On equilibrium solutions of aggregation–fragmentation problems

Abstract

A characteristic feature of particulate systems that evolve due to competition between aggregation and breakage is that they sometimes produce non-trivial steady-state particle size distributions. If such solutions satisfy detailed balance conditions, then they are equilibrium solutions. The conditions that must be satisfied by aggregation and fragmentation rate kernels in order for equilibrium solutions to be produced are elaborated, and it is shown that the rate kernels are uniquely determined by the aggregation and breakage rate constants for the reactions involving monomers. Consequently, for equilibrium systems there is a significant reduction in the amount of information needed in order to infer the general form for aggregation or breakage kernels, and we explore implications for constructing rate kernels by using atomistic simulations such as molecular dynamics.