A Model for Estimating the Dynamic Contact Angle with Molecular Dynamics Simulation

Abstract

The microscopic configuration of fluid interface near the wetting or dewetting front (i.e., moving contact line) is of significant interest in relation to many industrial processes. In this paper we report on molecular dynamics (MD) simulations conducted for investigation of the dependence of the microscopic contact angle θ on the speed of contact line relative to the solid surface, ΔV. Our simulations were made for a Couette flow geometry where two Lennard-Jones (LJ) liquids are sheared between two solid walls moving at a speed V in opposite directions. The two liquids are immiscible and have different wall-wetting properties. The liquid configuration remains unchanged with time, since ΔV=V at all the contact lines, for V below a certain critical value. The contact angle θ measured under such steady conditions varies monotonically with ΔV. Above the critical wall speed, however, the flow at the receding contact line, where the more wetting liquid of the two is being replaced by the less wetting one, starts becoming unsteady, as ΔV remains smaller than the critical wall speed. We show that the viscous and pressure forces measured from the MD simulation results can be reproduced by the Stokes flow model of Huh and Scriven (1971) using the MD-predicted value of θ at the given ΔV. It follows that, by the aid of Qian et al.'s formulation (2003) of the stress balance at the moving contact line, and by using the MD-predicted proportionality constant between the total wall-tangential force and ΔV, this model can reproduce the MD-predicted dependence of θ on ΔV. The model predictions, furthermore, give insight into the reason why the contact line flow becomes unsteady above the critical wall speed.