Evolution of a particulate ensemble with fluctuations in particle growth rates

The evolution of an ensemble of spherical crystals in a supersaturated solution is considered with allowance for fluctuations in crystal growth rates and initial crystal-size distribution. Two approaches for constructing the analytical solutions based on the saddle-point method and separation of radial and time functions are developed. Both methods yield similar desupersaturation dynamics, which agree well with the experimental data. The first method gives a crystal-size distribution function decaying with time, consistent with a decrease in solution supersaturation. The second method results in a distribution function with opposite dynamics and works only in the case of exponentially decaying initial crystal-size distribution. Therefore, the first method can be used to determine any characteristics of an ensemble of crystals based on calculating the moments of the distribution function. The use of the second, mathematically simpler method, is suitable only for describing the kinetics of supersaturation removal.