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### ·s»D¼ÐÃD¡G¡@( 2007-10-01 )

ºtÁ¿¥DÃD¡G¡]¨ú®ø¡^Unified Approach to the Hydrodynamic Boundary Conditions and Equations of Motion

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While widely used and accepted, the non-slip hydrodynamic boundary condition at the liquid-solid interface is controversial mainly due to the lack of a rigorous proof and its incompatibility with the moving contact line, defined as the (moving) inter- section of the immiscible fluid-fluid interface with the solid wall. The latter problem has been shown by Dussan and Davis in 1974 to yield diverging dissipation. We extend the Helmholtz theorem for the bulk fluid, which states that under given boundary conditions, the hydrodynamic equation of motion (the Stokes equation) may be deduced from the principle of minimum energy dissipation, to include the boundary condition as well. By treating the liquid and solid as molecules with different interactions, the minimization of the total dissipation (bulk plus interface) yields the Stokes equation plus the Navier boundary condition. Direct extension of this principle, through the phase field approach with the Cahn Hilliard free energy for the fluid-fluid interface, yields a consistent hydrodynamics in which the moving contact line problem is resolved. The results obtained from continuum calculations are in quantitative agreement with the molecular dynamic simulations.

Implications of our work will be discussed.