Numerical Simulations of Transient Interfacial Phenomena in Miscible Fluids

Abstract

To study theoretically interfacial (capillary) phenomena in miscible fluids, we consider a continuous medium with a composition gradient. We describe it with the model consisting of the heat and diffusion equations with convective terms and of the Navier-Stokes equations with an additional volume force written in the form of the Korteweg stresses arising from nonlocal interaction in the fluid. It is proportional to the square of the composition gradient with the proportionality coefficient depending on temperature. We carry out numerical simulations of this model and show that the capillary force can cause convection in the initially quiescent liquid. For physically realistic values of parameters the liquid motion, though decreasing rapidly in time, can probably be observed experimentally. The proportionality coefficient, k, is the same square gradient parameter in the Cahn-Hilliard theory for diffuse interfaces and for phase separation. We estimate it on the basis of measurements from spinning drop tensiometry and light scattering for two systems: poly(dodecyl acrylate)/dodecyl acrylate and glycerin/water. Because concentration and temperature gradients also cause buoyancy-induced convection, experiments must be performed in weightlessnes s. Therefore, long term, high quality weightlessness is required to test the predictions of the modeling, and we propose a photopolymerization system to create the concentration and temperature gradients. Transient Interfacial Phenomena in Miscible Polymer Systems (TIPMPS) and a Microgravity Science Glovebox experiment, Miscible Drop in Microgravity (MDMG) are both planned for the International Space Station.