Microfluidic Dynamic Wetting Flows: Modelling & Simulation

1. Microfluidic Dynamic Wetting Flows: Modelling & Simulation J.E. Sprittles (University of Oxford, U.K.) Y.D. Shikhmurzaev (University of Birmingham, U.K.) International Society of Coating Science & Technology Symposium, Atlanta

2. Inkjet Printers: Microfluidic Technologies • Key elements are the interaction of: • Drops with a solid - Dynamic Wetting • Drops with other drops - Coalescence

3. Dynamic Wetting Phenomena Emerging technologies Routine experimental measurement 1 Million Orders of Magnitude! 50nm Channels 27mm Radius Tube Millimetre scale Microfluidics Nanofluidics

4. Dynamic Wetting:Conventional Models

5. Dynamic Wetting: Conventional Models ‘Classical’ formulation Dynamic contact angle formula: Dynamic contact angle must be specified. has no solution. Model 1 Model 2 Model 3 (Young’s equation) (Navier slip) u=U No-slip (u=0) Slip region of size ~ l A `slip’ condition:

6. Conventional Modelling Dynamic Contact Angle Formula Assumption: A unique angle for each speed

7. Fibre Coating: Effect of Geometry Simpkins & Kuck 03

8. Capillary Rise: Effect of Geometry Sobolev et al 01

9. ) Drop Spreading: Effect of Impact Speed Bayer & Megaridis 06

10. U, cm/s Hydrodynamic Assist Vary Flow Rate Blake et al 99 Effect is not due to viscous bending (Wilson et al 06)

11. Dynamic Wetting:An Interface Formation Process

12. Physics of Dynamic Wetting Liquid-solid interface Solid Forming interface Formed interface • Make a dry solid wet. • Create a new/fresh liquid-solid interface. • Class of flows with forming interfaces.

13. Relevance of the Young Equation Static situation Dynamic wetting σ1e σ1 θe θd σ3 - σ2 σ3e - σ2e R R Dynamic contact angle results from dynamic surface tensions. Theangle is now determined by the flow field. Slip created by surface tension gradients (Marangoni effect)

14. f (r, t )=0 e1 n n θd e2 Interface Formation Modelling In the bulk (Navier Stokes): Interface Formation Model On free surfaces: On liquid-solid interfaces: At contact lines:

15. A Finite Element Based Computational Framework JES &YDS 2011, Viscous Flows in Domains with Corners, CMAME JES & YDS 2012, Finite Element Framework for Simulating Dynamic Wetting Flows, Int. J. Num. Meth Fluids. JES & YDS, 2012, The Dynamics of Liquid Drops and their Interaction with Surfaces of Varying Wettabilities, Phy. Fluids. JES & YDS, 2012, Finite Element Simulation of Dynamic Wetting Flows as an Interface Formation Process, to J. Comp. Phy. (In Press)

16. Mesh Resolution is Critical

17. Arbitrary Lagrangian Eulerian Mesh Based on the ‘spine method’ of Scriven and co-workers Microdrop simulation with impact, spreading and rebound

18. Dynamic Wetting of a Capillary

19. Capillary Rise: Models vs Experiments Interface formation & Lucas-Washburn ( ) vs experiments of Joos et al 90 Silicon oil of viscosity 12000cP for two capillary sizes (0.3mm and 0.7mm)

20. Lucas-Washburn vs Interface Formation After 50 secs LW IF After 100 secs LW IF Tube Radius = 0.74mm; Meniscus shape every 50secs Tube Radius = 0.36mm; Meniscus shape every 100secs

21. Comparison to Experiment Meniscus height h, in cm, as a function of time t, in seconds. Washburn Washburn Full Simulation Full Simulation JES & YDS 2012, J. Comp. Phy. (In press)

22. Speed-Angle Relationship t = 0 Asymptotic result (speed-angle formula) u=0 Equilibrium New effect: angle decreases with increasing speed

23. ‘Hydrodynamic Resist’ Dependence of the contact angle on geometry (capillary size) Smaller Capillaries Sobolevet al 01

24. Microdrop Impact and Spreading

25. Microdrop Impact ? 25mm water drop impacting at 5m/s. Experiments: Dong et al 06

26. Microdrop Impact 25mm water drop impacting at 5m/s. Pressure Scale Velocity Scale

27. Surfaces of Variable Wettability 1 Hydrophilic Hydrophobic 1.5

28. Flow Control on Patterned Surfaces Green: hydrophobic. Grey: hydrophilic. JES & YDS 2012, PoF

29. Coalescence of Liquid Drops:Models vs Experiments

30. Coalescence • Conventional model: cusp becomes • rounded in zero time -> infinite velocities • Interface formation: cusp is rounded in finite time Instant rounding Infinite bridge speed Gradual rounding Finite bridge speed Forming interface

31. Coalescence of Liquid Drops Experiment Simulation Developed framework can be adapted for coalescence. Thoroddsen’s Group: Ultra high-speed imaging Nagel’s Group: Sub-optical electrical measurements Thoroddsen et al 2005

32. Coalescence: Models vs Experiments Thoroddsen’s Optical Experiments Conventional Interface formation Nagel’s Electrical Measurements Bridge radius versus time: 2mm drops of 220cP water-glycerol.

33. Funding • Funding • This presentation is based on work supported by:

34. Thanks

35. Flow Characteristics

36. Microdrop Impact 25 micron water drop impacting at 5m/s on left: wettable substrate right: nonwettable substrate

37. Coalescence: Free surface profiles Time: 0 < t < 0.1 Conventional theory Interface formation theory Water- Glycerol mixture of 230cP

38. Influence of Viscosity Widening gap 3.3cP 230cP 48cP Conventional Thoroddsen’s Experiments Interface formation Nagel’s Experiments

39. Flow Over Surfaces of Variable Wettability

40. Periodically Patterned Surfaces • No slip – No effect.

41. Interface Formation vs MDS Solid 2 less wettable Qualitative agreement JES & YDS 2007, PRE; JES &YDS 2009 EPJ