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AN INTRODUCTION TO MICROFLUIDICS : Lecture n°2. Patrick TABELING, [email protected] ESPCI, MMN, 75231 Paris 0140795153. Outline of Lecture 1. 1 - History and prospectives of microfluidics 2 - Microsystems and macroscopic approach.

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AN INTRODUCTION TO

MICROFLUIDICS :

Lecture n°2

Patrick TABELING, [email protected]

ESPCI, MMN, 75231 Paris

0140795153


Outline of Lecture 1

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


Fluid mechanics of

microfluidics



Reynolds numbers are small in microsystems

Re = Ul/n ~ l2

One thus may think in the framework of Stokes equations


Microhydrodynamics

Stokes regime : inertial terms are neglected

Acceptable approximation in most case. Exceptions are

Micro-heat pipes and drop dispensers



Let us reverse U Reynolds

-U

If it is a Stokes solution, arrows must be inverted

everywhere



Because if we reverse U Reynolds

-U

We obtain a non plausible streamline pattern


Experiment Reynolds

Performed by

O Stern (2001)



Hele Shaw flows Reynolds


Darcy law governs Hele Shaw cells Reynolds

In a Hele Shaw cell, flows are potential


An important notion : the hydrodynamic resistance Reynolds

Increases as the system size decreases

Analogy with electrokinetics



Another important notion : the hydrodynamic capacity Reynolds

Deformable tube :

dP=k-1 dV/V

Example :

Volume V

Pressure P

Now Qm=rdV/dt

Thus Qm=mkdP/dt and hence C=km


U Reynolds

uc(t)

up(x,t)

The bottleneck effect


Question Reynolds: 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 Reynoldsmm deep

Expérience effectuée au MMN (2001)- Matthieu Cécillon


Beware of dead volumes Reynolds

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
A PDMS actuator, based on Multi-layer Soft Lithography Reynolds

Actuation channel

Glass slide

Working channel

PDMS

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


V ReynoldsC

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 Reynolds

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 concentration gradients

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


The boundary conditions realization of complex systems : an example is a chip for proteomics

for liquids


The slip length realization of complex systems : an example is a chip for proteomics

z

u

Navier Boundary Conditions

Slip length (or extrapolation length)


Pressure drop with a slip length realization of complex systems : an example is a chip for proteomics

DP

Flow rate Q

Depth b

Slip length LS


Microfluidics and capillarity realization of complex systems : an example is a chip for proteomics


Two or three things important realization of complex systems : an example is a chip for proteomics

to know in microfluidics


Laplace’s law realization of complex systems : an example is a chip for proteomics

S

R

V

At mechanical equilibrium : dE=0

Bubble


Capillary phenomena are important in microsystems realization of complex systems : an example is a chip for proteomics

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 realization of complex systems : an example is a chip for proteomics

…OFTEN PRODUCE COMPLEX MORPHOLOGIES; THIS IS DUE

TO HYDRODYNAMIC TURBULENCE


IN MICROFLUIDIC SYSTEMS, WE OBTAIN MUCH SIMPLER realization of complex systems : an example is a chip for proteomics

MORPHOLOGIES : ESSENTIALLY DROPLETS

Laure MENETRIER, 2004



Wetting are exceedingly important in microsytems geometry

3 cases

Complete wetting

Partial wetting

Desorption


Spreading parameter geometry

S>0 complete wetting

S<0 partial wetting or desorption


When S is non homogeneous, droplets spontaneously geometry

move on the surfaces

qA<qB

Good wetting (S ≈ 0)

Poor wetting (S <0)



Wetting properties of the walls are geometry

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))


NICE DROPS CAN BE PRODUCED geometry

IN MINIATURIZED SYSTEMS IN COMPLETE WETTING CONDITIONS

200mm


When oil fully wets the surface geometry

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 geometry

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 geometry

important instability to be aware of

Surface energy of a column

d

Surface energy of N spherical droplets

l

UNSTABLE


Applications :Digital microfluidics geometry

- 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.


Digital microfluidics geometry

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 geometry

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


One possibility is to cut the drops one by one SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

in a microfluidic system

Water drop

10mm

U

L0

u


DIFFERENT REGIMES, FOR INCREASING SIDE FLOWS SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

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


We would like also to control the drop break-up SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

Lf

VS

Finger


To break or not to break SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

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


Side where the contact angle SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

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 SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

C.J.Kim (2001)


Digital microfluidic devices based on electrowetting SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY


Liquid-liquid flows in microsystems may be used to produce SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

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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