Balmforth, NJ;
Craster, RV;
Hewitt, DR;
Hormozi, HS;
Maleki, A;
(2017)
Viscoplastic boundary layers.
Journal of Fluid Mechanics
, 813
pp. 929-954.
10.1017/jfm.2016.878.
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Abstract
In the limit of a large yield stress, or equivalently at the initiation of motion, viscoplastic flows can develop narrow boundary layers that provide either surfaces of failure between rigid plugs, the lubrication between plugged flow and a wall, or buffers for regions of predominantly plastic deformation. (Oldroyd 1947, Proc. Camb. Phil. Soc. 43, 383 - 395) presented the first theoretical discussion of these viscoplastic boundary layers, offering an asymptotic reduction of the governing equations and a discussion of some model flow problems. However, the complicated nonlinear form of Oldroyd’s boundary-layer equations has evidently precluded further discussion of them. In the current paper, we revisit Oldroyd’s viscoplastic boundary-layer analysis and his canonical examples of a jet-like intrusion and flow past a thin plate. We also consider flow down channels with either sudden expansions or wavy walls. In all these examples, we verify that viscoplastic boundary layers form as envisioned by Oldroyd. For each example, we extract the dependence of the boundary-layer thickness and flow profiles on the dimensionless yield-stress parameter (Bingham number). We find that, while Oldroyd’s boundary-layer theory applies to free viscoplastic shear layers, it does not apply when the boundary layer is adjacent to a wall, as has been observed previously for two-dimensional flow around circular obstructions. Instead, the boundary-layer thickness scales in a different fashion with the Bingham number, as suggested by classical solutions for plane-parallel flows, lubrication theory and, for flow around a plate, by (Piau 2002, J. Non-Newtonian Fluid Mech. 102, 193 - 218); we rationalize this second scaling and provide an alternative boundary-layer theory.
| Type: | Article |
|---|---|
| Title: | Viscoplastic boundary layers |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jfm.2016.878 |
| Publisher version: | https://doi.org/10.1017/jfm.2016.878 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10083540 |
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