An application of continuum theory on the case of one-dimensional sedimentation

The fundamental balance laws of the fluid phase and the disperse phase of suspension are presented. Constitutive equations are developed and the method of Lagrangian multipliers is used. The objective of this paper is to use the continuum theory of two-phase flow to model the one-dimensional sedimentation of particle through a fluid in the direction of vertical axis. After using the basic equations of motion and corresponding restrictions, the diffusion equation of quasi-steady sedimentation is derived. The fact that the diffusion equation is parabolic, when a diffusivity term is included, suggests the possibility that sedimentation problem could be solved numerically and then graphically presented.