Questioning a fundamental assumption of rheology: Observation of noninteger power expansions

Abstract

We report the most complete experimental evidence to date of noninteger power-law expansions for nonlinear viscoelastic properties. Our observations, made with a capillary suspension of spherical poly(methyl methacrylate) (PMMA) particles, falsify the universality of the standard assumption where shear stress nonlinearities arise as the amplitude cubed, e.g., σ ∼ O ( γ 0 3 ) in an oscillatory shear test at small amplitudes. In terms of material properties, our measurements require noninteger Taylor expansions about a linear reference state. Furthermore, distinct power-law exponents are found for the storage and loss signals. In this work, we conclusively demonstrate that the noninteger scaling is real and not an experimental artifact. Our experimental and data analysis methods ensure that we report the most complete result to date. While the noninteger scaling remains to be associated with underlying microstructural physics, the thorough experimental data reported herein demonstrate that such theoretical studies are worth pursuing.