The Governing Equations for Segregation

By expanding the terms given in Equations (5.5) through (5.7) and substituting the rate of jetsam inflow of particles for the control volume, the net change of jetsam concentrations becomes  

The differential equation describing the movement of jetsam concentration in the active layer may be written as  

In arriving at Equation (5.9), the boundary layer condition whereby Uy has been imposed the y-component of the species convection term has been ignored and thus the vertical movement of jetsam 

The diffusion flux in the active layer occurs as a result of particle collision in the continuously shearing active layer. The diffusion coefficient and the bulk velocity are determined by the flow model detailed in Chapter 4. by is the kinetic diffusivity which had been computed from the granular temperature as (Savage, 1983 Hsiau and Hunt, 1993) 

Here the percolation velocities for smaller (jetsam), Vps, and larger (flotsam) particles, VpL, are given by the following equations  

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