Interaction between an in-flow particle and phase change

The motion of a rigid particle which is in flight close to a solidifying or melting wall-embedded substrate is modelled for unsteady planar flow. The particle as well as the particle–substrate gap width are modelled as thin, which allows the equations governing fluid flow to be reduced to thin-layer form. The small Prandtl number limit is also exploited, which allows the fluid temperature to be obtained in closed form. Numerical simulations of the interactive system reveal four types of terminal solution behaviour, namely a collision (strictly near collision) between the substrate boundary and front, middle or back of the particle, or a fly-away phenomenon as the particle departs comparatively far from the substrate. For the case of a mid-body collision, a local analysis reveals an intricate asymptotic structure for the model solutions. The case of a rigid substrate and melting or solidifying particle is also examined.