Deformation of a droplet adhering to a solid surface in shear flow: onset of interfacial sliding

Abstract

In this paper we consider the dynamics of droplets attached to rough or chemically inhomogeneous solid substrates with a circular contact line as they are deformed in subcritical and supercritical simple shear flows. Our main interest is concentrated on identifying the portions of the contact line where the contact angle hysteresis condition is first violated, i.e. the portions of the contact line which slide first. To address this physical problem, we employ our fully implicit time integration algorithm for interfacial dynamics in Stokes flow. Our study reveals that droplets with small and moderate initial angles show an early period where both upstream and downstream sliding are equally favourable as well as a late downstream-favoured period. By contrast, droplets with large initial angles, after a rather small early equally favourable period, show a large period where downstream sliding is more favourable than the upstream sliding. Owing to the surface tension force, droplets with intermediate initial angles are shown to be more stable. Droplets with different viscosity ratio show similar behaviour with respect to the onset of interfacial sliding; however, the viscosity ratio strongly affects the rate of the interfacial deformation and the equilibrium conditions. An asymptotic behaviour for very small or large viscosity ratios is shown to exist.