  A pinned or free-floating rigid plate lying on the free surface of a thin
film of viscous fluid, which itself lies on top of a horizontal substrate that
is moving to the right at a constant speed is considered. The focus of the
present work is to describe how the competing effects of the speed of the
substrate, surface tension, viscosity, and, in the case of a pinned plate, the
prescribed pressure in the reservoir of fluid at its upstream end, determine
the possible equilibrium positions of the plate, the free surface, and the flow
within the film. The present problems are of interest both in their own right
as paradigms for a range of fluid-structure interaction problems in which
viscosity and surface tension both play an important role, and as a first step
towards the study of elastic effects.
