Fokker-Planck equation for particle growth by monomer attachment

Themis Matsoukas, Yulan Lin

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The population balance equation (PBE) for growth by attachment of a monomeric unit is described in the discrete domain by an infinite set of differential equations. Transforming the discrete problem into the continuous domain produces a series expansion which is usually truncated past the first term. We study the effect of this truncation and we show that by including the second-order term one obtains a Fokker-Planck approximation of the continuous PBE whose first and second moments are exact. We use this truncation to study the asymptotic behavior of the variance of the size distribution with growth rate that is a power-law function of the particle mass with exponent a. We obtain analytic expressions for the variance and show that its asymptotic behavior is different in the regimes a<1 2 and a>1 2. These conclusions are corroborated by Monte Carlo simulations.

Original languageEnglish (US)
Article number031122
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
StatePublished - Oct 9 2006

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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