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Selective withdrawal of a three-layer viscous fluid

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posted on 2023-05-21, 15:45 authored by Lachlan West, Jason CosgroveJason Cosgrove, Andrew BassomAndrew Bassom
Two dimensional, selective withdrawal of a three-layer fluid in a rectangular tank is considered. Each fluid is viscous, weakly compressible and miscible. The lowermost, heaviest fluid flows with constant speed out through line sinks located on the base and lower side walls of the tank. The uppermost and lightest fluid recharges the tank via line sources located along the top and on the upper side walls at a rate that matches the outward flux. If the line sinks are turned on suddenly, the interfaces between the fluids are drawn downward at different rates; this disparity arises due to the fact that the wave configurations that propagate along the two interfaces are not the same. Density and vorticity contours are presented and used to determine the time at which the middle transition layer of fluid begins to be withdrawn from the tank; at this point the rate of extraction of the most dense fluid is its greatest. Inviscid linearised interfaces are calculated which serve as checks on the early stage evolution of the full nonlinear model.

History

Publication title

Journal of Engineering Mathematics

Volume

133

Pagination

1-20

ISSN

1573-2703

Department/School

School of Natural Sciences

Publisher

Springer Netherlands

Place of publication

Netherlands

Rights statement

© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International (CC by 4.0) License, http://creativecommons.org/licenses/by/4.0/ which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

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  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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