Modelling of diffuse interfaces with temperature gradients

The work is devoted to capillary phenomena in miscible liquids under the assumption that they have a constant and the same density. The model consists of the heat equation, diffusion equation, and the Navier-Stokes equations with the Korteweg stress. We study several configurations corresponding to the microgravity experiments planned for the International Space Station. The basic conclusion of the numerical simulations is that transient capillary phenomena in miscible liquids exist and can produce convective flows sufficiently strong to be observed experimentally. In particular, there exists a miscible analogue to the Marangoni convection where the temperature gradient is applied along the transition zone between two fluids. Convection also appears if, instead of the temperature gradient, the case where the width of the transition zone varies in space is considered. Finally, similar to the immiscible case, miscible drops move in a temperature gradient.