will work with - the design must fit within the wafer with adequate margins. It is good practice to draw a margin and write in the mask the details of who made it, when it was made, type of design etc.  A few months later all designs start to look the same, and you will have a hard time knowing what changes were made or why a particular feature was added. Trust us on this!

\section{Procedure}
%Some of this material comes from my thesis 

Open AutoCAD (any version beyond AutoCAD 2000). The following rules must be followed:\\

1) Select microns as the unit with 0 precision {\tt Format&gt;Units}
 
2) Everything must be drawn using {\sc closed polylines}. A closed polyline can be drawn by using the polyline command and then drawing the last line by typing the command {\tt CLOSE} in the command line.  The conversion software needs close polylines because it has to recognize the inside and outside of a figure - and only closed figures have an inside and outside region. \\

3) Draw everything on a layer different from ZERO layer. Select a new layer and use it for drawing {\tt Format&gt;Layer}. Letâ€™s call the layer "FLOW". Choose a color for the layer. \\

4) Three functions may be useful for your drawing ORTHO, SNAP and GRID. Find out about them. A circle or a square or a polygon is a closed polyline in AutoCAD. Closed polylines can overlap - and there are various possibilities for conversion of overlapping figures. Most conversions program will do b and c as shown in Figure \ref{fig:overlap1} and Figure \ref{fig:overlap2}\\

\begin{marginfigure}
\includegraphics[width=2in, height =2in]{./pic/overlap2.jpg}
\caption{Complete encapsulation}
\label{fig:overlap1}
\end{marginfigure}

\begin{marginfigure}
\includegraphics[width=2in,height=2in]{./pic/overlap1.jpg}
\caption{Partial overlap}
\label{fig:overlap2}
\end{marginfigure}

5) It is good practice to draw a border around the diagram. Let us make a boundary of 24000 micron x 24000 micron (fitting an inch square). We use a double square because otherwise the conversion program may get confused (see 2) \\

6) Also, a good practice is to put identification marks and notes on the chip that tell who made it, when it was made etc as we mentioned earlier. This writing will also help identify which side was printed which can be hard to tell on a transparency\\

7) Note that because the lines are fairly thin we will need to put some ports at the end of the line where hollow metal pins can poke through the PDMS and connect put fluids into and out of the chip. That is the larger structure at the end of each line. We put in some triangular posts to prevent collapse.\\

8) We can also get started on the Control layer by opening a new layer as before (use a different color). Note how the valves are larger where they need to be activated. For the multiplexer note the cross-over channels used.  When making the control  layer you must consider the needs of alignment - make the figure as simple to align as possible. Put in many alignment marks - which can be crosses, or other kinds of figures.  The mask aligner allows rotation and x,y translations so your alignment mark must distinguish these movement (hence a circular alignment mark is a bad idea since you won't get rotational alignment\\

9) It is essential that the ports be separated and as far as possible from each other and other channels â€“ at least 2 mm away from all other channels (except the one it connects to of course!) and ports is a good rule of thumb. Since we need to poke pins into the ports and there is an element of error involved, this minimize the chance of the pin rupturing another channel or port and ruining your device. \\

\section {Preparing for Printing}
10)  Once the figure is done you need to prepare it for printing. This is done by creating a new file and separating out the layers. need to separate the control and flow layers, make allowances for polymer shrinkage and arrange them to be put on a wafer. We use 3â€ silicon wafer so 4 chips of the type drawn can fit in.   So we put them on separate files. Here we will plan to make the flow layer to be the thin layer. This is called the top down geometry, because the valve functions by a thin membrane moving downwards. The other geometry is the bottom up geometry with the control channel below the flow channels. \\

\begin{figure*}
\centering
\includegraphics[width=6in]{./pic/thick_thin.png}
\caption{Two Layer PDMS chip top-down}
\label{fig:thick_thin}
\end{figure*}

11) The thick layer (control) must be EXPANDED by ~1.6\% to compensate for the shrinkage in the fabrication. Expand the control layer using the SCALE command, selecting the entire chip and expanding by 1.016 from the center.\\

12) Save the files in AutoCAD 2000 .dwg or .dxf format and now you can send these off for printing.

\subsection{Positive and Negative, Emulsion side up or down}
You will also have to decide whether you design is to be printed negative or positive. If printed positive it will be used with positive photo-resists, and if negative it will use a negative photo-resist. (Negative means that the channels you made will be transparent and the rest will be dark like a negative of a photograph).  In our case the flow layer must be printed positive - since only positive DNQ-Novalac resists can be thermally re-flowed to create rounded channels. Emulsion type up makes any writing readable when the printed layer faces you. Emulsion type down is the opposite - now the writing appears in mirror reversal. You can use either - but make sure you know which is which, as it will help when you attach the transparency to the glass plate in photo-lithography. 

\chapter{Suggested References}
The biggest lament we hear from students is that the mathematical sophistication needed to read books on fluid mechanics and microfluidics can be scary. Yet, somehow this message has not reached the writers - unfortunately,  almost all of them assume some familiarity with vector calculus. I wish someone would write a sophisticated {\it and} non-mathematical book. For the time being, anyways, the resources I would recommend are:\\[0.1in]
 
1) Introduction to microfluidics, Patrick Tabeling ; translated by Suelin C, 2005, Oxford University Press \\[0.1in]
While the field is rapidly evolving, and will likely make this book obsolete in a few years, currently I believe it constitutes a balanced introduction. Chapters can be read independently of each other.  The book does require a moderate amount of mathematical sophistication.\\[0.1in]

2) Shape and Flow: The Fluid Dynamics of Drag, Ascher H Shapiro, 1964 Heinemann\\[0.1in]
This now out-of-print book is the best non-mathematical introduction to the basics of fluid mechanics.\\[0.1in]

3) National Committee for fluid mechanics Films \url{http://web.mit.edu/hml/ncfmf.html}\\[0.1in]
A set of freely available videos that are simply brilliant. They have aged very well even though it's now over 50 years since they were made. Just don't treat mercury in the same way they handle it! We know better now.\\[0.1in]

4) Feynman Lectures on Physics , Volume 2, Chapters 40 and 41 ``The Flow of Dry water'' and ``The Flow of Wet Water", Feymann, Leighton, Sands,  Addison Wesley \\[0.1in]
If you can tolerate a little mathematics, see a master in action. These lectures were meant for freshman undergraduates in Physics.\\[0.1in]

5) Random Walks in Biology, Howard C Berg, Princeton University Press(1993) \\[0.1in]
Howard Berg is most famous for work on the motility of bacteria. In this slim book (the kind of book I like), he tackles diffusion and related phenomena.  The book has mathematics, but it does not feel like he bludgeons you with it.\\[0.1in]

6) The science of soap films and soap bubbles, Cyril Isenberg, Dover Publications (1992)\\[0.1in]
A good introduction to surface tension and associated phenomena, with plenty of pretty pictures\\[0.1in]

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