Concentration of diffusional particles in viscous boundary sublayer of turbulent flow

The motion of inertial particles suspended in the viscous boundary sublayer of a wall-bounded turbulent flow is considered. We show that there is the diffusional region near the wall occupied by the particle moving in the local-equilibrium with the turbulent fluctuations which are modelled by Ornstein-Uhlenbeck process. The stationary spatial distribution of inertial particles is found for arbitrary Stokes number (dimensionless measure of the inertia). The weakly inertial particles placed in the diffusional region go away from the wall and escape the viscous sublayer. However, the direction of particle migration reverses when the Stokes number is getting larger than the critical value that we determine. The standard turbophoresis becomes more and more pronounced with the increase of Stokes number so that sufficiently inertial particles turn out to be trapped in the viscous boundary sublayer.