Coagulation by Random Velocity Fields as a Kramers Problem

TL;DR

This paper models particle coagulation in a fluid with random velocity fields, revealing a phase transition akin to a Kramers escape problem, dependent on particle inertia and velocity field composition.

Contribution

It establishes a novel connection between coagulation phase transition and Kramers escape problem, providing a phase diagram based on particle inertia and velocity field components.

Findings

Phase transition is related to a Kramers escape problem.

The phase diagram depends on particle inertia and velocity field composition.

The phase line is non-analytic at zero inertia.

Abstract

We analyse the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and non-coagulating phases. We show that the phase transition is related to a Kramers problem, and use this to determine the phase diagram, 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 non-analytic at epsilon=0, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realisations of this phase transition.