Theory of Non-Newtonian Flow. I. Solid Plastic System

Abstract

The relaxation process of viscous flow may be visualized as the sudden shifting of some small patch on one side of a shear surface with respect to the neighboring material on the other side of the shear surface. Any shear surface will divide a mosaic of such patches lying on the two sides of the surface. Except for the simplest systems, this mosaic of patches will be heterogeneous and can be described by groups each characterized by its mean relaxation time β_n, by x_n the fractional area of the shear surface which the group occupies and by α_n, a characteristic shear volume divided by kT. The resulting generalized expression for viscosity is $$\mathrm{\eta =}{\displaystyle \sum _{\text{n=1}}^n}\frac{x_n{\beta }_n}{{\alpha }_n}\frac{{\sinh }^{\text{−1}}{\beta }_nṡ}{{\beta }_nṡ}$$ , where ṡ is the rate of shear. This equation is applied to masticated natural rubber, polystyrene, X‐672 GR‐S, X‐518 GR‐S rubber, and Vistanex LM‐S polyisobutylene. All applications give good agreement with experiment. The known criticisms of Eyring's simple relaxation theory for viscous flow are reviewed, and are apparently taken care of in this general treatment.