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Drop Impact and Spreading on Surfaces of Variable Wettability

This study explores the behavior of drop impact and spreading on surfaces with different wettability properties. The conventional models for describing contact angle and contact line behavior are challenged, and the Shikhmurzaev model is investigated as an alternative approach. Numerical simulations using the finite element method are used to analyze the dynamics of drop impact and spreading on these surfaces.

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Drop Impact and Spreading on Surfaces of Variable Wettability

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  1. Drop Impact and Spreading on Surfaces of Variable Wettability J.E Sprittles Y.D. Shikhmurzaev Bonn 2007

  2. Motivation • Drop impact and spreading occurs in many industrial processes. • 100 million inkjet printers sold yearly. • NEW: Inkjet printing of electronic circuits. • Why study the ‘old problem’ of drops spreading on surfaces? Swansea 2007

  3. Worthington 1876 – First Experiments Swansea 2007

  4. Worthington’s Sketches Millimetre sized drops of milk on smoked glass. Swansea 2007

  5. Modern Day Experiments (mm drops of water) Courtesy of Romain Rioboo Swansea 2007

  6. Xu et al 03 Drops don’t splash at the top of Everest! Swansea 2007

  7. Renardy 03 et al - Pyramidal Drops • Impact of oscillating water drops on super hydrophobic substrates 1 4 2 3 Swansea 2007

  8. The Simplest Problem • How does a drops behaviour depend on: fluid properties, drop speed, drop size,.. etc? a Apex Height Contact Angle Swansea 2007 Spread Factor

  9. The Contact Angle • In equilibrium the angle defines the wettability of a solid-liquid combination. • How should we describe it in a dynamic situation? More Wettable (Hydrophilic) Less Wettable (Hydrophobic) Solid 2 Solid 1 Swansea 2007

  10. Modelling of Drop Impact and Spreading Phenomena • The Moving Contact Line Problem • Conventional Approaches and their Drawbacks • The Shikhmurzaev Model Swansea 2007

  11. The Moving Contact Line Problem Contact angle Inviscid Gas Liquid Contact line Solid Swansea 2007

  12. The Moving Contact Line Problem • No solution!!! Contact angle prescribed • Kinematic condition • Dynamic condition • Navier-Stokes • Continuity • No-Slip • Impermeability Swansea 2007

  13. The Conventional Approach One must: 1) Allow a solution to be obtained. 2) Describe the macroscopic contact angle. These are treated separately by: 1) Modifying the no-slip condition near the Contact Line (CL) to allow slip, e.g. 2) Prescribing the Contact Angle as a function of various parameters, e.g. Swansea 2007

  14. Experiments Show This Is Wrong… • Can one describe the contact angle as a function of the parameters? “There is no universal expression to relate contact angle with contact line speed”. (Bayer and Megaridis 06) “There is no general correlation of the dynamic contact angle as a function of surface characteristics, droplet fluid and diameter and impact velocity.” (Sikalo et al 02) Swansea 2007

  15. As in Curtain Coating Used to industrially coat materials. Conventional models: Fixed substrate speed => Unique contact angle Swansea 2007

  16. ‘Hydrodynamic Assist of Dynamic Wetting’ The contact angle depends on the flow field. Swansea 2007 See: Blake et al 1994, Blake et al 1999, Clarke et al 2006

  17. Angle Also Dependent On The Geometry: Flow Through a Channel • The contact angle is dependent on d and U. (Ngan & Dussan 82) U d U Conclusion: Angle is determined by the flow field Swansea 2007

  18. The Shikhmuraev Model’s Predictions Unlike conventional models: • The contact angle is determined by the flow field. • No stagnation region at the contact line. • No infinite pressure at the contact line => Numerics easier Swansea 2007

  19. Shikhmurzaev ModelWhat is it? • Generalisation of the classical boundary conditions. • Considers the interface as a thermodynamic system with mass, momentum and energy exchange with the bulk. • Used to relieve paradoxes in modelling of capillary flows such as ….. Swansea 2007

  20. Some Previous Applications Swansea 2007

  21. The Shikhmurzaev Model Qualitatively (Flow near the contact line) Width of interfacial layer Gas Liquid Solid Swansea 2007

  22. Shikhmurzaev Model • Solid-liquid and liquid-gas interfaces have an asymmetry of forces acting on them. • In the continuum approximation the dynamics of the interfacial layer should be applied at a surface. • Surface properties survive even when the interface's thickness is considered negligible. Surface tension Surface density Surface velocity Swansea 2007

