Investigation of wetting hydrodynamics using numerical simulations

Meniscus shapes from a simulation of a plate immersing into an infinitely deep liquid bath, for a range of outer length scales, have been obtained numerically. These have been compared with the leading-order prediction from a three-region asymptotic analysis done in the double limit, Capillary number, Ca→0, LS/LC→0, with Ca ln(LC/LS) of O(1), where LS and LC represent the slip length and an outer macroscopic length, respectively. For Ca<0.01, the numerically computed and the perturbation solutions show excellent agreement. Within this range of Ca, the meniscus slope at a distance 10LS from the dynamic contact line is geometry independent, that is, does not vary with changes in the outer length LC. The interface slope at this point can serve as an appropriate material boundary condition for the outer problem. For 0.01