# Localization-delocalization transition for inertial particles in wall-bounded random flow

Sergey Belan

^{1}, Alexander Chernykh^{2}, Gregory Falkovich^{3}^{1}

*Landau Institute for Theoretical Physics, Chernogolovka, Russia*

^{2}

*Institute of Automation and Electrometry, Novosibirsk, Russia*

^{3}

*Weizmann Institute of Science, Rehovot, Israel*

Turbophoresis is the tendency of particles to migrate in the direction of minima of turbulence intensity. It was recently suggested that the sign of turbophoresis can be actually opposite, so that particles agitated by turbulent fluid fluctuations go away from minima of fluctuations intensity if they are inertial enough. That means localization-delocalization transition upon the change of inertia: particles with small inertia go to a minimum of turbulence, while sufficiently inertial particles escape to infinity. We consider the motion of inertial particles near a wall in the case of inelastic particle-wall collisions. The phase diagram for the transition in the inertia-elasticity plane is found. If the restitution coefficient of particle velocity is smaller than some critical value, then the inelastic collapse occurs: the particles are localized near the wall for any inertia. The theoretical predictions are in a good agreement with the results of direct numerical simulations.

**Keywords:**Wall-bounded flows, Multiphase flows

**Figure 1:**The phase diagram of the localization-delocalization transition in inertia-elasticity plane: theory(line) and numerical simulations ().