Collisions and Crystal-Crysta IThe rate of secondary nucleation of ice, assumed to be proportional to the product of collision frequency and impact energy, has been quantitatively modeled using idealized representations of collisions between crystals and either other crystals or surfaces in the crystallizer. The crystal-crystallizer collisions were assumed to be driven by either steady or turbulent fluid motion and the crystal-crystal collisions were assumed to be driven by either gravitational forces or turbulent eddies. The models predict to a good approximation the experimentally determined dependence of the secondary nucleation of ice on crystal size, ice concentration, and agitation power. T. W. EVANS SCOPEIn many practical crystallizers the nucleation rate is dominated by interaction of crystals with their environment, that is, by secondary nucleation processes. Secondary nucleation is poorly understood and heavy reliance has been placed on empirical correlations of nucleation kinetics, Without a fundamental understanding of the processes governing secondary nucleation, the form of the function that can best correlate experimental results cannot be well established. Hence there is no sound basis for extrapolating results from one set of experimental conditions to others. As examples of the wide choice of functions available to correlate secondary nucleation, simplistic models based on the assumptions that secondary nucleation is proportional to the number of crystals, crystal perimeter, area, or mass would suggest that the nucleation rate should be proportional to the zeroth, first, second, or third moment of the crystal size distribution, that is,where N is the nucleation rate and p, the nth moment of the crystal size distribution. Other models of crystallization involve collision of crystals with each other, in which case the nucleation rates would be expected to be proportional to the square of the moments of the particle size distribution. Little can be said about which moments should be used without a statement of mechanism. Additional motivation for developing mechanistic models of secondary nucleation is provided by the need to determine the dependence of nucleation rate on design parameters such as agitation rate, scale of equipment, etc.In a previous paper (Evans et al., 1974), it has been shown that the factors influencing crystal surface morphology can be separated from those influencing collisions. In this paper, following leads provided by Clontz and McCabe (1971) and Ottenj and co-workers (1972, 1973), this concept is extended. Expressions are derived for the kinetics of secondary nucleation under the assumption that the rate of nucleation is proportional to collision frequency and collision energy for each of four idealized collision mechanisms. These include (1) collision of crystals with an impeller as the crystals are swept by the impeller in steady flow, (2) collision between crystals in a turbulent flow field and various surfaces in the crystallization, (3) collision between crystals ...

Experiments were designed to identify the mechanism of the secondary nucleation of ice in a vigorously agitated crystallizer. It has been shown that the nucleation rate is proportional to the product of two factors, one characterizing crystal morphology and the other the rate of removal of potential nuclei from the surfaces of the existing crystals. Consequently, the nucleation rate attributable to different mechanisms is additive and the rate is proportional to the number of collisions per crystal. The contribution to the secondary nucleation of ice, by collisions of crystals with the impeller, baffles, and other crystals in an agitated crystallizer have been identified by measurements in a batch crystallizer in which each of the different collision mechanisms could be suppressed.

As part of a continuing research program in water desalination by freezing, studies have been made on the performance of a well stirred continuous crystallizer producing ice by direct contact refrigeration. Photographs of the effluent revealed that the ice particles were disk shaped and that the particle size distributions in all cases passed through a maximum. Growth rates correlated well with values predicted from heat and mass transfer rates in the size range 0.6-2 mm but increased sharply at the smaller sizes. For average residence times ranging from 6.5 to 13 min, measured subcoolings varied from about 0.02 to 0.03°C and formed a very small fraction of the overall temperature driving force, while nucleation rates varied from 9 to 30 nuclei/(cm3 of slurry min) and could be correlated with the solution subcooling and the moments of the distribution but were independent of refrigerant temperature. Permeabilities of ice beds formed from the crystallizer product were found to be a strong function of both the method of bed formation and the size and shape of the crystals. An important practical result of the study was the indication that much larger ice production rates per unit crystallizer volume should be possible without sacrifice of crystal size.

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