A turbulent dispersion model for particles or bubbles

A model for dispersed two-phase flow is derived based on a Boltzmann equation. This model is shown to be compatible with the two-fluid model, and includes the source of dispersion. In this model, dispersion is the result of the correlation of the liquid velocity fluctuations with the number density (perhaps more appropriately, with the trajectories of the individual dispersed units). Using this derived force, and a very simple assumption regarding the correlation of the presence of a dispersed unit and the carrier fluid velocity, a form for this force can be derived. This form gives a force which is proportional to the scalar (dot) product of the fluid Reynolds stress tensor with the gradient of bubble number density. For isotropic turbulence, the force is proportional to the gradient of number density. The constant of proportionality depends on the ratio of the dispersed unit relaxation time to the liquid turbulence time scale.