Extension of the Eyring-Ree Theory of Non-Newtonian Flow

The Eyring-Ree theory of non-Newtonian flow is extended to the case of a continuous distribution of flow units. This results in an integral equation of the form F(ṡ)= ∫ 0∞G(t) arc sinh (ṡt)dt. This equation can be solved by integral transform methods to yield the unknown distribution function G(t) when the flow curve F(ṡ) is known as an analytic function. For the case of limited empirical data, approximation methods can be used to obtain G(t). Experimental data are shown for polyethylene at two temperatures and the distribution functions calculated.