Drops climbing uphill on a slowly oscillating substrate

We examine the dynamics of a two-dimensional drop on an inclined substrate vibrating vertically. The drop is assumed to be driven by its contact lines, while its shape is determined by a quasistatic balance of surface tension, gravity, and vibration-induced inertial force. It is shown that, if the dependence of the inertial force on time involves narrow/deep "troughs" and wide/low "plateaus," the drop can climb uphill. For thin drops, this conclusion is obtained analytically, whereas the general case is treated numerically. It is demonstrated that the nonlinear effects (associated with the large thickness of the drop) dramatically strengthen the drop's uphill motion.