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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

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An introduction to microfluidics lecture n 3

AN INTRODUCTION TO

MICROFLUIDICS :

Lecture n°3

Patrick TABELING, [email protected]

ESPCI, MMN, 75231 Paris

0140795153


An introduction to microfluidics lecture n 3

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


An introduction to microfluidics lecture n 3

Outline of Lecture 3

1 - Basic notions on diffusive processes

2 - Micromixing

3 - Microreactors.


An introduction to microfluidics lecture n 3

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


An introduction to microfluidics lecture n 3

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 :


An introduction to microfluidics lecture n 3

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.


An introduction to microfluidics lecture n 3

TROP VITE DIT

Le nombre de Peclet n’est pas nécessairement petit

dans les systèmes miniaturisés

….donc petit


An introduction to microfluidics lecture n 3

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


An introduction to microfluidics lecture n 3

Dispersion dans un écoulement uniforme

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

U

x

x=0

Avec s2=2Dt


An introduction to microfluidics lecture n 3

Dispersion de TAYLOR-ARIS

d

d doit etre très fin


An introduction to microfluidics lecture n 3

Origine microscopique de la diffusion moléculaire

  • 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


An introduction to microfluidics lecture n 3

Mixing in microsystems

- Mixing is difficult in microsystems


An introduction to microfluidics lecture n 3

There has been some clever and less clever ideas

FLOW

Poor transverse mixing for microfluidic systems


An introduction to microfluidics lecture n 3

HYDRODYNAMIC FOCUSING ALLOWS

On the order of

30 nm in the

extreme cases

TO MIX IN TENS OF MICROSECONDS

Austin et al, PRL (2002)


An introduction to microfluidics lecture n 3

Circular

micromixer

Quake, Scherer (2001)


An introduction to microfluidics lecture n 3

Transformation du boulanger


An introduction to microfluidics lecture n 3

In chaotic regimes, two close particles separate exponentially

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


An introduction to microfluidics lecture n 3

From Ottino’s book : « Chaotic Advection »


An introduction to microfluidics lecture n 3

The first chaotic micromixer was designed at Berkeley (1997)

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.


An introduction to microfluidics lecture n 3

Time periodic transverse flow

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)


An introduction to microfluidics lecture n 3

How it works (from a kinematical viewpoint)

U

U

Perturbation

is applied

Line is stretched

U

Perturbation

is stopped

Line is folded


An introduction to microfluidics lecture n 3

actuation channel

Glass slide

Working channel

EXPERIMENT

Micro-valve

25mm

200mm

Microvalve

1mm


An introduction to microfluidics lecture n 3

200 mm

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


An introduction to microfluidics lecture n 3

Under resonance conditions, the interface is stretched

in the active zone, and returns flat afterwards

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


An introduction to microfluidics lecture n 3

DETERMINING A PHASE DIAGRAM, USING THE VARIANCE

OF THE PDF OF THE CONCENTRATION FIELD

- Well mixed : the variance is small

- Unmixed : the variance is large


An introduction to microfluidics lecture n 3

EXPERIMENTAL PHASE DIAGRAM, REPRESENTING ISOLINES OF s2

Actuation

pressure

(bar)

Frequency (Hz)


An introduction to microfluidics lecture n 3

An efficient

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.


An introduction to microfluidics lecture n 3

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


An introduction to microfluidics lecture n 3

CHEMICALMICROREACTORS


An introduction to microfluidics lecture n 3

EXPERIMENTAL STUDY OF A CHEMICAL REACTION

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


An introduction to microfluidics lecture n 3

One may also measure the kinetics without mixing thoroughly

A

y

The T reactor

x

U

Diffusion-reaction zone where

the product C is formed

B


An introduction to microfluidics lecture n 3

EXPERIMENT

Reaction : Ca-CaGreen

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


An introduction to microfluidics lecture n 3

Fluorescence intensity fields obtained for the reaction

CaGr+Ca2+ (CaGr,Ca2+)

Ca

U

U

CaGreen

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


An introduction to microfluidics lecture n 3

t = (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 :


An introduction to microfluidics lecture n 3

C

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)


An introduction to microfluidics lecture n 3

EXPERIMENT IS WELL INTERPRETED BY THE THEORY

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) 


An introduction to microfluidics lecture n 3

Digital microfluidics is interesting for chemical

analysis, protein cristallization, elaborating novel emulsions,…

Ismagilov et al

(Chicago University)


An introduction to microfluidics lecture n 3

(Source : C. Delattre, MIT, MTL)

Can we produce much using microreactors ?

Can we move a mountain with a spoon ?


An introduction to microfluidics lecture n 3

The end


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