Periodic Exponential Shear of Complex Fluids

TL;DR

This paper introduces Periodic Exponential Shear (PES) flow, a new class of flow involving exponential stretching and rotation, with analytical, numerical, and preliminary experimental validation for viscoelastic fluids.

Contribution

It defines PES flow, analyzes its effects on viscoelastic fluids using the Oldroyd-B model, and demonstrates deformation-rate thickening behavior with initial experimental support.

Findings

PES flow causes exponential growth in stresses.

Repeated PES flow leads to stable oscillatory stresses.

Material function shows deformation-rate thickening.

Abstract

We define a class of flows with exponential kinematics termed Periodic Exponential Shear (PES) flow which involve periodic exponential stretching of fluid elements along with their rotation. We exhibit analytical and numerical results for PES flow by using the Oldroyd-B model for viscoelastic fluids. We calculate the growth in the shear and the normal stresses analytically as well as demonstrate that repeated application of the flow leads to stable oscillatory shear and normal stresses. We define a material function applicable to a periodic, unsteady shear flow and show numerically that this material function exhibits deformation-rate thickening behavior for viscoelastic fluids subject to PES flow. We demonstrate the feasibility of PES flow by presenting preliminary experimental results from a controlled-strain rate rheometer, using a Newtonian mineral oil.