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AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3. 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°3

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


Outline of Lecture 3

1 - Basic notions on diffusive processes

2 - Micromixing

3 - Microreactors.


Diffusion time for a 100 mm wide channel

(for a molecule such as fluorescein) :

This time may be too long, especially if one develops several chemical reactions on the same chip


Equation de diffusion advection

  • Dans le cas incompressible, l ’équation de diffusion advection est :

Ordre de grandeur :

Pe ~ 105 pour un colorant dans l ’eau agitée à des vitesses de 1cm/s

Un nombre sans dimension analogue

au nombre de Reynolds est :


Quelques propriétés de l’équation de diffusion-advection

La variance de la concentation décroit avec le temps

- si les CL sont périodiques ou si l’écoulement est

confiné dans un volume avec parois rigides imperméables.


TROP VITE DIT diffusion-advection

Le nombre de Peclet n’est pas nécessairement petit

dans les systèmes miniaturisés

….donc petit


Un problème fondamental : la diffusion d ’une petite tache dans un fluide au repos

C

C

t=0

t

x

x

Écart type s=(2Dt)1/2


Dispersion dans un écoulement uniforme tache dans un fluide au repos

  • A t =0, on impose C=C0 en x=0 sur une couche d ’épaisseur d

U

x

x=0

Avec s2=2Dt


Dispersion de TAYLOR-ARIS tache dans un fluide au repos

d

d doit etre très fin


Origine microscopique de la diffusion moléculaire tache dans un fluide au repos

  • On introduit un « marcheur » effectuant des sauts de longueur li le long d ’une ligne : (mouvement brownien)

li

On démontre :

La poxition du marcheur est :

Mouvement diffusif et front gaussien


Mixing in microsystems tache dans un fluide au repos

- Mixing is difficult in microsystems


There has been some clever and less clever ideas tache dans un fluide au repos

FLOW

Poor transverse mixing for microfluidic systems


HYDRODYNAMIC FOCUSING ALLOWS tache dans un fluide au repos

On the order of

30 nm in the

extreme cases

TO MIX IN TENS OF MICROSECONDS

Austin et al, PRL (2002)


Circular tache dans un fluide au repos

micromixer

Quake, Scherer (2001)


Transformation du boulanger tache dans un fluide au repos


In chaotic regimes, two close particles separate exponentially

In confined systems, this property is extremely favorable to mixing,



The first chaotic micromixer was designed at Berkeley (1997) exponentially

Thermal

actuator

Micromixer

J. Evans, D. Liepmann, D., and A.P. Pisano, 1997, “Planar Laminar Mixer,” Proceeding of the IEEE 10th Annual Workshop of Micro Electro Mechanical Systems (MEMS ’97), Nagoya, Japan, Jan, pp.96-101.


Time periodic transverse flow exponentially

Main Flow

Cross-channel micro-mixer(UCLA,1999)

Fluid A

V

time

-V

Fluid

B

400 mm

investigated by Y.K. Lee, C.M.Ho (1999), Mezic et al (1999)


How it works (from a kinematical viewpoint) exponentially

U

U

Perturbation

is applied

Line is stretched

U

Perturbation

is stopped

Line is folded


actuation channel exponentially

Glass slide

Working channel

EXPERIMENT

Micro-valve

25mm

200mm

Microvalve

1mm


200 exponentiallymm

A.Dodge, P. Tabeling, A. Hountoundji, M.C.Jullien (2004)


Under resonance conditions, the interface is stretched exponentially

in the active zone, and returns flat afterwards

A.Dodge, P. Tabeling, A. Hountoundji, M.C.Jullien (2004)


DETERMINING A PHASE DIAGRAM, USING THE VARIANCE exponentially

OF THE PDF OF THE CONCENTRATION FIELD

- Well mixed : the variance is small

- Unmixed : the variance is large


EXPERIMENTAL PHASE DIAGRAM, REPRESENTING ISOLINES OF exponentiallys2

Actuation

pressure

(bar)

Frequency (Hz)


An efficient exponentially

particle sorter, using resonance

RESONANCES

MAY BE USED TO SORT

PARTICLES :

BY CHANGING THE FREQUENCY OF THE PERTURBATION, ONE

OBTAINS A SYSTEM WHICH MIXES FLUIDS, FILTERS PARTICLES,

OR SIMPLY TRANSPORTS MATERIALS SIDE BY SIDE.



CHEMICAL exponentiallyMICROREACTORS


EXPERIMENTAL STUDY OF A CHEMICAL REACTION exponentially

A+B C IN A T MICROREACTOR

B

A

Channels 10mm deep,

500mm wide, various flow-rates

System made in glass, covered

by a silicon wafer, or in PDMS


One may also measure the kinetics without mixing thoroughly exponentially

A

y

The T reactor

x

U

Diffusion-reaction zone where

the product C is formed

B


EXPERIMENT exponentially

Reaction : Ca-CaGreen

C.Baroud, F Okkels, P Tabeling, L Menetrier, Phys. RevE67, 60104 (2003) 


Fluorescence intensity fields obtained for the reaction exponentially

CaGr+Ca2+ (CaGr,Ca2+)

Ca

U

U

CaGreen

C.Baroud, F Okkels, P Tabeling, L Menetrier, Phys. RevE67, 60104 (2003) 


t exponentially = (k A01/2 B01/2 )-1

Boundary conditions :

Characteristic time

of the reaction

x=0, A = A0 for y< 0

B =B0 for y> 0

Theory of the T-reactor for a second order reaction

The product C is governed by the following equation :


C exponentially

Agreement between theory and experiment

is good

width

Location

of the max

Conc.

y

Location

of the max.

x

Typical structure of

a concentration

profile of the product

across the channel

Width

x

Maximum

Conc.

THEORY

with one fitting parameter

k = 105 lM-1 s-1 (t = 1 ms)

x

C.Baroud et al, Phys. RevE (2003)


EXPERIMENT IS WELL INTERPRETED BY THE THEORY exponentially

mm

mm

THEORY

THEORY

y (mm)

y (mm)

X

Fitting the experiment with one free parameter

k = 105 LM-1 s-1 (t = 1 ms)

y

C.Baroud et al Phys. RevE67, 60104 (2003) 


Digital microfluidics is interesting for chemical exponentially

analysis, protein cristallization, elaborating novel emulsions,…

Ismagilov et al

(Chicago University)


(Source : C. Delattre, MIT, MTL) exponentially

Can we produce much using microreactors ?

Can we move a mountain with a spoon ?


The end exponentially


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