Numerical solution of Smoluchowski coagulation equation combined with Ostwald ripening

TL;DR

This paper presents a numerical method for solving the coupled Smoluchowski coagulation and Ostwald ripening equations, demonstrating the universal particle-volume distribution's asymptotic approach regardless of initial conditions.

Contribution

The authors develop a low-rank matrix-based numerical algorithm for efficiently solving coupled kinetic equations of coagulation and ripening.

Findings

Numerical solutions confirm convergence to a universal particle-volume distribution.

The method efficiently handles different initial distributions.

Results support the universality of the asymptotic distribution.

Abstract

The processes of simultaneous coagulation and Ostwald ripening of particles in the concluding stage of phase transformation are considered. We solve the integro-differential system of Smoluchowski-type kinetic and mass balance equations using a computationally efficient numerical algorithm based on low-rank matrices. We compare our numerical solutions for different initial particle-volume distributions with the universal distribution function for combined coagulation and Ostwald ripening. Our calculations confirm the tendency of a particulate ensemble to the universal particle-volume distribution to be approached asymptotically after a sufficiently long time, no matter what the initial particle-volume distribution might be.