On the stochastic approach to cluster size distribution during particle coagulation. I. Asymptotic expansion in the deterministic limit

Consideration is given to the stochastic problem of the coagulation of particles for the case of a size-independent coagulation kernel, and expressions are derived for the expectation value, variance and covariance of the cluster size distribution function, for both a discrete and a continuous spectrum of cluster sizes. The authors develop an asymptotic expansion in V-1 of these quantities (where V is the spatial volume), showing that as V to infinity the above expectation value tends to the deterministic result, and obtaining an explicit form for the first-order deviation from this expression for large (but finite) V. Analogous results are derived for the variance and covariance in the limit of large V. A discussion is given of the extent to which stochastic effects can produce significant changes to the deterministic results.