Coagulation in finite systems

Abstract The kinetics of a coagulation process in a finite system of particles placed in a volume V is studied. Under the usual assumption of coagulation theory, an equation is derived governing the time evolution of the probability W ( Q , t ) of finding in the system a given mass spectrum Q = { n 1 , n 2 , …, n g , …}, where n g is the number of particles containing g monomers. The probability W is shown to be a superposition of Poisson's distribution, the parameters of which are determined by a solution of the Smoluchowski equation while the coefficients are expressed in terms of the initial probability W ( Q ,0). Some exact results are established for linear models K ( g , l ) = gf ( l ) + lf ( g ), where K ( g , l ) is the usual collision frequency entering into the Smoluchowski equation.