title: Thick drops on a slowly oscillating substrate.
abstract: 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 ε(*), the drop climbs uphill. ε(*), however, strongly depends on the thickness of the drop, which, in turn, depends on the liquid's equilibrium contact angle β[over ¯]. In particular, there is a dramatic decrease in ε(*) when β[over ¯] 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.
authors.affiliation: Department of Mathematics, University of Limerick, Limerick, Ireland.
authors.forename: E S
authors.initials: ES
authors.lastname: Benilov
authors.forename: C P
authors.initials: CP
authors.lastname: Cummins