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Limited Coalescence

  • Avner Friedman
  • David S. Ross
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 3)

Abstract

In aerosol dynamics one models the evolution of the number density n(x, t) of particles of volume x at time t by the equation
$$ \begin{gathered} \frac{{\partial n(x,t)}} {{\partial t}} = - n(x,t)\int_0^\infty {\phi (x,\xi )n(\xi ,t)d\xi } \hfill \\ + \tfrac{1} {2}\int_0^x {\phi (x - \xi ,\xi )n(x - \xi ,t)n(\xi ,t)d\xi } \hfill \\ \end{gathered} $$
(1)
where φ(x, ξ) is the collision rate between particles of sizes x and ξ; here the first term on the right-hand side expresses loss of particles of size x due to coalescence with particles of any size ξ, and the second integral expresses the gain of particles of size x through coalescence of particles of sizes ξ and x — ξ with ξ ≤ x — ξ; the factor ½ is introduced when we remove the restriction ξ ≤ x — ξ.

Keywords

Journal Colloidal Mathematical Construct Physical Observation Mass Distri Scalar Transport Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Avner Friedman
    • 1
  • David S. Ross
    • 2
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Department of Mathematics and StatisticsRochester Institute of TechnologyRochesterUSA

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