An exact solution to nonstationary Smoluchowski's coagulation equation complicated by Ostwald ripening

The concluding stage of a phase transformation, governed by particle coagulation and Ostwald ripening processes, is considered. An exact solution to the non-stationary integrodifferential kinetic equation is constructed in a parametric form. Namely, the particle-volume distribution function, time, number of particles, volume of the condensed phase, and the average particle radius are derived as functions of liquid supersaturation. The analytical solution is found (i) for a constant collision-frequency function, and (ii) using the averaging of this function over all possible combinations of particle volumes for various coagulation mechanisms. It is shown that the particle-volume distribution function and average radius of particles are substantially different in cases of constant and averaged collision-frequency functions for shear coagulation and coagulation under gravity.

Automated summary

This study focuses on the concluding stage of a phase transformation and examines the particle coagulation and Ostwald ripening processes. An exact solution to the non-stationary integrodifferential kinetic equation is derived, providing relationships between the particle-volume distribution function, time, number of particles, volume of the condensed phase, average particle radius, and liquid supersaturation. The study also compares the particle-volume distribution function and average radius of particles in cases of constant and averaged collision-frequency functions for different coagulation mechanisms, such as shear coagulation and coagulation under gravity.