An exact analytical solution to unsteady population balance equation with particles coagulation

被引：6

作者：

Makoveeva, Eugenya V. ^{[1
]}

Alexandrov, Dmitri V. ^{[1
]}

机构：

[1] Ural Fed Univ, Dept Theoret & Math Phys, Lab Stochast Transport Nanoparticles Living Syst, Lab Multiscale Math Modeling, Lenin Ave 51, Ekaterinburg 620000, Russia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2024年 / 131卷

基金：

俄罗斯科学基金会;

关键词：

Phase transition; Smoluchowski equation; Saturated solution; Coagulation; Ostwald ripening; Metastable liquid; Particle-volume distribution; Supersaturation removal; INTERMEDIATE STAGE; SIZE DISTRIBUTION; CRYSTAL-GROWTH; GAMMA; SOLIDIFICATION; AGGREGATION; COALESCENCE; EVOLUTION; DYNAMICS; KINETICS;

D O I：

10.1016/j.cnsns.2024.107879

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the final step of a phase transition process in saturated solutions when particles coalescence (Ostwald ripening) and coagulation are possible to happen concurrently. A parametric solution to unsteady Smoluchowski integro-differential equation with constant coagulation kernel is found taking the diffusion mechanism of particles in the space of their volumes into account. The particle-size distribution is given by an exponentially decreasing bell-shaped function describing the experimental data at long times. The theory is extended to describe the cases of different coagulation mechanisms, hydrodynamic flows and external forces.

引用

页数：10

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