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Viscous flow beneath a viscous or plastic skin
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Ball, Thomasina V. and Balmforth, Neil J. (2023) Viscous flow beneath a viscous or plastic skin. Journal of Fluid Mechanics, 957 . A9. doi:10.1017/jfm.2023.17 ISSN 0022-1120.
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Official URL: https://doi.org/10.1017/jfm.2023.17
Abstract
When a viscous fluid spreads underneath a deformable surface skin or crust, the peeling dynamics at the fluid front can control the rate of advance rather than bulk self-similar flow. For an elastic skin, this control results in a quasi-static interior blister held at constant pressure that is matched to a narrow peeling region behind the fluid front. In this paper, the analogous problem is considered for a skin that deforms either viscously or plastically, or both. In particular, the deformable surface is assumed to be a thin plate of material governed by the Herschel–Bulkley constitutive law. We examine how such a skin controls viscous flow underneath, fed at constant flux and spreading as either a planar or axisymmetric current. As for an elastic skin, the peeling dynamics at the viscous fluid front again controls the rate of spreading. However, contrary to that situation, the mathematical matching problem for viscoplastic peeling is simplified considerably as a result of an integral constraint. Despite this, the structure of the peeling region is complicated significantly by any plasticity in the skin, which can create a convoluted peeling wave ahead of the main blister that features interwoven yielded and plugged sections of the plate.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Viscous flow -- Mathematical models, Plastics | ||||||||
| Journal or Publication Title: | Journal of Fluid Mechanics | ||||||||
| Publisher: | Cambridge University Press | ||||||||
| ISSN: | 0022-1120 | ||||||||
| Official Date: | 25 February 2023 | ||||||||
| Dates: |
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| Volume: | 957 | ||||||||
| Article Number: | A9 | ||||||||
| DOI: | 10.1017/jfm.2023.17 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Copyright Holders: | © The Author(s), 2023. Published by Cambridge University Press | ||||||||
| Date of first compliant deposit: | 6 January 2023 | ||||||||
| Date of first compliant Open Access: | 17 February 2023 | ||||||||
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