Pattern formation in buoyant-thermocapillary convection currents in thin liquid layers: A comparison of numerical simulations and experiments

Abstract

In this paper, we report on three-dimensional numerical simulations of buoyant-thermocapillary convection in thin liquid layers, to study the formation of hydrothermal waves (HTW) in environments typical of those encountered in material processing for single-crystal fabrication. Our model consists of a fluid with a Prandtl number of 16.1 in a rectangular geometry with step-like thickness. We observed a discontinuous change in the wavelength and propagation angle of the HTW at the boundary of the step, demonstrating that HTW are a locally unstable phenomenon dependent on the local thickness of the liquid layer. The drastic modification to the propagation angle was caused primarily by a combination of thermocapillary and viscous forces, while buoyancy effects increase the thickness-dependent variation of wavelengths and propagation angles. In addition, we achieved the first successful recreation of the oscillatory multi-cells (OMC) structure found by Riley and Neitzel [J. Fluid Mech. 359 (1998)], demonstrating that in contrast to OMC observed in strong buoyancy conditions, these are generated by the superimposition of HTW and steady multi-cells (SMC).