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

Ulf Lindblad

    Research output: Contribution to journalArticlepeer-review

    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.
    Original languageEnglish
    Pages (from-to)440-444
    JournalJournal of Colloid and Interface Science
    Volume309
    Issue number2
    DOIs
    Publication statusPublished - 2007

    Subject classification (UKÄ)

    • Food Engineering

    Free keywords

    • distribution
    • gamma
    • the Smoluchowski coagulation equation
    • exact solutions

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