Influence of slow rotation on the stability of a thermocapillary incompressible liquid flow in an infinite layer under zero-gravity conditions for small Prandtl number

Abstract

Instability of a thermocapillary flow arising in a rotating thin infinite liquid layer under zero-gravity conditions is investigated. Both boundaries of the layer are assumed to be plane and free and are subject to the tangential thermocapillary Marangoni force. A convective heat transfer at the boundaries is governed by Newton's law and the temperature of the fluid near the boundaries is a linear function of the coordinates. The axis of rotation is perpendicular to a liquid layer. The rotation is slow, which allows us to neglect the centrifugal force. The examined thermocapillary flow is described analytically, being an exact solution of the Navier–Stokes equations. According to the linear theory of stability the obtained neutral curves depict the dependence of the critical Marangoni number on the wave number at different values of the Taylor number for the small Prandtl number (Pr = 0.1). The behavior of the finite-amplitude perturbations beyond the stability threshold is studied numerically.