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1 - History and prospectives of microfluidics

2 - Microsystems and macroscopic approach.

3 - The spectacular changes of the balances of forces as

we go to the small world.

Outline of Lecture 2

- The fluid mechanics of microfluidics

- Digital microfluidics

microfluidics

Reynolds numbers are small in microsystems

Re = Ul/n ~ l2

One thus may think in the framework of Stokes equations

Stokes regime : inertial terms are neglected

Acceptable approximation in most case. Exceptions are

Micro-heat pipes and drop dispensers

Darcy law governs Hele Shaw cells

In a Hele Shaw cell, flows are potential

An important notion : the hydrodynamic resistance

Increases as the system size decreases

Analogy with electrokinetics

Another important notion : the hydrodynamic capacity

Deformable tube :

dP=k-1 dV/V

Example :

Volume V

Pressure P

Now Qm=rdV/dt

Thus Qm=mkdP/dt and hence C=km

Question : Show that the time to reach a steady state is given by

The expression

Response : C=m/E=πD2Lr/4E et R=12nl/b3w

with t=RC

Experiment in a microchannel, 1.4 mm deep

Expérience effectuée au MMN (2001)- Matthieu Cécillon

Because to reach a steady state, it takes a time t equal to

t ≈ RC then t ≈ kmR

One must avoid dead volumes, bubbles, etc..

A PDMS actuator, based on Multi-layer Soft Lithography

Actuation channel

Glass slide

Working channel

PDMS

A. Unger, H-P. Chou, T. Thorsen, A . Scherer et S. R. Quake, Science, 288, 113, (2000).

R

R

From the electrical point of view, pneumatic actuators are

represented by a capacitance/non linear resistance system .

They are not just diodes

Non linear

resistances

R=f(VC)

J.Goulpeau, A. Ajdari

P. Tabeling,J. Appl.Phys.

May 2005

No actuation : Large localized gradient

Actuation : Producing different

Concentration gradients

by changing the actuaction

parameters

Mechanical actuators dedicated to the generation of concentration gradients

Passive concentration

gradient generator (1)

The same, using mechanical

actuators

(1)Jeon et al, Nature Techn., 20, 826 (2002))

ELECTRICAL REPRESENTATIONS OF ELEMENTARY ACTIVE SYSTEMS

Mixer - Extractor

Microdoser

Mixer

Gradient concentration generator

Microdoser

Integrated actuators can be used to make progress in the realization of complex systems : an example is a chip for proteomics

for liquids

to know in microfluidics

Capillary phenomena are important in microsystems

Pressure drops

caused by capillarity

are ~ l-1 while

those due to

viscosity behave

like l0

THE PATTERNS WHICH DEVELOP IN “ORDINARY” TWO PHASE FLOWS

…OFTEN PRODUCE COMPLEX MORPHOLOGIES; THIS IS DUE

TO HYDRODYNAMIC TURBULENCE

IN MICROFLUIDIC SYSTEMS, WE OBTAIN MUCH SIMPLER

MORPHOLOGIES : ESSENTIALLY DROPLETS

Laure MENETRIER, 2004

When S is non homogeneous, droplets spontaneously

move on the surfaces

qA<qB

Good wetting (S ≈ 0)

Poor wetting (S <0)

Wetting properties of the walls are

important in microfluidic multiphase flows

Oil with or without surfactant (Span 80)

Water

Water

R Dreyfus, P.Tabeling, H Willaime, Phys Rev Lett, 90, 144505 (2003))

When oil fully wets the surface

Oil flow rate

(L/min)

Isolated water drops

Stratified regime

Pear necklace

Large-pearl necklace

Pears

Coalescence

Pearl necklace

Water flow rate (L/min)

WHEN THE FLUIDS PARTIALLY WET THE WALLS

Oil flow-rate (mL/mn)

Water flow-rate (mL/mn)

(R Dreyfus, P.Tabeling, H Willaime, Phys Rev Lett (2003))

Rayleigh instability is the most

important instability to be aware of

Surface energy of a column

d

Surface energy of N spherical droplets

l

UNSTABLE

Applications :Digital microfluidics

- Liquid liquid flows are used in microsystems, in several circumstances.

Producing drops of one liquid into another liquid

so as to generate emulsions, or perform screening

Producing bubbles in a microchannel flow so as

to increase heat exchange, or simply because the

liquid boils.

1 - In air

2 - In a liquid

The drop moves in air over a flat surface

The drop moves in a liquid

in a microchannel

Digital microfluidics is interesting for chemical

analysis, protein cristallization, elaborating novel emulsions,…

Ismagilov et al

(Chicago University)

AN EXAMPLE OF AN INTERESTING PROBLEM : REDUCING THE DROP SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

10mm

Suppose we are willing to reduce the drop size of an emulsion

DIFFERENT REGIMES, FOR INCREASING SIDE FLOWS

WHITE = WATER DROP, BLACK (IN THE CHANNEL) = HEXADECANE

Curve

suggested by

the theory

(Navot, 1999)

BREAKING

VS

(mm/s)

NON

BREAKING

0 1 2 3 4 5 x102

Lf (mm)

Laure MENETRIER, 2004

is smaller

qA<qB

Électrode

+V

qB=qA +1/2CV2

AN IMPORTANT PART OF DIGITAL MICROFLUIDICS

IS BASED ON ELECTROWETTING

A microfluidic network along which drops are driven

C.J.Kim (2001)

Liquid-liquid flows in microsystems may be used to produce

well controlled drops, emulsions,…

… provided the wetting properties of the exposed surfaces,

with respect to the working fluids, are appropriately chosen.

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