Faraday ripples, parametric resonance, and the Marangoni effect

In general, the combined actions of two destabilizing mechanisms do not sim ply add to each other. Here we show that there is a subtle interplay betwee n parametric excitation and thermal gradients leading to interfacial instab ility, overstability, and generation of surface waves. The case studied ref ers to the stability of a liquid layer with an open free surface subjected to a transverse temperature gradient (with the Marangoni effect) and also s ubjected to the simultaneous action of periodic vibrations normal to the la yer 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 excit ation of ripples with half the imposed vibration frequency, but their ampli tude depends on the Marangoni number. However, as the Marangoni number incr eases, the critical amplitude decreases from the excitation threshold of Fa raday ripples, and after passing through a minimum it monotonically increas es with increasing thermal gradient, Another salient finding is that the th reshold of the Marangoni overstability is found to be independent of the im posed vibration frequency and amplitude. (C) 2001 Academic Press.