Binary alloys separation in thin capillaries

Direct numerical simulation of the process of binary alloy separation in a thin non-uniformly heated circular capillary is carried out. The key point of the process under consideration is the assumption of the existence of a thin gas layer between the melt and the capillary wall due to non-wetting condition. Equations of interfacial hydrodynamics are used to describe the effect of separation, which allows us to develop a phenomenological model of the processes at the melt - solid boundary interface for mixtures of liquid metals. The finite difference method in combination with the explicit scheme is used for solving the problem. The calculations have been carried out on the supercomputer “PSU-Kepler” of the Scientific and Educational Center “Parallel and Distributed Calculations” in Perm State National Research University. Velocity and temperature fields, as well as the concentration of melt components in the volume and on the surface, are determined through numerical simulations. The dynamics of the separation process is described in detail. It has been found that the longitudinal temperature gradient and the non-wetting condition on the lateral capillary side generate a downward movement along the external boundary, which, together with adsorption and desorption effects, lead to the formation of volume concentration non-uniformity along the capillary. The temporal evolution of the volume concentrations difference along the capillary observed in experiments is reproduced numerically. The distributions of volume concentrations and the surface phase are studied as a function of both Marangoni number and adsorption-desorption coefficients. Concentration differences for alloy components are studied in relation to the capillary length. It has been shown that an increase in the capillary length leads to the strengthening of the separation effect. The qualitative and quantitative comparison of most characteristics demonstrates that the calculated data are in good agreement with the numerical results of the plane problem considered earlier and with the available experimental data. Numerical experiments show that the movement in the surface layer is quite intensive. The heavy component is transported by the convection flow towards the lower part of the capillary so that its concentration increases by the order of magnitude on the 1/8 part of the capillary surface.