Some exact and approximate solutions of the nonlinear Boltzmann equation with applications to aerosol coagulation

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Abstract
The nonlinear kinetic equation describing aerosol coagulation and deposition is studied analytically by a new method based upon successive coalescences. The method is illustrated by using a constant coagulation kernel and a deposition term which depends upon a power of the particle volume (zero or unity). The success of the method rests upon a novel use of the central limit theorem of statistics applied to causal systems. The techniques are of general interest in the solution of the nonlinear Boltzmann equation in the kinetic theory of gases and in the case studied show that the volume distribution of successive generations of coalescences tends rapidly to a gamma distribution. Closed form solutions are obtained with a constant coagulation kernel and a deposition rate that is proportional to any power of particle volume. Numerical results are obtained for several cases which indicate that the values m=0 and 1 for the deposition rate are not unreasonable for the purposes of general comment.

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