A Rheological Equation of State which Predicts Non-Newtonian Viscosity, Normal Stresses, and Dynamic Moduli

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Abstract
An equation of state is formulated from the classical Maxwell assumptions of superposition of the effects due to strain and rate of deformation in a strained fluid. Except for the form of the time derivative, these assumptions result in the usual expression for a Maxwell element. The time derivative of the stress, however, is computed with respect to a set of axes in the fluid which are rotating (with respect to fixed axes) at a rate measured by the vorticity of the assumed velocity distribution. The usual transformation between rotating and fixed reference axes introduces cross terms between the stress and vorticity components. The resulting equation of state predicts non‐Newtonian behavior and the simultaneous appearance of normal stresses. It reduces to the Newtonian case for low rates of shear (or for small relaxation times) and, if the cross terms are sufficiently small (but not otherwise), to the usual Maxwell element expression in the dynamic case. A common origin is thus assigned to these several phenomena. Reduced variable and distribution function procedures, at least in principle, should be as applicable to the viscosity and pressure phenomena as to dynamic data.

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