Singularity of Inertial Particle Concentration in the Viscous Sublayer of Wall-bounded Turbulent Flows

The exact kinetic equation for probability density function (PDF) of the velocity and the position of inertial particle transported by turbulent non-Gaussian fluid velocity fields in the viscous sublayer of wall-bounded turbulent flow is analyzed by the method of matched asymptotic expansions. It is shown that the particle concentration near the wall exhibits a power-law singularity giving rise to the phenomenon of particle accumulation. It is shown how the corresponding exponent depends upon the particle Stokes number. The result is in good agreement with previously published results of numerical simulations. A corresponding singularity is found for the standardized higher-order moments of particle velocity.