Migration of air bubbles, vapor figures, and brine pockers in ice under a temperature gradient

Abstract

Equations are derived for the speed and direction of migration of air-, vapor-, or brine-filled triaxial ellipsoidal cavities of any orientation, and expected velocities are computed for the spherical, cylindrical, and discoidal cases that have been investigated experimentally. In the case of air bubbles agreement is only fair for approximately spherical bubbles trapped during freezing and is somewhat better for drilled cylindrical holes open to the atmosphere. The lack of agreement and the considerable scatter in the data are probably due to uncontrolled variations in pressure and shape and to the slow accumulation of frost. In the case of discoidal vapor figures the agreement is much poorer and the scatter is much greater, probably because of large uncontrolled variations in shape, air content, and temperature of the figures. Calculation of the effect of small size, for which viscous flow of the vapor is important, shows it to be negligible for the figures used in the experiments. For spherical brine pockets at temperatures a few degrees or more below freezing agreement is fairly good, considering the uncertainties in the diffusion coefficient, but at the ice point the predicted speed is about 5 times that observed, probably because the brine concentration in the pockets at this temperature was not in fact zero as required by the theory.