Eur. Phys. J. Spec. Top. (2022) 231: 1115-1121
https://doi.org/10.1140/epjs/s11734-022-00522-9

Regular Article

A complete analytical solution of unsteady coagulation equations and transition between the intermediate and concluding stages of a phase transformation

Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation

^b dmitri.alexandrov@urfu.ru

Received: 17 July 2021
Accepted: 3 March 2022
Published online: 14 March 2022

Abstract

In this paper, a complete analytical solution to the unsteady kinetic equation of particle coagulation in a metastable liquid is constructed with allowance for an arbitrary initial particle-volume distribution function. Based on the analytical solution found, a theory of the transition of the phase transformation process from the intermediate stage to the coagulation stage is constructed. For this purpose, an exact analytical solution describing the intermediate stage of a phase transformation is used. It is shown that the maximum of the particle-volume distribution function decreases, and its right branch (“tail”) grows with increasing time during the coagulation stage.