Deviation of freezing rate from translation rate in the Bridgman-Stockbarger technique I. Very low translation rates

Abstract

An analytical solution is obtained for the deviations of freezing rate from translation rate in the Bridgman-Stockbarger technique. The equations include a finite length ampoule, differences in heat transfer coefficients between the two ends, insulation between the heater and cooler, and latent heat. The present result accounts for heat conduction only, and is valid for low travel rates, small ampoule diameters and/or high thermal conductivities. In all cases the freezing rate approaches the translation rate if the interface is sufficiently far from the ends of the ampoule. The length required to achieve this condition increases with increasing ampoule diameter, decreasing heat transfer coefficient, increasing thermal conductivity and increasing insulation thickness. This length shows a minimum versus the heater temperature for a fixed cooler temperature. The present results are in agreement with previously reported experimental data and numerical predictions.