Coagulation by random velocity fields as a Kramers Problem

Mehlig, Bernhard and Wilkinson, Michael (2004). Coagulation by random velocity fields as a Kramers Problem. Physical Review Letters, 92(25) p. 250602.




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, epsilon, and a measure of the relative intensities of potential and solenoidal components of the velocity field, Gamma. We find that the phase line is described by a function which is nonanalytic at Gamma= 0, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realizations of this phase transition.

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