A Lagrangian Stochastic Model for the Dispersion and Deposition of Brownian Particles

Abstract

A Lagrangian stochastic model for the dispersion and deposition of submicron-size particles is formulated and validated. The model satisfies the well-mixed condition, incorporates molecular diffusivity, and accounts for the effects of Reynolds number upon Lagrangian particle statistics. Reynolds number effects are found to be significant in the viscous sublayer and the buffer zone of a turbulent shear flow. The effects are due almost entirely to the change in the Lagrangian integral time scale. Sawford's correction to first-order Lagrangian stochastic models for the effects of Reynolds number is found to be appropriate for inhomogeneous turbulence even when the Taylor–Reynolds number Rλ ∼ O(0.1). The model predicts, in close accord with experiment and the results of direct numerical simulations, that the nondimensional particle deposition velocity K+ = 0.06Sc−2/3, where Sc is the Schmidt number. When Reynolds number effects are neglected, K+ is overpredicted by several orders of magnitude.