AN INTRODUCTION TO MICROFLUIDICS :

Lecture n°3

Patrick TABELING, patrick.tabeling@espci.frESPCI, MMN, 75231 Paris0140795153

1 - History and prospectives of microfluidics2 - Microsystems and macroscopic approach.3 - The spectacular changes of the balances of forces aswe go to the small world.

Outline of Lecture 1

- The fluid mechanics of microfluidics - Digital microfluidics

Outline of Lecture 2

1 - Basic notions on diffusive processes2 - Micromixing3 - Microreactors.

Outline of Lecture 3

Diffusion time for a 100 m 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

τ=l2

D~100s

Equation de diffusion advection

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

∂C∂t

+u∇C=DΔC+q

Un nombre sans dimension analogue au nombre de Reynolds est :

Pe =UlD

~advectiondiffusion

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

Quelques propriétés de l’équation de diffusion-advection

La variance de la concentation décroit avec le temps

∂ <C2 >∂t

=−D< ∇C( )2 >

- si les CL sont périodiques ou si l’écoulement est confiné dans un volume avec parois rigides imperméables.

Le nombre de Peclet n’est pas nécessairement petit dans les systèmes miniaturisés

Pe=UlD

~advectiondiffusion

~l2

….donc petit

C(x,t) =C0

4πDtexp−

x2

4Dt⎛ ⎝ ⎜

⎞ ⎠ ⎟

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

C

x

C

x

t=0 t

Écart type =(2Dt)1/2

Dispersion dans un écoulement uniforme

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

C(x, t) =C02π

exp−(x−Ut)2

2 2

⎛ ⎝ ⎜ ⎞

⎠Avec 2=2Dt

x=0

xU

∂ C

∂ t

= Deff

Δ C

DC

Dt

=

∂ C

∂ t

+ ( U ( z ) − V )

∂ C

∂ x '

= D

∂

2

C

∂ x '

2

DC

Dt

=

∂ C

∂ t

+ U ( z )

∂ C

∂ x

= D Δ C

Dispersion de TAYLOR-ARIS

d d doit etre très fin

Deff =D(1+αPe2)

Origine microscopique de la diffusion moléculaire

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

La poxition du marcheur est : x = li

1

n

∑

On démontre :

x2=li

2=nl

2

1

n

∑=Dt

Mouvement diffusif et front gaussien

li

- Mixing is difficult in microsystems

Mixing in microsystems

There has been some clever and less clever ideas

FLOW

Poor transverse mixing for microfluidic systems

HYDRODYNAMIC FOCUSING ALLOWS

TO MIX IN TENS OF MICROSECONDS Austin et al, PRL (2002)

On the order of30 nm in the extreme cases

Circular micromixer

Quake, Scherer (2001)

Transformation du boulanger

In chaotic regimes, two close particles separate exponentiallyIn confined systems, this property is extremely favorable to mixing,

From Ottino’s book : « Chaotic Advection »

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.

Main Flow

Time periodic transverse flow

V

-V

time

Cross-channel micro-mixer(UCLA,1999)

400 m

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

Fluid A

FluidB

How it works (from a kinematical viewpoint)

U

Perturbation is appliedLine is stretched

Perturbationis stoppedLine is folded

U

U

EXPERIMENTEXPERIMENT

200m

25m

1mm

actuation channel

Glass slide Working channel

Microvalve

Micro-valve

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

200 m

Under resonance conditions, the interface is stretchedin the active zone, and returns flat afterwards

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

QuickTime™ et undécompresseur H.263

sont requis pour visionner cette image.

DETERMINING A PHASE DIAGRAM, USING THE VARIANCEOF THE PDF OF THE CONCENTRATION FIELD

σ2 =<C(x)−Cmean>2

- Well mixed : the variance is small

- Unmixed : the variance is large

QuickTime™ et un décompresseurH.263 sont requis pour visualiser

cette image.

EXPERIMENTAL PHASE DIAGRAM, REPRESENTING ISOLINES OF 2

Actuationpressure(bar)

Frequency (Hz)

RESONANCESMAY BE USED TO SORTPARTICLES :

BY CHANGING THE FREQUENCY OF THE PERTURBATION, ONEOBTAINS A SYSTEM WHICH MIXES FLUIDS, FILTERS PARTICLES,OR SIMPLY TRANSPORTS MATERIALS

SIDE BY SIDE.

An efficient particle sorter, using resonance

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

CHEMICAL MICROREACTORS

EXPERIMENTAL STUDY OF A CHEMICAL REACTIONA+B C IN A T MICROREACTOR

Channels 10m deep,500m wide, various flow-ratesSystem made in glass, coveredby a silicon wafer, or in PDMS

A

B

The T reactor

Diffusion-reaction zone wherethe product C is formed

A

B

Quantitative analysis of Molecular Interaction in a Microfluidic Channel : The T sensor,A.E.Kamholz, B Weigl, B Finlayson, P Yager, Anal Chem, 71, 5340 (1999)

x

One may also measure the kinetics without mixing thoroughly

U

y

EXPERIMENT

Reaction : Ca-CaGreen

C.Baroud, F Okkels, P Tabeling, L Menetrier, Phys. Rev E67, 60104 (2003) 

Ca

CaGreen

Fluorescence intensity fields obtained for the reactionCaGr+Ca2+ (CaGr,Ca2+)

U

U

C.Baroud, F Okkels, P Tabeling, L Menetrier, Phys. Rev E67, 60104 (2003) 

Theory of the T-reactor for a second order reaction

U∂C∂x

=DC∂2C∂y2 +kAB

The product C is governed by the following equation :

U∂A∂x

=DA∂2A∂y2 −kAB

U∂B∂x

=DB∂2B∂y2 −kAB = (k A0

1/2 B01/2 )-1

Characteristic time of the reactionx=0, A = A0 for y< 0

B =B0 for y> 0

Boundary conditions :

Width

Locationof the maxConc.

C

y

Typical structure ofa concentration profile of the productacross the channel

width

Locationof the max.

Agreement between theory and experimentis good

MaximumConc.

THEORY with one fitting parameter k = 105 lM-1 s-1 ( = 1 ms)C.Baroud et al, Phys. RevE (2003)

x

x

x

EXPERIMENT IS WELL INTERPRETED BY THE THEORY

THEORY THEORY

m m

Fitting the experiment with one free parameter k = 105 LM-1 s-1 ( = 1 ms)

X

y

y (m) y (m)

C.Baroud et al Phys. Rev E67, 60104 (2003) 

Digital microfluidics is interesting for chemical analysis, protein cristallization, elaborating novel emulsions,…

Ismagilov et al(Chicago University)

(Source : C. Delattre, MIT, MTL)

Can we produce much using microreactors ?

Can we move a mountain with a spoon ?

The end