Theoretical predictions for upper-convected Maxwell fluids in mixed shear and planar extensional flows

Alberto Castellanos Campillo,Juan Pablo Aguayo Vallejo,Ángel Enrique Chávez Castellanos,Rafael Herrera Nájera

doi:10.1063/5.0010178

Alberto Castellanos Campillo, Juan Pablo Aguayo Vallejo + Show 2 more

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https://doi.org/10.1063/5.0010178

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Abstract

Using a single flow-type parameter, we obtain analytic expressions for the unsteady and steady stress distribution for upper-convected Maxwell fluids in mixed shear and planar extensional flows, experimentally achieved in a four-roll mill. We propose two expressions to quantify the shear and extensional contributions to the strain rate magnitude. Finally, we conduct an analysis on the appearing rheological functions by defining apparent shear viscosity as a function of the flow-type parameter and the Weissenberg number.

Highlights

The study of the rheological properties for non-Newtonian fluids, especially polymeric solutions, is a task of great interest, both from a fundamental and a practical point of view.[1]
This study focuses on mixed shear and planar extensional flows, that is, 0 < α < 1
Against the typical assumption of pure shear and pure extensional flows, real flows are of a mixed nature

Summary

INTRODUCTION

The study of the rheological properties for non-Newtonian fluids, especially polymeric solutions, is a task of great interest, both from a fundamental and a practical point of view.[1]. There is a strong technological interest in controlling the behavior of fluids in a variety of flow regimes that are not accessible to experimental measurements.[11] This has highlighted the need for the study of rheological properties of fluids, especially in extensional flows,[11,13–16] the development of computational techniques able to access extensional flows and mixed flows,[1,17–22] and study of flow classification criteria.[23,24]. With this in mind, for the mixed flows experimentally achieved in a four-roll mill, where the extensional and rotational contributions may be continuously varied, we obtain, through a theoretical analysis, the stress response of upper-convected Maxwell (UCM) fluids. We use the definitions presented in the official nomenclature for material functions describing the response of a viscoelastic fluid to various shearing and extensional deformations by Dealy.[25]

THE FLOW-TYPE PARAMETER

STRESS DISTRIBUTION FOR UCM FLUIDS IN MIXED FLOWS

QUANTIFYING SHEAR AND EXTENSIONAL CONTRIBUTIONS

APPARENT SHEAR VISCOSITY FOR UCM FLUIDS IN MIXED FLOWS

CONCLUDING REMARKS