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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.

The algebraic proof of the fundamental theorem concerning pure shear, by making use only of the notion of orthogonal projector, is presented. It has been shown that the state of pure shear is the same for all singular symmetric traceless tensors in E3, up to the rotation.