Thick drops on a slowly oscillating substrate

We examine the evolution of a liquid drop on an inclined substrate oscillating vertically. The oscillations are weak and slow, which makes the liquid's inertia and viscosity negligible (so that the drop's shape is determined by a balance of surface tension, gravity, and vibration-induced inertial force). No assumptions are made about the drop's thickness, which extends our previous results on thin drops [Benilov, Phys. Rev. E 84, 066301 (2011)] to more realistic situations. It is shown that, if the amplitude of the substrate's oscillations exceeds a certain threshold value epsilon(*), the drop climbs uphill. epsilon(*), however, strongly depends on the thickness of the drop, which, in turn, depends on the liquid's equilibrium contact angle (beta) over bar. In particular, there is a dramatic decrease in epsilon(*) when (beta) over bar exceeds a certain threshold, which means that thick drops climb uphill for a much weaker vibration of the substrate. At the same time, the frequency range of the substrate's vibration within which drops climb uphill becomes much narrower.