Linear oscillatory cellular thermocapillary convection in liquid layers

Abstract

A linear stability analysis is performed on a thermal, stratified liquid layer with a deformable thermocapillary surface. The objective is to investigate the possibility and conditions for existence of oscillatory cellular convection in the linear thermocapillary system. In general, the principle of the exchange of stabilities for the onset of cellular convection in liquid layers with deformable surfaces may not hold, especially for systems with small Prandtl numbers. This study discloses the characteristics of a linear oscillatory convection and associated interfacial wave in a thermocapillary liquid layer. The Marangoni number for the onset of oscillatory convection as overstability as well as the corresponding wave number and frequency for various Prandtl and Crispation numbers are determined based on the linear stability theory. The characteristics for overstability in the thermocapillary system are treated for both surface cooling and heating cases. The regions for existence of overstability and the effects of the Prandtl and Crispation numbers are investigated.