Gravitational effects on the deformation of a droplet adhering to a horizontal solid surface in shear flow

Abstract

In this paper we investigate the gravitational effects on the deformation of a three-dimensional droplet adhering to a horizontal rough solid surface in steady shear Stokes flows. Our study considers both positive and negative Bond numbers for viscous and inviscid droplets. When the interfacial system is initially at hydrostatic equilibrium, our study shows that the Bond number affects the deformation of viscous droplets with moderate and large initial contact angles in a different way than those for small angles owing to the interplay between the viscous and surface tension forces. Inviscid droplets with different initial contact angles show similar behavior as the Bond number increases, i.e., their deformation is monotonically decreased owing to the monotonic decrease of the droplets’ height and thus the exerted pressure force. Our study identifies the gravitational effects of the onset of interfacial sliding, i.e., on the portions of the contact line which slide first due to violation of the hysteresis condition. When the interfacial system is not at hydrostatic equilibrium at the flow initiation, its dynamic evolution is more complicated owing to the combined action of the shear flow with the gravitational forcing due to the difference between the initial shape with the hydrostatic one. Our computational results are accompanied with an analysis of the forces on the droplet which provides physical insight and identifies the three-dimensional nature of the interfacial deformation.