Effect of solid–liquid density change on dendrite tip velocity and shape selection

Phase-field simulations are used to examine tip velocity and shape selection in free dendritic growth of a pure substance into an undercooled melt in the presence of a density change between the solid and liquid. The dendrite is assumed to grow two-dimensionally inside a Hele-Shaw cell. The phase-field model is coupled with a previously developed two-phase diffuse interface model to simulate the flow in the liquid that is induced by the density change. The predicted dependence of the dendrite tip growth Péclet number on the relative density change is compared with an available analytical solution and good agreement is obtained. The simulations verify that the dendrite tip selection parameter, modified to account for the different densities of the solid and liquid phases, is independent of the relative density change.