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Exact solutions of temperature-dependent Smoluchowski equations

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journal contribution
posted on 2024-03-26, 16:31 authored by AI Osinsky, NV Brilliantov

We report a number of exact solutions for temperature-dependent Smoluchowski equations (TDSEs). These equations quantify the ballistic agglomeration, where the evolution of densities of agglomerates of different size is entangled with the evolution of the mean kinetic energy (partial temperatures) of such clusters. The obtained exact solutions may be used as a benchmark to assess the accuracy and computational efficiency of the numerical approaches, developed to solve the TDSEs. Moreover, they may also illustrate the possible evolution regimes in these systems. The exact solutions have been obtained for a series of model rate coefficients, and we demonstrate that there may be an infinite number of such model coefficient which allow exact analysis. We compare our exact solutions with the numerical solutions for various evolution regimes; an excellent agreement between numerical and exact results proves the accuracy of the exploited numerical method.

History

Author affiliation

School of Computing and Mathematical Sciences, University of Leicester

Version

  • AM (Accepted Manuscript)

Published in

Journal of Physics A: Mathematical and Theoretical

Volume

55

Issue

42

Pagination

425003

Publisher

IOP Publishing

issn

1751-8113

eissn

1751-8121

Copyright date

2022

Available date

2024-03-26

Language

English

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