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In steady, solid-liquid two-phase turbulent flows, there exist two typical patterns of the vertical distribution of particle concentration. The pattern I shows a maximum concentration at an elevation above the bed. The pattern II shows an increase of the particle concentration downward over the whole vertical, with the maximum at the bed. Most of the theories on particle concentration distribution have been done with the pattern II, and it is lack of a successful theory covering both of the two patterns. This paper reviews the particle distribution theories, including the diffusion theory, the mixture theory, the energy theory, the similarity theory, the stochastic theory and the kinetic theory. The kinetic theory is also applied to describe the vertical distribution of particle concentration in both dilute and dense flows.
There are two typical patterns of the vertical distribution of particle concentration. The pattern I shows a maximum concentration at an elevation above the bed. The pattern II shows an increase of the particle concentration downward over the whole vertical, with the maximum at the bed. Most of the theories on particle concentration distribution have been done with the pattern II, and it is lacking a successful theory covering both of the two patterns. This paper reviews the particle distribution theories , including the diffusion theory, the mixture theory, the energy theory, the similarity theory, the stochastic theory and the kinetic theory. The kinetic theory is also applied to describe the vertical distribution of particle concentration in both dilute and dense flows.