Stability of Marangoni convection in a thin film under the influence of vertical vibrations

Abstract

In this article we consider impact of vertical vibration on longwave Marangoni convection in a thin layer heated from below. The thermal conductivity of the lower solid boundary is assumed high. Vibration period is comparable with the characteristic time of the film evolution, vibration amplitude is of the order of the layer thickness. We have demonstrated that under above conditions the vibration results only in the gravity modulation in the conventional amplitude equation. The stability study showed that in the absence of noise, vibrations do not change the threshold for convection; in the presence of noise, the layer is destabilized. Nonlinear calculations confirmed the last conclusion – subcritical occurrence of convection was detected. An asymptotic analysis, describing the transition with increasing vibration frequency from parametric influence to an averaged description, is also performed.