Wake transitions and melting dynamics of a translating sphere in warm liquid

We investigate the three-dimensional melting dynamics of an initially spherical particle translating in a warmer liquid using sharp-interface simulations that fully resolve both solid and fluid phases with the Stefan condition. A wide parameter space is explored, spanning initial Reynolds number ( $\textit{Re}_0$ ), Stefan number ( $\textit{St}$ ) and Richardson number ( $\textit{Ri}$ ). In the absence of buoyancy ( $\textit{Ri}= 0$ ), the interface evolution is governed by canonical wake bifurcations. Four regimes are identified: an axisymmetric regime ( $\textit{Re}_0\lt 212$ ) with a rounded front and planar rear; a steady planar-symmetric regime ( $212\lt \textit{Re}_0\lt 273$ ) with an inclined rear plane; a periodic planar-symmetric regime ( $273\lt \textit{Re}_0\lt 355$ ) where vortex shedding emerges in the wake; and a chaotic regime ( $\textit{Re}_0\gt 355$ ) with fluctuating stagnation points and a more rounded rear. Despite these differences, all regimes exhibit a tendency towards melt-rate homogenisation over time. Besides, we introduce an aspect-ratio-based surface-area formulation that yields a predictive model, accurately capturing volume evolution across regimes. Hydrodynamic loads also reflect the coupling between shape and flow: drag follows rigid-sphere correlations only at moderate $\textit{Re}_0$ ; planar rears enhance drag at higher $\textit{Re}_0$ ; lift appears only in symmetry-broken regimes and reverses late in time; torque reorients the rear plane towards vertical, consistent with free-body experiments. When buoyancy is included, assisting configurations ( $\textit{Ri}\gt 0$ ) suppress recirculation and maintain quasi-spherical shapes, whereas opposing or transverse buoyancy ( $\textit{Ri}\lt 0$ ) destabilises wakes and promotes tilted planar rears. These results provide a unified framework for convection-driven melting across laminar, periodic and chaotic wakes, with implications for geophysical and industrial processes.