Novel criteria for the development of monotonic and oscillatory instabilities in a two-layer film

Abstract

The development of the Marangoni instability in a two-layer film in the presence of a transverse temperature gradient and a heat source/sink at the liquid-liquid interface is investigated. The problem is solved by means of a linear stability theory and nonlinear simulations. Novel criteria for the development of monotonic and oscillatory instabilities have been formulated. It has been found that the nonlinear development of a monotonic instability leads to a rupture of the bottom layer or the top layer. Numerous types of nonlinear film evolution have been observed in the case of an oscillatory instability, among them alternating roll patterns of different scales and orientations, temporally non-periodic motions, and the rupture of either layer.