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

2. James Sprittles BAMC 2007 Wettability More Wettable (Hydrophilic) Less Wettable (Hydrophobic) Solid 1 Solid 2

3. James Sprittles BAMC 2007 The Problem How do variations in the wettability of a substrate affect the flow of an adjacent liquid? No slip – No effect. Solid 1 Solid 2 What happens in this region? Shear flow in the far field

4. James Sprittles BAMC 2007 Molecular Dynamics Simulations Courtesy of Professor N.V. Priezjev More wettable Dense => Surface tension -’ve More wettable Dense => Surface tension -’ve Less wettable Rarefied => Surface tension +’ve Less wettable Rarefied => Surface tension +’ve

5. James Sprittles BAMC 2007 Equilibrium Contact Angle and Equilibrium Surface Tension Require a mathematical definition of wettability. The Young equation: a force balance at the contact line. The contact line

6. James Sprittles BAMC 2007 Interface Formation Solid 1 Solid 2 Flow drives the interface out of equilibrium. Thermodynamics fights to return the interface to its equilibrium state. In the continuum approximation the microscopic layer is a surface of zero thickness. Surface possesses intrinsic properties such as a surface tension, ; surface velocity, and surface density,. Each solid-liquid interface has a different equilibrium surface tension. Gradients in surface tension. Microscopic interfacial layer in equilibrium.

7. James Sprittles BAMC 2007 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:

8. James Sprittles BAMC 2007 Solid-Liquid Boundary Conditions – Interface Formation Equations Equation of state Transition in wettability at x=y=0. Input of wettability

9. James Sprittles BAMC 2007 Solid-Liquid Boundary Conditions – Interface Formation Equations Bulk Solid facing side of interface: No-slip Layer is for VISUALISATION only. Tangential velocity Surface velocity

10. James Sprittles BAMC 2007 Solid-Liquid Boundary Conditions – Interface Formation Equations Bulk Solid facing side of interface: Impermeability Continuity of surface mass Normal velocity Layer is for VISUALISATION only.

11. James Sprittles BAMC 2007 Results Consider solid 1 (x 0). Coupled, nonlinear PDEs were solved using the finite element method.

12. James Sprittles BAMC 2007 Results 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.

13. James Sprittles BAMC 2007 Results - The Generators of Slip Results show that variations in slip are mainly caused by variations in surface tension as opposed to shear stress variations. 1) Deviation of shear stress on the interface from equilibrium. 2) Surface tension gradients. 1) Deviation of shear stress on the interface from equilibrium. 2) Surface tension gradients.

14. James Sprittles BAMC 2007 Conclusions + Further Work IFM is able to naturally incorporate variations in wettability. Surface interacts with the bulk in order to attain its new equilibrium state. Relate size of the effect back to the equilibrium contact angle. This effect is qualitatively in agreement with molecular dynamics simulations and is here realised in a continuum framework. More complicated situations may now be considered –Intermittent patterning –Drop impact on chemically patterned surfaces

15. James Sprittles BAMC 2007 Drop Impact on a Chemically Patterned Surface One is able to control droplet deposition by patterning a substrate Courtesy of Darmstadt University - Spray Research Group

16. James Sprittles BAMC 2007 Thanks!

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