8.1 Introduction

Having determined some properties of suspensions in equilibrium, we turn our attention to suspensions that are subject to external forces and seek ways of describing their response. It is evident that the approach taken to study the response of a single particle to applied forces is not useful in suspensions. That approach would require the solution of the fluid equations of motion subject to the usual boundary conditions on the surface of each of the particles. The level of difficulty may be appreciated from the fact that the fluid force acting on either one of the particles in a freely moving pair is known only approximately.

It is also evident that a suspension in motion cannot be regarded as a homogeneous medium, as we did in the last chapter, where we took advantage of the fact that, in a homogeneous suspension in equilibrium, the particles have the same pressures, temperatures and velocities as the fluid around them. As Chapters 3 6 have shown, this enormous simplification seldom occurs. Thus, the equations that apply to homogeneous fluids in motion are not generally applicable to suspensions.

A method that has proven successful in the description of suspension motions is based on the idea that the particles, being large in number, may be described as a continuous medium, obeying its own set of conservation equations. In this context, we recall that we regard fluids as continuous media even though they are composed of molecules and molecular voids. This is possible because of...