Crucial flow stabilization and multiple instability branches of gravity-driven films over topography

Abstract

In this paper, we present experimental results on the linear instability of gravity-driven viscous films flowing down a strongly undulated incline. To systematically investigate the relation between the eddies which form in the troughs of sufficiently steep undulations and the corresponding stability maps, we vary the liquid's viscosity experimentally. We report on a rich variety of phenomena, which is provoked by the corrugation of the underlying substrate, including: (a) transitions from long-wave to short-wave type instability, (b) a disjoining of the instability branches leading to formation of isles in the stability map, (c) flow destabilization, but also, (d) very strong stabilization of the flow up to a factor of two for arbitrary linear disturbances and even up to a factor of four for linear short-wave disturbances. To our knowledge, this is the first experimental work, which reports on any of these phenomena for gravity-driven liquids flowing down an undulated incline. Since structured substrates turn out to hold an enormous potential for crucial film flow stabilization, we present a first approach for a topography shape, based on the shape of the eddy, which is optimized in terms of flow stability.