Superposition of steady shear flow upon orthogonal small-amplitude oscillation from a rotarance theory

Abstract

The novelty of this work is in its prediction of the non-Newtonian behavior of polymeric liquids in the orthogonal superposition of small-amplitude oscillatory shear flow upon steady shear flow. We do so using rotarance theory, namely, by considering only the orientability of the macromolecules in suspension. We arrive at explicit analytical solutions for the complex viscosity as a function of the steady shear rate and of the frequency of the superposed oscillation. Our results explain the canonical laboratory observations of orthogonal superposition: (α) the real part of the complex viscosity as a function of frequency decreases with increasing steady shear rate, (β) the curves of minus the imaginary part as a function of frequency go through a maximum, and (γ) the independence of the steady mean shear stress from the superposed oscillation. We compare our predictions with those of parallel superposition and discover that the further the macromolecular structure from axisymmetric, I3/I1=1, the greater the difference between parallel and superposition. In other words, studying both directions of superposition of either part of the complex viscosity uncovers the most important feature of macromolecular structure, the moment ratio, I3/I1, and thus, the macromolecular orientability.