Stochastic formulation of particle kinetics in wall-bounded two-phase flows

This paper presents a generalized framework of stochastic modeling for particle kinetics in wall-bounded flow. We modified a reflected Brownian motion process and straightforwardly obtained a Kramers equation for particle probability density function (PDF). After the wall effects were accounted for as a drift from zero in the mean displacement and suppression in the diffusivity of a particle, an analytical solution was worked out for PDF. Three distinguishable mechanisms were identified to affect the profile of particle probability distribution: external forces, turbophoresis effect, and wall-drift effect. The proposed formulation covers the Huang et al. (2009) model of a wall that produces electrostatic repulsion force and van der Waals force, as well as Monte-Carlo solutions for the Peter and Barenbrug (2002) model under a variety of relaxation times. Moreover, it successfully reproduces the two patterns of particle concentration profiles observed in experiments of sediment-laden open-channel flows. The strength of the wall-drift effect was found to be connected with the interaction frequency between particle and wall. Further exploration of the relationship among flow turbulence, particle inertia, and particle concentration is worthwhile.