1. Hydrodynamic Slip Boundary Condition for the Moving Contact Line in collaboration with Xiao-Ping Wang (Mathematics Dept, HKUST) Ping Sheng (Physics Dept, HKUST)

2. No-Slip Boundary Condition ?

3. from Navier Boundary Condition to No-Slip Boundary Condition : slip length, from nano- to micrometer Practically, no slip in macroscopic flows : shear rate at solid surface

6. No-Slip Boundary Condition ? Apparent Violation seen from the moving/slipping contact line Infinite Energy Dissipation (unphysical singularity)

7. Previous Ad-hoc models: No-slip B.C. breaks down Nature of the true B.C. ? (microscopic slipping mechanism) If slip occurs within a length scale S in the vicinity of the contact line, then what is the magnitude of S ?

8. Molecular dynamics simulations for two-phase Couette flow Fluid-fluid molecular interactions Wall-fluid molecular interactions Densities (liquid) Solid wall structure (fcc) Temperature System size Speed of the moving walls

9. Modified Lennard-Jones Potentials for like molecules for molecules of different species for wetting property of the fluid

10. tangential momentum transport boundary layer

11. The Generalized Navier B. C. when the BL thickness shrinks down to 0 viscous partnon-viscous part Origin?

12. nonviscous part viscous part uncompensated Young stress

13. Uncompensated Young Stress missed in Navier B. C. Net force due to hydrodynamic deviation from static force balance (Young’s equation ) NBC NOT capable of describing the motion of contact line Away from the CL, the GNBC implies NBC for single phase flows.

14. Continuum Hydrodynamic Modeling Components: Cahn-Hilliard free energy functional retains the integrity of the interface (Ginzburg-Landau type) Convection-diffusion equation (conserved order parameter) Navier - Stokes equation (momentum transport) Generalized Navier Boudary Condition

15. molecular positions projected onto the xz plane

16. Symmetric Coutte V=0.25 H=13.6 near-total slip at moving CL no slip

17. symmetric Coutte V=0.25 H=13.6 asymmetric Coutte V=0.20 H=13.6 profiles at different z levels

18. asymmetric Poiseuille g ext =0.05 H=13.6

19. The boundary conditions and the parameter values are both local properties, applicable to flows with different macroscopic/external conditions (wall speed, system size, flow type).

20. Summary: A need of the correct B.C. for moving CL. MD simulations for the deduction of BC. Local, continuum hydrodynamics formulated from Cahn-Hilliard free energy, GNBC, plus general considerations. “Material constants” determined (measured) from MD. Comparisons between MD and continuum results show the validity of GNBC.