  23. f (r, t )=0 e1 n n θd e2 Shikhmurzaev Model On free surfaces: At contact lines: On liquid-solid interfaces: Swansea 2007

  24. What if (the far field) ? On free surfaces: At contact lines: On liquid-solid interfaces: Swansea 2007

  25. Summary • Classical Fluid Mechanics => No Solution • Conventional Methods Are Fundamentally Flawed • The Shikhmurzaev Model Should Be Investigated Swansea 2007

  26. Our Approach • Bulk: Incompressible Navier-Stokes equations • Boundary: Conventional Model (for a start!) • Use Finite Element Method. • Assume axisymmetric motion (unlike below!). Swansea 2007

  27. Numerical Approach • Use the finite element method: Velocity and Free Surface quadratic Pressure Linear • The ‘Spine Method’ is used to represent the free surface • ~2000 elements • Second order time integration Swansea 2007

  28. The Spine Method(Scriven and co-workers) Nodes define free surface. The Spine Swansea 2007 Nodes fixed on solid.

  29. Code Validation • Consider large deformation oscillations of viscous liquid drops. • Compare with results from previous investigations, Basaran 91 and Meradji 01. • Compare aspect ratio of drop as a function of time. • Starting position is Swansea 2007 Microgravity Experiment

  30. Second Harmonic – Large Deformation For Re=100, f2 = 0.9 Swansea 2007

  31. Second Harmonic – Large Deformation (cont) • Aspect ratio of the drop as a function of time. • A damped wave. Swansea 2007

  32. Fourth Harmonic – Large Deformation For Re=100, f4 = 0.9 Swansea 2007

  33. Drop Impact on a Hydrophilic (Wettable) Substrate Re=100, We=10, β = 100, . Swansea 2007

  34. The Experiment – Water on GlassCourtesy of Dr A. Clarke (Kodak) Swansea 2007

  35. Drop Impact on a Hydrophobic (non-wettable) Substrate Re=100, We=10, β = 100, . Swansea 2007

  36. The Experiment – Water on HydrophobeCourtesy of Dr A. Clarke (Kodak) Swansea 2007

  37. High Speed Impact Radius = 25 mm, Impact Speed = 12.2 m/s Re=345, We=51, β = 100, . Swansea 2007

  38. Non-Spherical Drops on Hydrophobic Substrates Radius = 1.75mm, Impact Speed = 0.4 m/s, Re=1435, We=8, . Swansea 2007

  39. Impact + Spreading of Non-Spherical Dropson Hydrophobic Substrates Swansea 2007

  40. Impact + Spreading of Non-Spherical Dropson Hydrophobic Substrates The Pyramid! Swansea 2007

  41. Impact + Spreading of Non-Spherical Dropson Hydrophobic Substrates Experiment shows pinch off of drops from the apex Swansea 2007

  42. Impact + Spreading of Non-Spherical Dropson Hydrophobic Substrates As in experiments, drop becomes toroidal Swansea 2007

  43. Current Work • Quantitatively compare results against experiment. • Incorporate the Shikhmurzaev model. • Consider variations in wettability …. Swansea 2007

  44. How to Incorporate Variations in Wettability? • Technologically, why are flows over patterned surfaces important? • What are the issues with modelling such flows? • How will a single change in wettability affect a flow? • How about intermittent changes? Swansea 2007

  45. Using Patterned Surfaces • Manipulate free surface flows using unbalanced surface tension forces. Swansea 2007

  46. Mock 05 et al - Drop Impact onto Chemically Patterned Surfaces • Pattern a surface with areas of differing wettability. • ‘Corrects’ deposition. Swansea 2007

  47. Mock 05 et al - Drop Impact onto Chemically Patterned Surfaces Courtesy of Professor Roisman • Pattern a surface to ‘correct’ deposition. Swansea 2007

  48. What if there is no free surface? Do variations in the wettability affect an adjacent flow? The Problem What happens in this region? Shear flow in the far field Solid 2 Solid 1 Swansea 2007

  49. Molecular Dynamics Simulations More wettable Compressed Less wettable Rarefied Swansea 2007 Courtesy of Professor N.V. Priezjev

  50. Hydrodynamic Modelling:Defining Wettability • Defining wettability The contact line Solid 1 • The Young equation: Swansea 2007

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