Coagulation by Random Velocity Fields as a Kramers Problem

We analyze the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and noncoagulating phases. We show that the phase transition is related to a Kramers problem, and we use this to determine the phase diagram in two dimensions, as a function of the dimensionless inertia of the particles, ϵ, and a measure of the relative intensities of potential and solenoidal components of the velocity field, Γ. We find that the phase line is described by a function which is nonanalytic at ϵ=0, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realizations of this phase transition.