STOCHASTIC DESCRIPTION OF DISPERSE SYSTEMS

We discuss a stochastic approach to describe some aggregation processes that occur in disperse systems. We view these processes as stochastic and Markovian and we construct a master equation for the probability distribution function P(m, t) to have m(k) aggregates of size k at time t. From this equation we show that the mean size of a cluster obeys the Smoludhowski's equation, in terms of which the usual description of aggregating systems is made. In this way it is then exhibited that the usual statistical description is contained in the stochastic description as a particular case. The type of additional information that is contained in the latter with respect to the former description is pointed out; it is also indicated how the higher order moments of P(m, t) may be calculated and its relation with the fluctuations in the number of clusters is given, We also comment on the relation between the method developed in this work and others used in the literature.