The directional motion of sessile drops can be induced by slanted mechanical vibrations of the substrate. As previously evidenced , 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 $$ grows linearly with $A$. We extract the mobility, defined as $s=\frac{\Delta }{\Delta A}$. It is found that $s$ can show a sharp maximal value close to the resonance frequency of the first axisymmetric mode $f_p$. The value of $s$ tends to be almost independent on $\eta$ below 50 cSt, while $s$ decreases significantly for higher $\eta$. Also, it is found that for peculiar sets of parameters, particularly with $f$ far enough from $f_p$, the drop moves in the reverse direction. Finally, we draw a relationship between $$ and the averaged values of the dynamical contact angles at both sides of the drop over one period of oscillation.

中文翻译：

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振动无柄滴的定向运动：定量研究

固着液滴的定向运动可以由基板的倾斜机械振动引起。如前所述，机械振动会引起液滴变形，该变形结合了轴对称和反对称模式。在本文中，我们通过在较大范围的参数（即幅度）中进行的实验来建立定量趋势$\mathrm{一种}$ 和频率 $F$ 的力，液体粘度 $\eta$ 基材与施力轴之间的角度 $\alpha$。这些实验是在弱钉扎基板上进行的。对于大多数参数集，平均速度$$随着$ A $线性增长。我们提取迁移率，定义为$ s = \ frac {\ Delta} {\ Delta A} $。已经发现，$ s $可以显示接近第一轴对称模式$ f_p $的共振频率的急剧的最大值。低于50 cSt的$ \ eta $时，$ s $的值往往几乎独立，而较高的\\ eta $则$ s $显着下降。而且，发现对于特殊的参数集，尤其是$ f $距离$ f_p $足够远时，下降沿相反方向移动。最后，我们绘制了$$和一个振荡周期内液滴两侧的动态接触角平均值之间的关系。