Science China Technological Sciences

, Volume 57, Issue 10, pp 2001–2011 | Cite as

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

  • HongBo Ma
  • XuDong FuEmail author


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.


stochastic formulation Kramers equation reflected Brownian motion wall-bounded flow two-phase flow concentration profile 


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© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic EngineeringTsinghua UniversityBeijingChina

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