Simulation of the sedimentation of melting solid particles

This study is motivated by the fact that dispersed two-phase flows are often accompanied by interfacial activities such as chemical reaction and phase change. Toward an understanding of the role of interfacial transport, we numerically simulate the sedimentation of melting solid particles in a Newtonian fluid. The fluid flow and solid motion determine the fluid–solid heat transfer and hence the melting rate. The thermal convection and interfacial morphology, in return, affect the motion of both phases. The two-dimensional Navier–Stokes and energy equations are solved at moderate Reynolds numbers by a finite-element method, and the melting interface is determined from the local heat flux. The motion of each solid particle is tracked using an arbitrary Lagrangian–Eulerian scheme. Results show that the sedimentation of melting particles is largely governed by the competition between the upward flow of the warm upstream fluid and the downward flow of the cold melt. A single particle settling in a channel may be pushed away from the centerline toward the wall. A pair of particles interact in a complex way, separating at low Grashof number Gr and attracting each other at high Gr. These results have interesting implications for the formation of microstructures in interfacially active two-phase flows.