Faraday Ripples, Parametric Resonance, and the Marangoni Effect

In general, the combined actions of two destabilizing mechanisms do not simply add to each other. Here we show that there is a subtle interplay between parametric excitation and thermal gradients leading to interfacial instability, overstability, and generation of surface waves. The case studied refers to the stability of a liquid layer with an open free surface subjected to a transverse temperature gradient (with the Marangoni effect) and also subjected to the simultaneous action of periodic vibrations normal to the layer. Stability is examined in the weak viscosity approximation by applying a multiscale method. To a first approximation, whatever the imposed thermal gradient, vibrations with fairly large amplitude are responsible for excitation of ripples with half the imposed vibration frequency, but their amplitude depends on the Marangoni number. However, as the Marangoni number increases, the critical amplitude decreases from the excitation threshold of Faraday ripples, and after passing through a minimum it monotonically increases with increasing thermal gradient. Another salient finding is that the threshold of the Marangoni overstability is found to be independent of the imposed vibration frequency and amplitude. Copyright 2001 Academic Press.