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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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slide1

AN INTRODUCTION TO

MICROFLUIDICS :

Lecture n°2

Patrick TABELING, [email protected]

ESPCI, MMN, 75231 Paris

0140795153

slide2

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

slide3

Fluid mechanics of

microfluidics

slide5

Reynolds numbers are small in microsystems

Re = Ul/n ~ l2

One thus may think in the framework of Stokes equations

slide6

Microhydrodynamics

Stokes regime : inertial terms are neglected

Acceptable approximation in most case. Exceptions are

Micro-heat pipes and drop dispensers

slide8

Let us reverse U

-U

If it is a Stokes solution, arrows must be inverted

everywhere

slide10

Because if we reverse U

-U

We obtain a non plausible streamline pattern

slide12

Experiment

Performed by

O Stern (2001)

slide15

Darcy law governs Hele Shaw cells

In a Hele Shaw cell, flows are potential

slide16

An important notion : the hydrodynamic resistance

Increases as the system size decreases

Analogy with electrokinetics

slide18

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

slide19

U

uc(t)

up(x,t)

The bottleneck effect

slide20

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

slide21

Experiment in a microchannel, 1.4 mm deep

Expérience effectuée au MMN (2001)- Matthieu Cécillon

slide22

Beware of dead volumes

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

Actuation channel

Glass slide

Working channel

PDMS

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

slide24

VC

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

slide25

No actuation : Large localized gradient

Actuation : Producing different

Concentration gradients

by changing the actuaction

parameters

slide26

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))

slide27

ELECTRICAL REPRESENTATIONS OF ELEMENTARY ACTIVE SYSTEMS

Mixer - Extractor

Microdoser

Mixer

Gradient concentration generator

Microdoser

slide28

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

slide30

The slip length

z

u

Navier Boundary Conditions

Slip length (or extrapolation length)

slide31

Pressure drop with a slip length

DP

Flow rate Q

Depth b

Slip length LS

slide33

Two or three things important

to know in microfluidics

slide34

Laplace’s law

S

R

V

At mechanical equilibrium : dE=0

Bubble

slide35

Capillary phenomena are important in microsystems

Pressure drops

caused by capillarity

are ~ l-1 while

those due to

viscosity behave

like l0

slide36

THE PATTERNS WHICH DEVELOP IN “ORDINARY” TWO PHASE FLOWS

…OFTEN PRODUCE COMPLEX MORPHOLOGIES; THIS IS DUE

TO HYDRODYNAMIC TURBULENCE

slide37

IN MICROFLUIDIC SYSTEMS, WE OBTAIN MUCH SIMPLER

MORPHOLOGIES : ESSENTIALLY DROPLETS

Laure MENETRIER, 2004

slide39

Wetting are exceedingly important in microsytems

3 cases

Complete wetting

Partial wetting

Desorption

slide40

Spreading parameter

S>0 complete wetting

S<0 partial wetting or desorption

slide41

When S is non homogeneous, droplets spontaneously

move on the surfaces

qA<qB

Good wetting (S ≈ 0)

Poor wetting (S <0)

slide43

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))

slide44

NICE DROPS CAN BE PRODUCED

IN MINIATURIZED SYSTEMS IN COMPLETE WETTING CONDITIONS

200mm

slide45

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)

slide46

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))

slide47

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

slide48

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.

slide49

Digital microfluidics

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

slide50

Digital microfluidics is interesting for chemical

analysis, protein cristallization, elaborating novel emulsions,…

Ismagilov et al

(Chicago University)

slide51

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

slide52

One possibility is to cut the drops one by one

in a microfluidic system

Water drop

10mm

U

L0

u

slide53

DIFFERENT REGIMES, FOR INCREASING SIDE FLOWS

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

slide56

To break or not to break

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

slide57

Side where the contact angle

is smaller

qA<qB

Électrode

+V

qB=qA +1/2CV2

AN IMPORTANT PART OF DIGITAL MICROFLUIDICS

IS BASED ON ELECTROWETTING

slide61

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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