Numerical Simulation of Solidification of Colloidal Suspensions Inside a Differentially-Heated Cavity

Abstract

Development of the solid-liquid interface, distribution of the particle concentration field, as well as the development of thermo-solutal convection during solidification of colloidal suspensions in a differentially-heated cavity is investigated. The numerical model is based on the one-fluid-mixture approach combined with the single-domain enthalpy-porosity model for phase change. The linear dependence of the liquidus concentration of the nanoparticles was assumed. A colloidal suspension consisting of water and copper, and alumina nanoparticles were considered. In the current investigation, the nanoparticle size selected was 2 nm. The suspension was solidified unidirectionally inside a square differentially-heated cavity that was cooled from the left side. It was found that the solid-liquid interface changed its morphology from a planar shape to a dendritic one as the solidification process proceeds in time, due to the constitutional supercooling that resulted from the increased concentration of particles at the solid-liquid interface rejected from the crystalline phase. Initially, the flow consisted of two vortices rotating in opposite directions. However, at later times only one counter clockwise rotating cell survived. Changing the material of the particle to alumina results in crystallized phase with a higher concentration of particles if it is compared to that of the solid phase resulted from freezing the copper-water colloidal suspension. Decreasing the segregation coefficient destabilize the solid-liquid interface, and increase the intensity of the convection cell with respect to that of the case of no particle rejection. At slow freezing rates, the crystal phase resulted consisted of lower particle content if it is compared to that resulted from higher freezing rate.