Marangoni and Natural Convection in a Horizontal Layer of Viscoplastic Fluid with Concentration Dependent Yield Stress. Exact Analytical Solutions

Abstract

A variety of exact analytical solutions describing natural and thermocapillary convection in a horizontal single and double layer system consisting of Newtonian and viscoplastic fluids subjected to a longitudinal temperature gradient is constructed. Transport and rheological parameters of the media depend on the local concentration. A non-homogeneous concentration field is induced by mass transfer in vertical direction and by the Soret effect. The lower boundary of the system is a solid wall with no-slip, while the upper one is a free boundary. It was demonstrated that, depending on the governing parameters of the system, a viscoplastic layer may be entirely or partially yielded or completely unyielded. If the yield stress is the function of concentration, the latter determines positions of yielded and unyielded regions. The dependence of the flow patterns (appearance and position of unyielded regions), velocity profile and mass and heat transfer rate on the governing parameters have been studied. Special attention was paid to the effect of concentration dependence of the yield stress and to the Soret effect.