Transcript Document
Hydrodynamic Slip Boundary Condition for the Moving Contact Line in collaboration with Xiao-Ping Wang (Mathematics Dept, HKUST) Ping Sheng (Physics Dept, HKUST) v slip 0 ? No-Slip Boundary Condition v slip 0 from Navier Boundary Condition to No-Slip Boundary Condition v slip ls : shear rate at solid surface ls : slip length, from nano- to micrometer Practically, no slip in macroscopic flows slip s v /U l / R 0 coss 2 1 No-Slip Boundary Condition ? Apparent Violation seen from the moving/slipping contact line Infinite Energy Dissipation (unphysical singularity) 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 ? 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 Modified Lennard-Jones Potentials U ff 4[( / r) ff ( / r) ] 12 6 U wf 4 wf [( wf / r) wf ( wf / r) ] 12 6 ff 1 for like molecules ff 1 for molecules of different species wf for wetting property of the fluid boundary layer tangential momentum transport The Generalized Navier B. C. ~f slip Gx vx ~f ~ Gx zx (0) when the BL thickness shrinks down to 0 Y ~ ~ zx (0) [ z vx ](0) zx (0) viscous part non-viscous part Origin? uncompensated Young stress Y Y 0 ~ (0) (0) (0) zx zx nonviscous part zx s ,d dx int 0 ,Y zx viscous part 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. 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 molecular positions projected onto the xz plane near-total slip at moving CL no slip vx / V 1 Symmetric Coutte V=0.25 H=13.6 v x (x) profiles at different z levels symmetric Coutte V=0.25 H=13.6 asymmetric Coutte V=0.20 H=13.6 asymmetric Poiseuille gext=0.05 H=13.6 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). 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.