Asymptotic solutions to the Smoluchowski's coagulation equation with singular gamma distributions as initial size spectra

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Abstract

Smoluchowski's coagulation equation is studied for the kernel K (u, v) = E(u(alpha)v(beta) + u(beta) v(alpha)) with real, non-negative alpha, beta and E, using gamma distributions with a singularity at zero volume as initial size spectra. As the distribution parameter of the gamma distribution, p, approaches its lower limit (p -> 0) the distribution becomes similar to pv(p-1) 1 for small v. Asymptotic solutions to the coagulation equation are derived for the two cases p -> 0 and v -> 0. The constant kernel (alpha = beta = 0) is shown to be unique among the studied kernels in the sense that the p -> 0 asymptote and the v 0 asymptote differ.

Details

Authors
  • Ulf Lindblad
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Food Engineering

Keywords

  • distribution, gamma, the Smoluchowski coagulation equation, exact solutions
Original languageEnglish
Pages (from-to)440-444
JournalJournal of Colloid and Interface Science
Volume309
Issue number2
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes