3.2.4.11. Suspension Equation

In treating the suspension as a continuum, we introduce an evolution equation for particle volume fraction, $\phi$ , as

(3.41) $\pt{\phi} + \v\bcdot\grad\phi + \div\vector{N} = 0.$

The particle volume fraction is defined as the total summed volume of particles per volume of the particle medium. (3.41) represents a balance between the stored particles, the convected particle flux, and the diffusive particle flux, $N$ . Several mechanisms which include Brownian motion, sedimentation, hydrodynamic particle interactions, and gradients in suspension viscosity may contribute to the diffusive particle flux. Specification of the appropriate flux model must then be carried out to close the definition of the conservation equation.