Solidification using smoothed particle hydrodynamics

We show how the numerical particle method smoothed particle hydrodynamics (SPH) can be used to the simulate the freezing of one and two-component (binary alloy) systems. We first study the freezing of a pure a liquid, and compare our computations against exact results for one and two dimensional systems, including cases where there are point sources and the boundary of the system is irregular. The agreement with theory, where it is available, is very satisfactory. We then consider a two-component system which is initially entirely liquid and model it by a set of liquid SPH particles together with a set of virtual solid SPH particles which initially have no mass. During the thermal evolution and solidification of the system, mass is transferred from the liquid SPH particles to the ice (solid) SPH particles. For a binary melt, as the volume fraction of the solid increases the composition of the liquid is enriched in the component of the alloy that does not form the solid phase. In the case of salty water, this component is the salt. We find that the variation of temperature and liquid composition calculated with SPH is in close agreement with previous theories of mushy layers and gives similar agreement with experiment. In this initial study we simplify the calculations by assuming the solid particles remain in the position where they are formed: a good approximation for the case where the solution is cooled from above to form ice leaving behind a relatively light residual liquid, or cooled from below leaving behind a relatively heavy liquid. We compare our results with experiments on the freezing from below of an aqueous sodium nitrate solution [Nature 314 (1985) 703], and find that the agreement is very satisfactory.