AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3

1. AN INTRODUCTION TO MICROFLUIDICS : Lecture n°3 Patrick TABELING, patrick.tabeling@espci.fr ESPCI, MMN, 75231 Paris 0140795153

2. 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

3. Outline of Lecture 3 1 - Basic notions on diffusive processes 2 - Micromixing 3 - Microreactors.

4. 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

5. 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 :

6. 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.

7. TROP VITE DIT Le nombre de Peclet n’est pas nécessairement petit dans les systèmes miniaturisés ….donc petit

8. 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

9. 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

10. Dispersion de TAYLOR-ARIS d d doit etre très fin

11. 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

12. Mixing in microsystems - Mixing is difficult in microsystems

13. There has been some clever and less clever ideas FLOW Poor transverse mixing for microfluidic systems

14. HYDRODYNAMIC FOCUSING ALLOWS On the order of 30 nm in the extreme cases TO MIX IN TENS OF MICROSECONDS Austin et al, PRL (2002)

21. Circular micromixer Quake, Scherer (2001)

22. Transformation du boulanger

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

24. From Ottino’s book : « Chaotic Advection »

25. 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.

26. 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)

27. How it works (from a kinematical viewpoint) U U Perturbation is applied Line is stretched U Perturbation is stopped Line is folded

28. actuation channel Glass slide Working channel EXPERIMENT Micro-valve 25mm 200mm Microvalve 1mm

30. 200 mm A.Dodge, P. Tabeling, A. Hountoundji, M.C.Jullien (2004)

31. 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)

32. 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

33. EXPERIMENTAL PHASE DIAGRAM, REPRESENTING ISOLINES OF s2 Actuation pressure (bar) Frequency (Hz)

34. 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.

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

36. CHEMICALMICROREACTORS

37. 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

38. 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

39. EXPERIMENT Reaction : Ca-CaGreen C.Baroud, F Okkels, P Tabeling, L Menetrier, Phys. RevE67, 60104 (2003) 

40. 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) 

41. 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 :

42. 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)

43. 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) 

44. Digital microfluidics is interesting for chemical analysis, protein cristallization, elaborating novel emulsions,… Ismagilov et al (Chicago University)

45. (Source : C. Delattre, MIT, MTL) Can we produce much using microreactors ? Can we move a mountain with a spoon ?