Viscous Flow Over a Chemically Patterned Surface

1. Viscous Flow Over a Chemically Patterned Surface J.E. Sprittles Y.D. Shikhmurzaev James Sprittles ECS 2007

2. Overview • 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? James Sprittles ECS 2007

3. MotivationUsing Patterned Surfaces • Free surface flows due to unbalanced surface tension forces. • Structured film formation, virtual (capillary) walls,.. Solid 1 More Wettable Solid 2 Solid 1 James Sprittles ECS 2007

4. Motivation:Drop Impact on Chemically Patterned Surfaces • Use surface patterning to ‘correct’ deposition. • For high accuracy ink-jet printing of structures. James Sprittles ECS 2007 Courtesy of Darmstadt University - Spray Research Group

5. 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 James Sprittles ECS 2007

6. Molecular Dynamics Simulations More wettable Compressed Less wettable Rarefied James Sprittles ECS 2007 Courtesy of Professor N.V. Priezjev

7. Hydrodynamic Modelling:Defining Wettability • Defining wettability The contact line Solid 1 • The Young equation: James Sprittles ECS 2007

8. Hydrodynamic Modelling:Which Model? • No-Slip No effect • Slip Models (e.g. Navier Slip) There is no theta! • A Problem.. We have no tools! James Sprittles ECS 2007

9. Qualitative Picture • Consider region of interest. • What happens when flow drives fluid particles along the interface? • Mass, momentum and energy exchange between surface and bulk. • The process of interface formation. • Fluid particles are driven into areas of differing wettability. • Surface properties take a finite time to relax to their new equilibrium state. Bulk Interfacial Layer: For Visualisation Only Solid 2 Solid 1 James Sprittles ECS 2007

10. Interface Formation Equations – Hydrodynamic of Interfaces • Surface possesses integral properties such as a surface tension, ; surface velocity, and surface density, . • Surface density is related to surface tension: Equation of State • Equilibrium surface density defines wettability: Input of Wettability James Sprittles ECS 2007

11. The Interface Formation Modelfor Constant Wettability • If then we have Navier Slip Bulk Interfacial Layer: For Visualisation Only. In the continuum limit.. James Sprittles ECS 2007

12. Solid-Liquid Boundary Conditions – Interface Formation Equations Tangential velocity Surface velocity Bulk Layer is for VISUALISATION only. In the continuum limit… Solid facing side of interface: No-slip James Sprittles ECS 2007

13. Solid-Liquid Boundary Conditions – Interface Formation Equations Normal velocity Continuity of surface mass Bulk Layer is for VISUALISATION only. In the continuum limit… James Sprittles ECS 2007 Solid facing side of interface: Impermeability

14. Problem Formulation • 2D, steady flow of an incompressible, viscous, Newtonian fluid over a stationary flat solid surface (y=0), driven by a shear in the far field. • Bulk • Navier Stokes equations: • Boundary Conditions • Shear flow in the far field, which, using gives: James Sprittles ECS 2007

15. Results - Streamlines • Consider solid 1 (x<0) more wettable than solid 2 (x>0). • Coupled, nonlinear PDEs were solved using the finite element method. James Sprittles ECS 2007

16. Results – Different Solid Combinations • Consider different solid combinations. James Sprittles ECS 2007

17. Results – Size of The Effect • Consider the normal flux out of the interface, per unit time, J. • We find: • The constant of proportionality is dependent on the fluid and the magnitude of the shear applied. James Sprittles ECS 2007

18. Results - The Generators of Slip • Variations in slip are mainly caused by variations in surface tension. 1) Deviation of shear stress on the interface from equilibrium. 2) Surface tension gradients. James Sprittles ECS 2007

19. Periodically Patterned Surface • Consider Solid 1 More Wettable. • Consider a=1 -> Strips Have Equal Width. James Sprittles ECS 2007

20. Results - Streamlines Solid 2 less wettable Qualitative agreement James Sprittles ECS 2007

21. Results – Velocity Profiles Tangential (slip) velocity varies around its equilibrium value of u=9.8. Fluxes are both in and out of the interfacial layer. Overall mass is conserved. James Sprittles ECS 2007

22. Conclusions + Further Work • IFM is able to naturally incorporate variations in wettability. • This effect is qualitatively in agreement with molecular dynamics simulations and is here realised in a continuum framework. • Effects cannot be captured with ‘Slip Models’. • Full parametric investigation is in: Sprittles & Shikhmurzaev, Phys. Rev. E 76, 021602 (2007). • More complicated flows may now be considered. James Sprittles ECS 2007

23. Thanks! James Sprittles ECS 2007

24. Numerical Analysis of Formula for J Shapes are numerical results. Lines represent predicted flux James Sprittles ECS 2007

25. Deviation of The Actual Contact Angle => Non Equilibrium Surface Tensions Left: Curtain Coating Experiments (+) vs Theory (lines) Blake et al 1999 Wilson et al 2006 Right: Molecular Dynamics Koplik et al 1989 James Sprittles ECS 2007

26. Interface Formation Equations + Input of Wettability Transition in wettability centred at x=y=0. Input of wettability James Sprittles ECS 2007