Theory of the rheological properties of dispersions.

In the mechanics of continua the theories of two types of substances have been mainly considered, those of Hookean elastic solids and of Newtonian fluids. I t is common knowledge that there are many substances of great importance which cannot be classified under either heading. Some of these substances exhibit both elastic and viscous properties; they flow under the influence of applied stresses, but on removal of stress part of their deformation is gradually recovered, a phenomenon known as elastic recovery. The aim of the present paper is twofold. First, we shall derive a set of fundamental differential equations which describe the properties of flow of substances which show elastic recovery. These equations contain a number of parameters, and it is the second aim of this paper to relate these parameters to structural properties of such materials. Many of the substances which exhibit elastic recovery are two-phase systems forming colloidal sols, or dispersions consisting of independent solid micelles embedded in a viscous fluid. They can be represented by a simplified physical model in which the micelles are considered to be elastic spheres, while the fluid is treated according to the classical theory of hydrodynamics. This is a model which we were able to treat without undue mathematical difficulties, while on the other hand sols are also of considerable experimental interest. Although we shall restrict ourselves to dispersions, the resulting equations of flow are of a very general nature if we do not specify the parameters by the expressions which connect them with the structure of the dispersions. We, therefore, hope that these equations may also be applicable to other substances. On the other hand, we are aware that they can be generalized in various ways, but in the present paper it is our intention to present them in their simplest form. 2