Microfluidics and “Lab-on-a-Chip” Modules Societal and economic trends likely to affect your...

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 E’s

NY Times, March 4, 2004Thomas FriedmanBANGALORE, 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

Images from http://www.micronics.net/products/

http://www.micronics.net/technologies/h-filter.swf

Another “Lab-on-a-Chip”

Images from http://www.calipertech.com/pdf/DNA_Assay.pdf/

Sip reagents into storage wells



Mix and react sample with reagent

ATP-dependent kinetics at 37 ˚C



Flow products to separation column

Run electrophoretic separation

Electrophoretic separation

Time (s)

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 E’s 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 < 10–3 m in microfluidics

Mean free distance molecules travel prior to molecule-molecule collisions

= kT/(√2πP2) for ideal gases; = 6.5 x 10–8 m for air at STP ~ O() for liquids

where k is Boltzmann’s 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(5x10–10 m)

L

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


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


How does a small L influence things in the continuum flow region?


How does a small L influence things in the continuum flow region?

•Viscous Forces tend to dominate Inertial Forces

Re = VL/ Reynolds Numberwhere 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)


How else does a small L influence things?

•Viscous Forces tend to dominate Body Forces (e.g. due to gravity)

Gr = gL3∆/() <<1 Grashof Numberwhere g=10 m/s2, ∆ is density difference, and is mean density

Temperature and concentration gradients don’t tend to produce strong natural convectionin microscopic systems


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.


Surface Forces are important in microsystems(Surface-to-Volume ratio is proportional to L–1)

•Surface Forces can rival Viscous Forces

ViscousCapillary

•Another way to think about the Capillary number

Ca = (Characteristic Viscous ∆P)/(Capillary pressure difference)

= µV/ Capillary Number (Ca)where is surface tension (dyne/cm), µ is viscosity (g/cm-s)

PG – PL = 2 cos/L PL PGL


Surface Forces are important in microsystems

Typical values for Surface Tension (dyne/cm or mN/m) near 25 ˚C

Liquid-Vapor Systems

Water 72Propylene carbonate 41Ethanol 22Perfluorpentane 10Hg 486

Liquid-Liquid Systems

Water/n-Butyl Alcohol 2Water/Benzaldehyde 16Water/Benzene 35Water/n-Heptane 50Water/Flourcarbon polymer 57


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 bigcompared to gravity as dimensions shrink.


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).

- - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + +

+ + + + + + + + + +

+ - - + - + -+ +- + + - - + - + - +

+ - + - + - + - + - + - + - + -+ - + - + - + - + - + - + - + -

neutral

net +

negatively charged surface

solution with cations and anions


- - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + +

+ + + + + + + + + +

+ - - + - + -+ +- + + - - + - + - +

+ - + - + - + - + - + - + - + -+ - + - + - + - + - + - + - + -

negatively charged surface

+ -

Veo

Veo = DE/4πµ 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


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

∂t+ v ⋅∇v = –

1

ρ∇P + FB + ν∇ 2v

∇ ⋅v = 0

What forces are represented by these vector equations?


Nondimensionalize the Navier-Stokes Equations using

V as characteristic VelocityL/V as characteristic Time (alternative, L2/)L as characteristic LengthV/L as characteristic Pressure

where Re = VL/

€

Re∂v

∂t+ v ⋅∇v

⎛

⎝ ⎜

⎞

⎠ ⎟ = –∇P + ∇ 2v

∇ ⋅v = 0

If Re –> 0, then forces on left hand side become less important


The remaining forces show up in the Boundary Conditions applied at surfaces between two phases:

Some conventional boundary conditions:

No slip at solids vt = 0No penetration of fluids at impermeable boundaries vn = 0No gradients at symmetry lines n•∆v = 0

For gas-liquid and immiscible liquid-liquid interfaces we’ll 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:

Electroosmosis can look like a “slip” velocity at the charged surface: vt = Veo

€

1

∂vt

∂n 1

= μ2

∂vt

∂n 2


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, soit can look like an interfacial slip velocity.

Microfluidics and “Lab-on-a-Chip” Modules Societal and economic trends likely to affect your...

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