Limited Coalescence

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


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
$$ \begin{gathered} \frac{{\partial n(x,t)}} {{\partial t}} = - n(x,t)\int_0^\infty {\phi (x,\xi )n(\xi ,t)d\xi } \hfill \\ + \tfrac{1} {2}\int_0^x {\phi (x - \xi ,\xi )n(x - \xi ,t)n(\xi ,t)d\xi } \hfill \\ \end{gathered} $$
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.


Journal Colloidal Mathematical Construct Physical Observation Mass Distri Scalar Transport Equation 
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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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