Empirical size-dependent growth rate models are studied for their effect on the population density distributions from a continuous, mixed suspension, mixed product removal (CMSMPR) crystallizer. The growth rate models and/or their corresponding population density distributions are examined for continuity, convergence of moments, versatility, and their obility to fit experimental data.A new empirical size-dependent growth rate model is proposed which has properties superior to those of previous models. Experimental steady state data are presented to illustrate the application of the model to actual CMSMPR crystallization systems.It is now general1 held that crystal growth consists of three basic steps (6r:1. the diffusion of solute molecules from the bulk of the solution to the crystal-solution interface, followed by 2. a surface reaction as the solute molecules arrange themselves into the crystal lattice, and 3. the diffusion of the heat of crystallization from the crystal solution interface back into the bulk of the solution. The effect of the last step on the overall crystal growth rate has not been extensively studied. However, in most crystallization systems where the heat of crystallization is relatively low, the effect of step ( 3 ) on the overall growth process is probably small in comparison with the first two steps.In studying the crystallization of sodium chloride, Rumford and Bain (8) found the growth rate to be essentially diffusion controlled at temperatures above 50°C. and reaction controlled at temperatures lower than 50°C. Hence, in crystal growth both diffusion and surface reaction can be important or only one mechanism can be controlling.For most crystallization systems, the diffusion resistance is less than the resistance due to the surface reaction, and the growth rate is reaction controlled. These systems obey McCabe's AL law and have crystal growth rates which are independent of crystal size.However, a number of crystalline materials exhibit crystal growth rates which are a function of crystal size where u is the relative crystal-solution velocity, ri is the interfacial growth rate, and r', and B are constants.From this investigation it was concluded that crystal growth rate is independent of crystal size per se. The apparent effect of size [Equation ( l ) ] results from the larger crystals having a higher settling velocity and hence a greater relative crystal-solution velocity. Since the diffusion boundary layer and the diffusion resistance decrease as the velocity increases, the growth rate of crystals in a mixed suspension would be expected to increase with size, if the growth rate is not reaction controlled.Bennett (1 ) , however, presents data which indicate crystal growth rates inversely proportional to crystal size. Bennett believes that this effect is caused by classification taking place at boiling surfaces where the supersaturation may be considerably higher than in the bulk of the crystal suspension. He proposes that this surface classification dominates the opposite tendency of t...

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