The Influence of Velocity Gradient on the Relation Between Viscosity and Concentration in Cuprammonium Solutions of Cellulose

The numerous equations which have hitherto been employed to relate the viscosity of solutions of high polymers to the concentration of the solute have neglected to recognize explicitly the influence which velocity gradient (rate of shear) has upon the observed viscosity of non‐Newtonian liquids. Consequently, the theoretically important, intrinsic viscosity, calculated on the basis of these equations, from data obtained on a solution in the anomalous region, is found to have a different value for each velocity gradient prevailing during measurement. A modification of the Baker‐Philippoff equation has been developed empirically having the advantage that it yields a uniform value for the intrinsic viscosity of a given solution regardless of changes in velocity gradient. This new equation: $${\eta }_r={\left(\text{1+}\frac{c}{\lambda }\right)}^8+\left(k_i-\frac{8}{\lambda }\right)\mathrm{c,}$$ has been found to agree well with data on cuprammonium solutions of cellulose in concentrations below 0.5 g per 100 ml. The parameter λ, interpreted as a function of velocity gradient, is found to increase with gradient, while k_i, which is shown to be the intrinsic viscosity η_i, is found to have a constant value characteristic of the solute. It appears that the second constant appearing in other recent equations in addition to the intrinsic viscosity, may be interpreted as a velocity gradient adjustment term. The algebraic series into which the various recent equations can be expanded to express η_r are strikingly similar to each other and to a proposed equation based on the Eyring reaction‐rate theory.