Limiting partition coefficient in a tubular ice system for progressive freeze-concentration

A tubular ice system is effective for the scale-up of progressive freeze-concentration. The effective partition coefficient, K, as an index for the effectiveness of progressive freeze-concentration, is defined by the ratio of solute in ice and liquid phase. K is dependent both on the ice crystal growth rate and the mass transfer coefficient at the ice-liquid interface, as described by the concentration polarization model. The limiting partition coefficient, K0, corresponds to K at the infinitesimal ice crystal growth rate and/or infinite mass transfer at the interface. K0 is an important process parameter for progressive freeze-concentration. A method is proposed for determining K0 experimentally for a tubular ice system. K0 increased with increase in the concentration of solute, which suggests that K0 is not determined by the equilibrium process but by the nonequilibrium process at the ice-liquid interface.