Chem E 486 Designing Educational Lab-on-a-Chip Modules
Microfluidics and Lab-on-a-Chip Modules Societal and economic trends likely to affect your career. What is a Lab-on-a-Chip? -Examples of the technology -Rationale for using it -What is the role for Chem Es Societal and economic trends NY Times, March 4, 2004 Thomas Friedman BANGALORE, India
Jerry Rao wants to do your taxes. Ah, you say, you've never heard of Jerry Rao, but the name sounds vaguely Indian. Anyway, you already have an accountant. Well, Jerry is Indian. He lives in Bangalore. And, you may not know it, but he may already be your accountant. Societal and economic trends Societal and economic trends Societal and economic trends - Questions to think about
What advantages/disadvantages do U.S. educated have vis-a-vis various internationally-educated Chem Es? What aspects of Chem E are easiest to outsource? Which are the hardest? What Chem E employment sectors are likely to stay in USA? What are their distinguishing traits? What is a Lab-on-a-Chip? Images from http://www.istat.com/products/ Why Lab-on-a-Chip instead of regular analysis?
Data from http://www.istat.com/products/docs/151420.pdf Another Lab-on-a-Chip example http://www.micronics.net/technologies/h-filter.swf Images from http://www.micronics.net/products/ Another Lab-on-a-Chip Sip reagents into storage wells
Images from http://www.calipertech.com/pdf/DNA_Assay.pdf/ Another Lab-on-a-Chip ATP-dependent kinetics at 37 C Mix and react sample with reagent Images from http://www.calipertech.com/pdf/DNA_Assay.pdf/ Another Lab-on-a-Chip
Electrophoretic separation Flow products to separation column Time (s) Run electrophoretic separation Images from http://www.calipertech.com/pdf/DNA_Assay.pdf/
Do you have what it takes to design a Lab-on-a-Chip? Key Elements (all done at the micro-scale): Flow of fluids in channels Automated control of thermal and fluid stystems Chemical Reactions Mass Transfer/Separations As Chem Es you have the technical foundation needed, but now need to learn SPECIFIC information, FAST! Specific information will come from Taking a short-course
Talking to experts Working on prototype problems (Tuesday, Wednesday) Doing simulation-based research (Tuesday, Wednesday Life-long learning---do it or stagnate as a professional. Physics of Microfluidics (a.k.a. Flows for L < 1 mm) Some important length-scales for the physics of fluids L
Characteristic geometry for the flow domain L < 103 m L in microfluidics Mean free distance molecules travel prior to molecule-molecule collisions = kT/(2PP2) for ideal gases; = 6.5 x 108 m for air at STP ~ O()
for liquids where k is Boltzmanns constant, T is absolute temp, P is pressure, and the symbol ~O(x) can be though to mean has an order of magnitude of x Molecular diameter ~ O(5x1010 m) Physics of Microfluidics Flow traits are dictated by comparison of and to L An important ratio is Kn = /L, the Knudsen Number When L > , one often uses molecular dynamics approaches
Physics of Microfluidics Length-scale ratios dictate approach for understanding flow An important ratio is Kn = /L, the Knudsen Number Relevant Region Continuum flow region is traditional Chem E fluid mechanics Physics of Microfluidics How does a small L influence things in the continuum flow region? Physics of Microfluidics
How does a small L influence things in the continuum flow region? Viscous Forces tend to dominate Inertial Forces Re = VL/ Reynolds Number where V is characteristic fluid velocity, and is kinematic viscosity Examples Ant Brain vs. Human Brain Streamlines at a T-junction (w/ and w/o inertia) Physics of Microfluidics How else does a small L influence things?
Viscous Forces tend to dominate Body Forces (e.g. due to gravity) Gr = gL3/() <<1 Grashof Number where g=10 m/s2, is density difference, and is mean density Temperature and concentration gradients dont tend to produce strong natural convection in microscopic systems Physics of Microfluidics In short, the flows you will be working with here obey the same basic physics taught in Chem E fluids, so
Look at dimensionless groups from your Fluids course to see how L changes their magnitude Usually means viscous drag is a major factor in microfluidics But, some additional continuum forces that were ignored by the macro-focus of Traditional Fluids also need to be considered. Physics of Microfluidics Surface Forces are important in microsystems (Surface-to-Volume ratio is proportional to L1) Surface Forces can rival Viscous Forces Viscous Capillary
= V/ Capillary Number (Ca) where is surface tension (dyne/cm), is viscosity (g/cm-s) Another way to think about the Capillary number Ca = (Characteristic Viscous P)/(Capillary pressure difference) L
PL PG PG PL = 2 cos/L Physics of Microfluidics Surface Forces are important in microsystems Typical values for Surface Tension (dyne/cm or mN/m) near 25 C Liquid-Vapor Systems Water
Physics of Microfluidics Physics of Microfluidics Physics of Microfluidics Other Surface-related dimensionless groups Bond Number (Bo) Gravitational Forces/Surface Forces Bo = gL2/ Rise of a liquid in a capillary is evidence that surface forces are big
compared to gravity as dimensions shrink. Physics of Microfluidics Other Surface-related dimensionless groups Bond Number (Bo) Gravitational Forces/Surface Forces Bo = gL2/ Rise of a liquid in a capillary is evidence that surface forces are big compared to gravity as dimensions shrink.
Physics of Microfluidics An additional surface driven flow in microfluidic devices is called electroosmosis. Electroosmosis is actually a flow driven by a body force that is important only very near charged surfaces (usually within nanometers of a surface). solution with cations and anions neutral net + + - + - + - + - + - + - + - + + - + - + - + - + - + - + - + -
- - - - - - - - - - - - - - - - - - negatively charged surface Physics of Microfluidics Veo = DE/4P for a capillary is the zeta potential (a measure of surface charge), D is the dielectric constant of the medium, E is the applied electric field Veo + +
+ + + + ++ + ++ + + ++ - - - - - - - - - - - - - - - - - - negatively charged surface - Physics of Microfluidics So, how do we incorporate these various physics into models? We need governing equations and boundary conditions. For a Newtonian, incompressible fluid start with Navier-Stokes Equations: v 1 + v v = P + FB + 2 v
t v = 0 What forces are represented by these vector equations? Physics of Microfluidics Nondimensionalize the Navier-Stokes Equations using V L/V L
V/L as characteristic Velocity as characteristic Time (alternative, L2/) as characteristic Length as characteristic Pressure v Re + v v = P + 2 v t v = 0
where Re = VL/ If Re > 0, then forces on left hand side become less important Physics of Microfluidics The remaining forces show up in the Boundary Conditions applied at surfaces between two phases: Some conventional boundary conditions: No slip at solids No penetration of fluids at impermeable boundaries No gradients at symmetry lines
vt = 0 vn = 0 nv = 0 For gas-liquid and immiscible liquid-liquid interfaces well need to talk, but the basic idea is generally: Normal interfacial stress balance: P2 P1 = 2H where H is the interface mean curvature Tangential interfacial stress balance:
1 v t v = 2 t n 1 n Electroosmosis can look like a slip velocity at the charged surface: vt = Veo 2
Physics of Microfluidics Highlighted some similarities and differences from traditional Fluids Reduced importance of inertia simplifies Navier-Stokes Equations Discussed role of surfaces and dimensionless numbers that describe surfaces forces Introduces some strategies where surface forces enter models Accurately modelling free surface flows at finite Ca is an area of active research. Electroosmosis was introduced as a body force that happens very near surfaces, so it can look like an interfacial slip velocity.
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