Re-Entrant Corner for a White-Metzner Fluid

Stephen Chaffin,Julia Rees,Nicholas Monk,William Zimmerman

doi:10.3390/fluids6070241

Abstract

Viscoelastic fluids can be difficult to model due to the wide range of different physical behaviors that polymer melts can exhibit. One such feature is the viscous elastic boundary layer. We address the particular problem of a viscoelastic shear-dependent fluid flowing past a corner and investigate how the properties of the boundary layer change for a White-Metzner fluid. The boundary layer equations are derived and the upstream layer is matched with the far-field flow. It was found that if the fluid is sufficiently shear thinning then the viscoelastic boundary layer formulation fails due to the inertial forces becoming dominant. The depth of the boundary layer is controlled by the shear-thinning parameters. These effects are not a feature of other shear-thinning models, such as the Phan-Thien-Tanner model. This study provides insight in the different effects of some commonly used viscoelastic models in corner flows in the upstream boundary layer, the downstream boundary layer is not addressed.

Highlights

Boundary layer structures are ubiquitously found in non-Newtonian fluids due to the myriad of complex competing behaviors, such as those arising from the competing effects of viscoelasticity and viscosity [2,3]
The upstream boundary layer near a re-entrant corner has been studied for the case of a WM fluid
A similarity solution possessing a similar structure to the upper-convective Maxwell (UCM) case was found

Summary

Introduction

Viscoelastic fluids can be difficult to model due to the wide range of different physical behaviors that polymer melts can exhibit. One such feature is the viscous elastic boundary layer. This study provides insight in the different effects of some commonly used viscoelastic models in corner flows in the upstream boundary layer, the downstream boundary layer is not addressed. The classic geometry in which to study viscoelastic boundary layer effects is the re-entrant corner, wedge flows [4] have been studied. The first analytical approach for investigating the properties of viscoelastic stresses in corner flows was presented by Lipscomb et al [10] for the case of a second order fluid, this model is invalid in regimes with large velocity gradients.

Methods

Results

Conclusion