Revisiting boundary layer flows of viscoelastic fluids

TL;DR

This paper reevaluates high Reynolds number boundary layer flows of viscoelastic fluids, correcting previous incomplete models, and finds that viscoelasticity causes boundary layer thinning and increased stress, challenging prior assumptions.

Contribution

It provides a correct reformulation of the boundary layer problem for viscoelastic fluids and demonstrates the effects of viscoelasticity on flow and stress, contradicting earlier studies.

Findings

Viscoelasticity increases boundary layer stress and velocity.

Boundary layer thickness decreases with higher viscoelastic flow parameter.

Results are supported by asymptotic analysis.

Abstract

In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly reformulate the problem and solve the governing equations using a Chebyshev collocation scheme. By analysing the decay of the solutions to the far-field we determine the correct stress boundary conditions required to solve problems of this form. Our results show that both the fluid velocity within the boundary layer and the stress at the solid boundary increase due to the effect of viscoelasticity. As a consequence of this, we predict a thinning of the boundary layer as the value of the dimensionless viscoelastic flow parameter is increased. These results contradict a number of prominent studies in the literature but are supported by results owing from an asymptotic analysis based on the assumption of the smallness of the non-dimensional viscoelastic flow parameter.