The phenomenon in which a solid phase moves in a liquid phase while undergoing melting and solidification is observed in the transport of phase change materials, such as ice slurry flows. When the solid phase is treated as a rigid body, its equations of motion should be expressed in a form that incorporates the effects of melting and solidification into the equations for rigid-body dynamics. In particular, the mass and inertia moment of the solid phase vary in time, and the position of its centre of mass (COM) shifts if the phase change is non-uniform. However, existing studies have generally neglected these effects and adopted the same form as the rigid-body dynamic equations. In this study, using an approach analogous to the derivation of fluid dynamic equations, we derive the equations of motion for a solid phase moving in a liquid phase while melting and solidification. The surface of the solid is assumed to deform at the Stefan velocity determined by the Stefan condition. Accordingly, mass, momentum and angular momentum fluxes flow in and out across the surface due to the Stefan velocity and the induced jet associated with density change. By considering these momentum fluxes, the translational and rotational equations of motion are derived from the translational and angular momentums balance, respectively. The derived equations differ formally from the conventional rigid-body dynamic equations owing to the additional flux terms due to density change and the COM shift due to non-uniform deformation.
Suzuki et al. (Mon,) studied this question.