Cox–Merz rules from phenomenological Kelvin–Voigt and Maxwell models

Abstract

The Cox–Merz rule (CMR) is commonly used for identifying similarities between the rheological results obtained from incremental and oscillatory fluid deformation tests. The CMR states that the steady state viscosity ηss(γ˙) and the complex viscosity η∗(ω) are similar when the equivalence ω↔γ˙ is considered. The empirical applicability of the CMR for diverse food material has been tested in recent decades, showing non-conclusive results for a diversity of foods. This work used the Kelvin–Voigt and Maxwell phenomenological models of power-law fluids to obtain equivalences between the steady state and the complex viscosities. Modified CMR rules (MCMR) were derived using first-harmonic balances for the underlying differential equations governing the strain dynamics. It is shown that the structure and applicability of the MCMR depended on the underlying model. Only the loss modulus was involved in the viscosity estimation for Kelvin–Voigt models while the traditional CMR was consistent with Maxwell model in the low-frequency regimen.