Directional motion of vibrated sessile drops : a quantitative study

The directional motion of sessile drops can be induced by slanted mechanical vibrations of the substrate. As previously evidenced \cite{Brunet07,Brunet09,Noblin09}, the mechanical vibrations induce drop deformations which combine 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 $\eta$ and the angle between the substrate and the forcing axis $\alpha$. 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 $s=\frac{\Delta <v>}{\Delta A}$. It is found that $s$ can show a sharp maximal value close to the resonance frequency of the first axisymmetric mode $f_p$. The value of $s$ tends to be almost independent on $\eta$ below 50 cSt, while $s$ decreases significantly for higher $\eta$. Also, it is found that for peculiar sets of parameters, particularly with $f$ far enough from $f_p$, 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.