Linear and nonlinear stability of hydrothermal waves in planar liquid layers driven by thermocapillarity

Abstract

A shallow planar layer of liquid bounded from above by gas is set into motion via the thermocapillary effect resulting from a thermal gradient applied along its interface. Depending on the physical properties of the liquid and the strength of the gradient, the system is prone to departure from its equilibrium state and to the consequent development of an oscillatory regime. This problem is numerically investigated for the first time by means of two-phase direct numerical simulations fully taking into account the presence of a deformable interface. Obliquely travelling hydrothermal waves (HTWs), similar to those first described by Smith and Davis [J. Fluid Mech. 132, 119-144 (1983)], are reported presenting good agreement with linear stability theory and experiments. The nonlinear spatiotemporal growth of the instabilities is discussed extensively along with the final bulk flow for both the liquid and gas phases. Our study reveals the presence of interface deformations which accompany the HTWs pattern with a certain time-delay. The local interface heat fluxes are found to be significantly affected by the transient nature of the HTWs, contradicting the results of previous single-phase studies. (C) 2013 AIP Publishing LLC.