Separation of Binary Alloys in Thin Capillaries

Abstract

A direct numerical simulation of the process of binary alloy separation in a thin nonuniformly heated circular capillary is carried out. The key point of this process is the assumption of the existence of a thin gas layer between the melt and the boundary of the reservoir due to the non-wetting conditions. This effect was described using the equations of interphase hydrodynamics, which made it possible to construct a phenomenological model of the processes at the melt-solid interface for mixtures of liquid metals. The problem was solved by the finite difference method in combination with an explicit scheme on the PGNIU-Kepler supercomputer at the Research and Education Center “Parallel and Distributed Computing” of the Perm State National Research University. The velocity and temperature fields, as well as the concentration of melt components in the bulk and on the surface, were determined through numerical simulation. The dynamics of the separation process is described. It is shown that the longitudinal temperature gradient and the non-wetting conditions on the lateral surface create a downward motion of the melt along the boundary, which, together with the adsorption and desorption effects, leads to the formation of volumetric nonuniformity of the concentration of the mixture components along the capillary. The experimentally observed time dependence of the difference in the volume concentrations of the components at the ends of the capillary is reproduced. The distribution of volume concentrations of the components and the surface phase along the capillary is analyzed at various values of the adsorption and desorption coefficients and the Marangoni number. The dependence of the concentration difference for the melt components at the ends of the capillary as function of its length is studied. It is found that the separation effect intensifies with an increase in the capillary length. A qualitative and quantitative comparison of most of the characteristics demonstrates a good correlation of the calculation results with the data previously obtained for the plane problem and the available experimental data. A numerical experiment shows that the motion in the surface layer is rather intense. The heavy component is transported by the convective flow to the lower part of the capillary so that its concentration increases by almost an order of magnitude on 1/8 of the capillary surface.