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Unformatted text preview: Molecular hydrodynamics of the moving contact line in collaboration with Ping Sheng ( Physics Dept, HKUST ) XiaoPing Wang ( Mathematics Dept, HKUST ) Tiezheng Qian Mathematics Department Hong Kong University of Science and Technology SISSA Trieste Italy, May 2007 The noslip boundary condition and the moving contact line problem The generalized Navier boundary condition (GNBC) from molecular dynamics (MD) simulations Implementation of the new slip boundary condition in a continuum hydrodynamic model (phasefield formulation) Comparison of continuum and MD results A variational derivation of the continuum model, for both the bulk equations and the boundary conditions, from Onsagers principle of least energy dissipation (entropy production) Wetting phenomena: All the real world complexities we can have! Moving contact line: All the simplifications we can make and all the simulations, molecular and continuum , we can carry out! Numerical experiments Offer a minimal model with solution to this classical fluid mechanical problem, under a general principle governing thermodynamic irreversible processes NoSlip Boundary Condition , A Paradigm = slip v = slip v ? n from Navier Boundary Condition to NoSlip Boundary Condition : slip length , from nano to micrometer Practically, no slip in macroscopic flows = s slip l v / / R l U v s slip : shear rate at solid surface s l R U / (1823) 1 2 cos = + s Youngs equation (1805): s d velocity discontinuity and diverging stress at the MCL a R a dx x U The HuhScriven model Shear stress and pressure vary as (linearized NavierStokes equation) 8 coefficients in A and B, determined by 8 boundary conditions for 2D flow Dussan and Davis, J. Fluid Mech. 65 , 7195 (1974): 1. Incompressible Newtonian fluid 2. Smooth rigid solid walls 3. Impenetrable fluidfluid interface 4. Noslip boundary condition Stress singularity: the tangential force exerted by the fluid on the solid surface is infinite. Not even Herakles could sink a solid ! by Huh and Scriven (1971). a) To construct a continuum hydrodynamic model by removing condition (3) and/or (4). b) To make comparison with molecular dynamics simulations Koplik, Banavar and Willemsen, PRL (1988) Thompson and Robbins, PRL (1989) Slip observed in the vicinity of the MCL Boundary condition ??? Continuum deduction of molecular dynamics ! Numerical experiments done for this classic fluid mechanical problem Immiscible twophase Poiseuille flow The walls are moving to the left in this reference frame, and away from the contact line the fluid velocity near the wall coincides with the wall velocity. Near the contact lines the noslip condition appears to fail , however. The discrepancy between the microscopic stress and suggests a breakdown of local hydrodynamics ....
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 Winter '08
 JARVIS
 Math

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