The effect of heat currents on the stability of the liquid solid interface

(Received 7 October 1991, accepted 6 January 1992)

Abstract
Rapid changing of the temperature of a liquid in equilibrium with its solid can lead to instabilities of the interface in two ways : the change in pressure, induced by a temperature change at the interface, leads to a uniaxial stress which can cause a Grinfeld instability at the capillary wavelength ; a temperature gradient is set up which modifies the effective gravity at the interface. When the effective gravity becomes negative, the interface is unstable at very long wavelengths. For a superfluid, such as ⁴He, the situation is more complex. If we ignore surface dissipation, there is still a small critical temperature gradient across the solid above which the interface is unstable. However surface dissipation - in particular the growth resistance - pushes the instability to huge temperature gradients, ones which cannot be realised experimentally. The only instability that can be seen is caused by uniaxial stress.