Viscoelastic laminar drag bounds in pipe flow

TL;DR

This paper establishes bounds on laminar drag in viscoelastic pipe flow, linking flow properties to Newtonian fluids, and provides analytical insights into effective viscosity and shear-thinning behavior.

Contribution

It introduces bounds on viscoelastic laminar drag based on Newtonian fluid properties and offers an analytical interpretation of shear-thinning phenomena.

Findings

Viscoelastic flow friction is bounded by solvent and total viscosity Newtonian flows.

Flow of viscoelastic solutions exhibits lower friction factors due to increased strain rates.

Effective viscosity correlates with the conformation tensor, explaining shear-thinning.

Abstract

The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the solution. The lower friction factor for the flow of the solution when compared to the latter is tracked to an increased strain rate needed to enhance viscous dissipation. Lastly, we show analytically that the effective viscosity varies similarly to the radial diagonal component of the conformation tensor as observed numerically in turbulent flows, and give a lucid interpretation of shear-thinning through a sequence of underlying constitutive physical phenomena.