A statistical model to predict streamwise turbulent dispersion from the wall at small times

Data from simulations are used to develop a statistical model that can provide the streamwise dispersion distribution of passive particles released from the wall of a turbulent flow channel. It is found that a three-point gamma probability density function is the statistical distribution that can describe the dispersion of particles with Schmidt numbers ranging from 6 to 2400 at relatively short times after the release of the particles. Scaling arguments are used to physically justify and predict the parameters of the gamma three-point distribution. The model is used to predict particle separation that can occur in turbulent flow under special conditions. Close to the channel wall, turbulent convection is not the dominant transport mechanism, but molecular diffusion can dominate transport depending on the Schmidt number of the particles. This leads to turbulence-induced separation rather than mixing, and the currently proposed model can be used to predict the level of separation. Practically, these results can be applied for separating very small particles or even macromolecules in dilute suspensions. Published by AIP Publishing.