Anomalous aggregation regimes of temperature-dependent Smoluchowski equations

A. I. Osinsky, N. V. Brilliantov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities, with constant rate coefficients, the temperature-dependent equations describe both - the evolution of the densities as well as cluster temperatures, which determine the agglomeration rates. To solve these equations, we develop a Monte Carlo technique based on the low-rank approximation for the aggregation kernel. Using this highly effective approach, we perform a comprehensive study of the kinetic phase diagram of the system and reveal a few surprising regimes, including permanent temperature growth and "density separation"regime, with a large gap in the size distribution for middle-size clusters. We perform scaling analysis and classify the aggregation kernels for the temperature-dependent equations. Furthermore, we conjecture the lack of gelation in such systems. The results of the scaling theory agree well with the simulation data.

Original languageEnglish
Article number034119
JournalPhysical Review E
Volume105
Issue number3
DOIs
Publication statusPublished - Mar 2022

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