Mathematical modeling of dispersed media flows in the presence of nucleation, coagulation and phase transitions

Abstract

A model of motion of a gas-dispersed medium in the presence of processes of nucleation, coagulation and phase transitions has been constructed. A homogeneous nucleation model is used to describe the nucleation process. It is believed that the process of cluster coagulation occurs due to their Brownian motion. The analysis of the solution of the coagulation equation in the particular case of monodisperse clusters in the presence of a source and sink of particles is carried out. To determine the rate of phase transitions the Hertz-KnudsenLangmuir formula is used. The calculations were carried out on the basis of a quasi-one-dimensional model within the equilibrium approximation (when the velocities and temperatures of the phases coincide). As a result of the study the main properties of the flow of a two-phase mixture in a channel in the presence of nucleation, coagulation, and phase transformations have been established. It is shown that the vapor temperature increases along the channel and reaches the saturation temperature at some distance from the channel entrance. Calculations have shown that the coagulation process has a rather strong effect on the distribution of cluster sizes along the channel.