Analytic model for the ballistic adsorption of polydisperse mixtures

We study the ballistic adsorption of a polydisperse mixture of spheres onto a line. Within a mean-field approximation, the problem can be analytically solved by means of a kinetic equation for the gap distribution. In the mean-field approach, the adsorbed substrate is replaced by a set of effective particles having the same size, equal to the average diameter of the spheres in the original mixture. The analytic solution in;the case of binary mixtures agrees quantitatively with direct Monte Carlo simulations of the model, and qualitatively with previous simulations of a related model in d = 2. [S1063-651X(99)05705-0].