Date of Original Version
When boundary conditions arising from the usual hydrodynamic assumptions are applied, analyses of dynamic wetting processes lead to a well-known nonintegrable 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 contact line processes. The calculations reveal that up to Capillary number Ca50.15, the velocity along an arc of radius 10Li (Li is an inner, microscopic length scale! from the dynamic contact line is independent of the macroscopic length scale a for a.103Li , and compares well to the leading order analytical ‘‘modulated-wedge’’ flow field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] for Capillary number Ca,0.1. Systematic deviations between the numerical and analytical velocity field occur for 0.1,Ca,0.15, caused by the inadequacy of the leading order analytical solution over this range of Ca. Meniscus shapes produced from calculations in a truncated domain, where the modulated-wedge velocity field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] is used as a boundary condition along an arc of radius R 51022a from the dynamic contact line, agree well with those using two inner slip models for Ca
Somalinga, Sandesh and Arijit Bose. "Numerical Investigation of Boundary Conditions for Moving Contact Line Problems." Physics of Fluids. 12(3):499-510. March 2000. Available at http://link.aip.org/link/?phf/12/499.