Parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow from rotarance theory

Abstract

The power of a macromolecular theory for the transport properties of a polymeric liquid increases with the number of analytical expressions for its most important material functions. In this work, we add another of these canonical function to our recent series of material function derivations for rotarance theory. By rotarance theory, we mean the explanation of the elasticity of polymeric liquids by use of (i) the diffusion equation to get the orientation distribution in Euler coordinates, and (ii) the integration in phase space using this distribution to get the target material function. In this paper, we target parallel superposition of oscillatory shear flow upon steady shear flow. We arrive at analytical expressions for both parts of the complex viscosity in parallel superposition. We find that these explain the classic experimental observations in parallel superposition: (a) the maximum in the real part of the complex viscosity, and (b) the negative values of minus its imaginary part, and (c) the independence of the steady mean shear stress from the superposed oscillation.