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Hydrodynamic Slip Boundary Condition for the Moving Contact Line

Hydrodynamic Slip Boundary Condition for the Moving Contact Line. in collaboration with Xiao-Ping Wang ( Mathematics Dept, HKUST ) Ping Sheng ( Physics Dept, HKUST ). ?. No-Slip Boundary Condition. from Navier Boundary Condition to No-Slip Boundary Condition.

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Hydrodynamic Slip Boundary Condition for the Moving Contact Line

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  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-SlipBoundary Condition

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

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

  5. 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 Sin the vicinity of the contact line, then what is the magnitude of S ?

  6. Molecular dynamics simulationsfor 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

  7. Modified Lennard-Jones Potentials for likemolecules for molecules of different species for wetting property of the fluid

  8. boundary layer tangential momentum transport

  9. The Generalized NavierB. C. when the BL thickness shrinks down to 0 viscous part non-viscous part Origin?

  10. uncompensated Young stress nonviscous part viscous part

  11. Uncompensated Young Stressmissed in Navier B. C. • Net force due to hydrodynamic deviation from static force balance (Young’s equation) • NBCNOTcapable of describing the motion of contact line • Away from the CL, the GNBC implies NBCfor single phase flows.

  12. Continuum Hydrodynamic ModelingComponents: • 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

  13. molecular positionsprojected onto the xz plane

  14. near-total slipat moving CL SymmetricCoutte V=0.25 H=13.6 no slip

  15. profiles at different z levels symmetric Coutte V=0.25 H=13.6 asymmetricCoutte V=0.20 H=13.6

  16. asymmetric Poiseuillegext=0.05 H=13.6

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

  18. 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.

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