Stability of a Submerged Frozen Crust

Consideration is given to the stability of a thin frozen crust of infinite extent growing between two different fluid materials. A linear, inviscid stability analysis is employed to obtain an estimate for the crust breakup time. The stability formulation parallels that of Rayleigh and Kelvin for the generation of waves at the plane interface between two different fluids and is used to develop formulas defining necessary conditions for frozen crust breakup. An approximate crust breakup criterion is proposed, viz, that the crust growth (or crystallization) time exceed the crust breakup time. The criterion shows reasonable agreement with experimental observations of the stability of a growing frozen crust in a gravity field alone (Rayleigh instability).