Viscoplastic corner eddies

When viscous fluid in a corner is disturbed, eddies can form in the absence of inertia. Examples of flow configurations in which this motion occurs include flow through an abrupt contraction and over a cavity. Six decades ago, Moffatt (J. Fluid Mech., vol. 18, 1964, pp. 1–18) calculated the slow vis...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 941
Main Authors Taylor-West, Jesse J., Hogg, Andrew J.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 25.06.2022
Subjects
Aquatic reptiles
Boundary layers
Corner flow
Dimensionless numbers
Eddies
Fluid flow
Fluids
Inertia
JFM Papers
Newtonian fluids
Non Newtonian fluids
Plugs
Scaling
Viscoplastic materials
Viscous flow
Viscous fluids
Vortices
Yield strength
Yield stress
plastic materials
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Summary:When viscous fluid in a corner is disturbed, eddies can form in the absence of inertia. Examples of flow configurations in which this motion occurs include flow through an abrupt contraction and over a cavity. Six decades ago, Moffatt (J. Fluid Mech., vol. 18, 1964, pp. 1–18) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous ‘Moffatt eddies’. In this study we examine corner flows of viscoplastic materials, a class of non-Newtonian fluids which exhibit solid-like behaviour for stresses below a yield stress. Specifically, we consider a Bingham fluid, for which the material is perfectly rigid at stresses below the yield stress. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-Lagrangian method, and analytically, by employing a viscoplastic boundary layer formulation and scaling arguments. We measure the depth of the static plug as a function of the Bingham number (dimensionless yield stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid adjacent to the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2022.352