AN INTRODUCTION TO MICROFLUIDICS : Lecture n°2

1. AN INTRODUCTION TO MICROFLUIDICS : Lecture n°2 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. Fluid mechanics of microfluidics

4. Navier-Stokes equations

5. Reynolds numbers are small in microsystems Re = Ul/n ~ l2 One thus may think in the framework of Stokes equations

6. Microhydrodynamics Stokes regime : inertial terms are neglected Acceptable approximation in most case. Exceptions are Micro-heat pipes and drop dispensers

7. Propriétés des écoulements à très petit nombre de Reynolds

8. Let us reverse U -U If it is a Stokes solution, arrows must be inverted everywhere

9. This solution cannot be Stokes U

10. Because if we reverse U -U We obtain a non plausible streamline pattern

12. Experiment Performed by O Stern (2001)

13. Flows in cavities at low Reynolds numbers

14. Hele Shaw flows

15. Darcy law governs Hele Shaw cells In a Hele Shaw cell, flows are potential

16. An important notion : the hydrodynamic resistance Increases as the system size decreases Analogy with electrokinetics

17. Flows in rectangular ducts

18. Another important notion : the hydrodynamic capacity Deformable tube : dP=k-1 dV/V Example : Volume V Pressure P Now Qm=rdV/dt Thus Qm=mkdP/dt and hence C=km

19. U uc(t) up(x,t) The bottleneck effect

20. Question : Show that the time to reach a steady state is given by The expression Response : C=m/E=πD2Lr/4E et R=12nl/b3w with t=RC

21. Experiment in a microchannel, 1.4 mm deep Expérience effectuée au MMN (2001)- Matthieu Cécillon

22. Beware of dead volumes Because to reach a steady state, it takes a time t equal to t ≈ RC then t ≈ kmR One must avoid dead volumes, bubbles, etc..

23. A PDMS actuator, based on Multi-layer Soft Lithography Actuation channel Glass slide Working channel PDMS A. Unger, H-P. Chou, T. Thorsen, A . Scherer et S. R. Quake, Science, 288, 113, (2000).

24. VC R R From the electrical point of view, pneumatic actuators are represented by a capacitance/non linear resistance system . They are not just diodes Non linear resistances R=f(VC) J.Goulpeau, A. Ajdari P. Tabeling,J. Appl.Phys. May 2005

25. No actuation : Large localized gradient Actuation : Producing different Concentration gradients by changing the actuaction parameters

26. Mechanical actuators dedicated to the generation of concentration gradients Passive concentration gradient generator (1) The same, using mechanical actuators (1)Jeon et al, Nature Techn., 20, 826 (2002))

27. ELECTRICAL REPRESENTATIONS OF ELEMENTARY ACTIVE SYSTEMS Mixer - Extractor Microdoser Mixer Gradient concentration generator Microdoser

28. Integrated actuators can be used to make progress in the realization of complex systems : an example is a chip for proteomics

29. The boundary conditions for liquids

30. The slip length z u Navier Boundary Conditions Slip length (or extrapolation length)

31. Pressure drop with a slip length DP Flow rate Q Depth b Slip length LS

32. Microfluidics and capillarity

33. Two or three things important to know in microfluidics

34. Laplace’s law S R V At mechanical equilibrium : dE=0 Bubble

35. Capillary phenomena are important in microsystems Pressure drops caused by capillarity are ~ l-1 while those due to viscosity behave like l0

36. THE PATTERNS WHICH DEVELOP IN “ORDINARY” TWO PHASE FLOWS …OFTEN PRODUCE COMPLEX MORPHOLOGIES; THIS IS DUE TO HYDRODYNAMIC TURBULENCE

37. IN MICROFLUIDIC SYSTEMS, WE OBTAIN MUCH SIMPLER MORPHOLOGIES : ESSENTIALLY DROPLETS Laure MENETRIER, 2004

38. Droplets can be made using a “hydrodynamic focusing” geometry

39. Wetting are exceedingly important in microsytems 3 cases Complete wetting Partial wetting Desorption

40. Spreading parameter S>0 complete wetting S<0 partial wetting or desorption

41. When S is non homogeneous, droplets spontaneously move on the surfaces qA<qB Good wetting (S ≈ 0) Poor wetting (S <0)

42. In liquid, one may easily change S by adding surfactants water oil

43. Wetting properties of the walls are important in microfluidic multiphase flows Oil with or without surfactant (Span 80) Water Water R Dreyfus, P.Tabeling, H Willaime, Phys Rev Lett, 90, 144505 (2003))

44. NICE DROPS CAN BE PRODUCED IN MINIATURIZED SYSTEMS IN COMPLETE WETTING CONDITIONS 200mm

45. When oil fully wets the surface Oil flow rate (L/min) Isolated water drops Stratified regime Pear necklace Large-pearl necklace Pears Coalescence Pearl necklace Water flow rate (L/min)

46. WHEN THE FLUIDS PARTIALLY WET THE WALLS Oil flow-rate (mL/mn) Water flow-rate (mL/mn) (R Dreyfus, P.Tabeling, H Willaime, Phys Rev Lett (2003))

47. Rayleigh instability is the most important instability to be aware of Surface energy of a column d Surface energy of N spherical droplets l UNSTABLE

48. Applications :Digital microfluidics - Liquid liquid flows are used in microsystems, in several circumstances. Producing drops of one liquid into another liquid so as to generate emulsions, or perform screening Producing bubbles in a microchannel flow so as to increase heat exchange, or simply because the liquid boils.

49. Digital microfluidics 1 - In air 2 - In a liquid The drop moves in air over a flat surface The drop moves in a liquid in a microchannel

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