Theory of Non-Newtonian Flow. III. A Method for Analyzing Non-Newtonian Flow Curves

The historical development of the rate theory of viscosity is briefly reviewed. The Ree‐Eyring equation of generalized viscosity, $$\mathrm{\eta =}{\displaystyle \sum _{\text{n=1}}^m}{\mathrm{(x}}_n{\beta }_n{\mathrm{/\alpha }}_n\mathrm{)(}{\sinh }^{\text{−1}}{\beta }_n{\mathrm{ṡ/\beta }}_n\mathrm{ṡ)}$$ is applied successfully in a variety of cases. (For the definitions of the symbols in this equation, reference is made to the text.) We develop here a new method for determining the parameters x_n/α_n and β_n in Eq. (A). According to the method, these parameters are uniquely determined. When we used the parameters determined by the new method, the viscosities for solutions of poly‐γ‐benzyl‐l‐glutamate were calculated from Eq. (A). It is found that Eq. (A) is much superior to other frequently applied viscosity equations. Upon calculating the Newtonian viscosities η_s for fairly concentrated solutions of polyacrylonitrile and of nitrated pine pulp, the following empirical formula is found: $${\eta }_s{\mathrm{\simeq KC}}^2{\mathrm{M\beta }}_p^{\frac{1}{2}}$$ . Here K is a characteristic constant for a solution; C the concentration; M the molecular weight; and β_p is the ``principal'' relaxation time. In dilute solutions, Eq. (B) reduces to the form η_s≃K′CM.