On the onset of motion of sliding drops

In this article we numerically investigate the onset of motion of liquid drops in contact with a plane and homogeneous substrate with contact angle hysteresis. The drops are driven by a body force F = ρgV, where ρ is the density of the liquid, g is the acceleration of gravity, and V is the volume of the drop. We compare two protocols to vary the bond number Bo = λ(v)/λ(c) by changes of either the drop size λ(v) = V(1/3) or the capillary length λ(c) = (γ/ρg)(1/2) where γ is the interfacial tension, revealing that the transition between pinned and steady moving states can be either continuous or discontinuous. In a certain range both pinned and moving states can be found for a given bond number Bo, depending on the history of the control parameters g and V. Our calculations are extended to arbitrary combinations of static advancing and receding contact angles and provide a comprehensive picture of the depinning transition induced by a quasi-static variation of the control parameters. Finally, we demonstrate that the particular form of the contact line mobility in our model has an impact on the interfacial shape of steady moving drops.