Phase transitions in the distribution of inelastically colliding inertial particles
Abstract
It was recently suggested that the direction of particle drift in inhomogeneous temperature or turbulence depends on the particle inertia: weakly inertial particles localize near minima of temperature or turbulence intensity (effects known as thermophoresis and turbophoresis), while strongly inertial particles fly away from minima in an unbounded space. The problem of a particle near minima of turbulence intensity is related to that of two particles in a random flow, so that the localizationdelocalization transition in the former corresponds to the pathcoalescence transition in the latter. The transition is signaled by the sign change of the Lyapunov exponent that characterizes the mean rate of particle approach to the minimum (a wall or another particle). Here we solve analytically this problem for inelastic collisions and derive the phase diagram for the transition in the inertiainelasticity plane. An important feature of the diagram is the region of inelastic collapse: if the restitution coefficient β of particle velocity is smaller than the critical value {β }_{0}={exp}(π /\sqrt{3}), then the particle is localized for any inertia. We present direct numerical simulations which support the theory and in addition reveal the dependence of the transition of the flow correlation time, characterized by the Stokes number.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2016
 DOI:
 10.1088/17518113/49/3/035102
 arXiv:
 arXiv:1503.04190
 Bibcode:
 2016JPhA...49c5102B
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter  Statistical Mechanics;
 Physics  Fluid Dynamics
 EPrint:
 11 pages, 4 figures