Numerical investigation of boundary conditions for moving contact line problems

When boundary conditions arising from the usual hydrodynamic assumptions ar e applied, analyses of dynamic wetting processes lead to a well-known nonin tegrable stress singularity at the dynamic contact line, necessitating new ways to model this problem. In this paper, numerical simulations for a set of representative problems are used to explore the possibility of providing material boundary conditions for predictive models of inertialess moving c ontact line processes. The calculations reveal that up to Capillary number Ca = 0.15, the velocity along an arc of radius 10L(i) (L-i is an inner, mic roscopic length scale) from the dynamic contact line is independent of the macroscopic length scale a for a > 10(3)L(i), and compares well to the lead ing order analytical "modulated-wedge" flow field [R. G. Cox, J. Fluid Mech . 168, 169 (1986)] for Capillary number Ca < 0.1. Systematic deviations bet ween the numerical and analytical velocity field occur for 0.1 < Ca < 0.15, caused by the inadequacy of the leading order analytical solution over thi s range of Ca. Meniscus shapes produced from calculations in a truncated do main, where the modulated-wedge velocity field [R. G. Cox, J. Fluid Mech. 1 68, 169 (1986)] is used as a boundary condition along an arc of radius R = 10(-2)a from the dynamic contact line, agree well with those using two inne r slip models for Ca < 0.1, with a breakdown at higher Ca. Computations in a cylindrical geometry reveal the role of azimuthal curvature effects on ve locity profiles in the vicinity of dynamic contact lines. These calculation s show that over an appropriate range of Ca, the velocity field and the men iscus slope in a geometry-independent region can potentially serve as mater ial boundary conditions for models of processes containing dynamic contact lines. (C) 2000 American Institute of Physics. [S1070-6631(00)00402-5].