Directional motion of vibrated sessile drops: a quantitative study

Abstract

The directional motion of sessile drops can be induced by slanted mechanical vibrations of the substrate, which induce drop deformations combining both axisymmetric and antisymmetric modes. In this paper, we establish quantitative trends from experiments conducted within a large range of parameters, namely, the amplitude A and frequency f of the forcing, the liquid viscosity η, and the angle between the substrate and the forcing axis α. These experiments are carried out on weak-pinning substrates. For most parameters sets, the averaged velocity ⟨v⟩ grows linearly with A. We extract the mobility, defined as s=Δ⟨v⟩/ΔA. It is found that s can show a sharp maximal value close to the resonance frequency of the first axisymmetric mode f[subscript p]. The value of s tends to be almost independent on η below 50 cSt, while s decreases significantly for higher η. Also, it is found that for peculiar sets of parameters, particularly with f far enough from f[subscript p], the drop moves in the reverse direction. Finally, we draw a relationship between ⟨v⟩ and the averaged values of the dynamical contact angles at both sides of the drop over one period of oscillation.