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Wetting as a Macroscopic and Microscropic Process

Wetting as a Macroscopic and Microscropic Process. J.E. Sprittles (University of Birmingham / Oxford, U.K.) Y.D. Shikhmurzaev (University of Birmingham, U.K.) Seminar at KAUST, February 2012. ‘Impact’ . A few years after completing my PhD. Wetting: Statics. Wettable (Hydrophilic).

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Wetting as a Macroscopic and Microscropic Process

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  1. Wetting as a Macroscopic and Microscropic Process J.E. Sprittles (University of Birmingham / Oxford, U.K.) Y.D. Shikhmurzaev (University of Birmingham, U.K.) Seminar at KAUST, February 2012

  2. ‘Impact’ A few years after completing my PhD.....

  3. Wetting: Statics Wettable (Hydrophilic) Non-Wettable (Hydrophobic)

  4. Wetting: Dynamics

  5. Capillary Rise 27mm Radius Tube Stangeet al 03 50nm x 900nm Channels Han et al 06 1 Million Orders of Magnitude!!

  6. Polymer-Organic LED (P-OLED) Displays

  7. Inkjet Printing of P-OLED Displays Microdrop Impact & Spreading

  8. Modelling: Why Bother? • - Recover Hidden Information • - Map Regimes of Spreading 3 – Experiment Millimetres in Milliseconds - Riobooet al (2002) Flow Inside Solids – Marston et al 2010 Microns in Microseconds - Dong et al (2002)

  9. Dynamic Contact Angle • Required as a boundary condition for the free surface shape. r r t Pasandideh-Fard et al 1996

  10. ) U Speed-Angle Formulae Dynamic Contact Angle Formula Young Equation σ1 σ3 - σ2 Assumption: A unique angle for each speed R

  11. ) Drop Impact Experiments Bayer & Megaridis 06

  12. Capillary Rise Experiments Sobolevet al 01

  13. Dynamic Wetting:An Interface Formation Process

  14. 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.

  15. 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)

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

  17. 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, Finite Element Simulation of Dynamic Wetting Flows as an Interface Formation Process, to JCP. JES & YDS, 2012, The Dynamics of Liquid Drops and their Interaction with Surfaces of Varying Wettabilities, to PoF.

  18. Mesh Resolution Critical

  19. Arbitrary LagrangianEulerian Mesh Control

  20. Drop Impact

  21. Impact at Different Scales Millimetre Drop Microdrop Nanodrop

  22. Pyramidal (mm-sized) Drops Experiment of Renardyet al, 03.

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

  24. Microdrop Impact Pressure Scale Velocity Scale

  25. Microdrop Impact ?

  26. Hidden Dynamics

  27. Surfaces of Variable Wettability 1 1.5

  28. Flow Control on Patterned Surfaces JES & YDS 2012, to PoF

  29. Dynamics of Flow Through a Capillary

  30. Steady Propagation of a Meniscus

  31. Flow Characteristics

  32. ‘Hydrodynamic Resist’ Smaller Capillaries

  33. Summary: Dynamic Wetting Models Meniscus shape unchanged by dynamic wetting Meniscus shape dependent on speed of propagation. Hydrodynamic Resist: Meniscus shape influenced by geometry Dynamic Dynamic Dynamic Equilibrium Equilibrium Equilibrium Meniscus Washburn Model Basic Dynamic Wetting Models Interface Formation Model and Experiments

  34. Capillary Rise: Models vs Experiments • Compare to experiments of Jooset al 90 and conventional Lucas-Washburn theory • Lucas-Washburn assumes: • Poiseuille Flow Throughout • Spherical Cap Meniscus • Fixed (Equilibrium) Contact Angle

  35. Lucas-Washburn vs Full Simulation R = 0.074cm; every 50secs R = 0.036cm; every 100secs

  36. Comparison to Experiment Washburn Washburn Full Simulation Full Simulation JES & YDS 2012, to JCP

  37. Wetting as a Microscopic Process:Flow through Porous Media

  38. Problems and Issues

  39. Problems and Issues • Micro: Pore scale dynamics of: • Menisci in wetting front • Ganglia • Macro (Darcy-scale) dynamics of: • Entire wetting front • Ganglia in multiphase system • Multi-scale porosity: • Motion on a microporous substrate

  40. Physical Reality

  41. Continuum Model • Simplest Case First: Full Displacement (no ganglia formation) Kinematic boundary condition Dynamic boundary condition ?

  42. Wetting Front: Modes of Motion Threshold mode Wetting mode

  43. Some Unexplained Effects ) 1). T. Delker, D. B. Pengra & P.-z. Wong, Phys. Rev. Lett.76, 2902 (1996). g z 2). M. Lago & M. Araujo, J. Colloid & Interf. Sci.234, 35 (2001).

  44. Suggested Description ) Non-Washburnian ) z ) g 2/3 of height in 2 mins 1/3 of height in many hours Washburnian

  45. Developed Theory ) z g Random Fluctuations ‘Break’ Threshold Mode YDS & JES 2012, JFM; YDS & JES 2012, to PRE

  46. Flow over a Porous Substrate

  47. Wetting: Micro-Macro Coupling Spreading on a Porous Medium

  48. Current State of Modelling • 1) Contact Line Pinned • 2) Shape Fixed as Spherical Cap

  49. The Reality Equilibrium shape is history-dependent.

  50. Spreading on a Porous Substrate θD θw U θd

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