![Page 1: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/1.jpg)
AN INTRODUCTION TO MICROFLUIDICS :
Lecture n°3
Patrick TABELING, [email protected], MMN, 75231 Paris0140795153
![Page 2: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/2.jpg)
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
![Page 3: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/3.jpg)
1 - Basic notions on diffusive processes2 - Micromixing3 - Microreactors.
Outline of Lecture 3
![Page 4: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/4.jpg)
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
![Page 5: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/5.jpg)
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
![Page 6: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/6.jpg)
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.
![Page 7: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/7.jpg)
Le nombre de Peclet n’est pas nécessairement petit dans les systèmes miniaturisés
Pe=UlD
~advectiondiffusion
~l2
….donc petit
![Page 8: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/8.jpg)
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
![Page 9: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/9.jpg)
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
![Page 10: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/10.jpg)
∂ 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)
![Page 11: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/11.jpg)
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
![Page 12: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/12.jpg)
- Mixing is difficult in microsystems
Mixing in microsystems
![Page 13: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/13.jpg)
There has been some clever and less clever ideas
FLOW
Poor transverse mixing for microfluidic systems
![Page 14: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/14.jpg)
HYDRODYNAMIC FOCUSING ALLOWS
TO MIX IN TENS OF MICROSECONDS Austin et al, PRL (2002)
On the order of30 nm in the extreme cases
![Page 15: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/15.jpg)
![Page 16: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/16.jpg)
![Page 17: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/17.jpg)
![Page 18: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/18.jpg)
![Page 19: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/19.jpg)
![Page 20: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/20.jpg)
![Page 21: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/21.jpg)
Circular micromixer
Quake, Scherer (2001)
![Page 22: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/22.jpg)
Transformation du boulanger
![Page 23: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/23.jpg)
In chaotic regimes, two close particles separate exponentiallyIn confined systems, this property is extremely favorable to mixing,
![Page 24: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/24.jpg)
From Ottino’s book : « Chaotic Advection »
![Page 25: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/25.jpg)
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.
![Page 26: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/26.jpg)
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
![Page 27: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/27.jpg)
How it works (from a kinematical viewpoint)
U
Perturbation is appliedLine is stretched
Perturbationis stoppedLine is folded
U
U
![Page 28: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/28.jpg)
EXPERIMENTEXPERIMENT
200m
25m
1mm
actuation channel
Glass slide Working channel
Microvalve
Micro-valve
![Page 29: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/29.jpg)
![Page 30: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/30.jpg)
A.Dodge, P. Tabeling, A. Hountoundji, M.C.Jullien (2004)
200 m
![Page 31: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/31.jpg)
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.
![Page 32: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/32.jpg)
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
![Page 33: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/33.jpg)
QuickTime™ et un décompresseurH.263 sont requis pour visualiser
cette image.
EXPERIMENTAL PHASE DIAGRAM, REPRESENTING ISOLINES OF 2
Actuationpressure(bar)
Frequency (Hz)
![Page 34: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/34.jpg)
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
![Page 35: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/35.jpg)
A.Dodge, P. Tabeling, A. Hountoundji, M.C.Jullien (2004)
![Page 36: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/36.jpg)
CHEMICAL MICROREACTORS
![Page 37: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/37.jpg)
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
![Page 38: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/38.jpg)
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
![Page 39: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/39.jpg)
EXPERIMENT
Reaction : Ca-CaGreen
C.Baroud, F Okkels, P Tabeling, L Menetrier, Phys. Rev E67, 60104 (2003)
![Page 40: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/40.jpg)
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)
![Page 41: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/41.jpg)
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 :
![Page 42: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/42.jpg)
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
![Page 43: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/43.jpg)
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)
![Page 44: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/44.jpg)
Digital microfluidics is interesting for chemical analysis, protein cristallization, elaborating novel emulsions,…
Ismagilov et al(Chicago University)
![Page 45: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/45.jpg)
(Source : C. Delattre, MIT, MTL)
Can we produce much using microreactors ?
Can we move a mountain with a spoon ?
![Page 46: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/46.jpg)
![Page 47: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/47.jpg)
![Page 48: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/48.jpg)
![Page 49: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/49.jpg)
![Page 50: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/50.jpg)
![Page 51: AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3](https://reader033.vdocument.in/reader033/viewer/2022061612/5681359f550346895d9d1247/html5/thumbnails/51.jpg)
The end