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Linear Taylor–Couette stability of a transversely isotropic fluid
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Holloway, Craig R., Dyson, Rosemary J. and Smith, D. J. (David J.) (2015) Linear Taylor–Couette stability of a transversely isotropic fluid. Proceedings of the Royal Society A : mathematical, physical and engineering sciences, 471 (2178). pp. 1-13. 20150141. doi:10.1098/rspa.2015.0141 ISSN 1364-5021.
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Official URL: http://dx.doi.org/10.1098/rspa.2015.0141
Abstract
Fibre-laden fluids are found in a variety of situations, while Couette devices are used for flow spectroscopy of long biological molecules, such as DNA and proteins in suspension. The presence of these fibres can significantly alter the rheology of the fluid, and hence must be incorporated in any modelling undertaken. A transversely isotropic fluid treats these suspensions as a continuum with an evolving preferred direction, through a modified stress tensor incorporating four viscosity-like parameters. We consider the axisymmetric linear stability of a transversely isotropic viscous fluid, contained between two rotating co-axial cylinders, and determine the critical wave and Taylor numbers for varying gap width and inner cylinder velocity (assuming the outer cylinder is fixed). Through the inclusion of transversely isotropic effects, the onset of instability is delayed, increasing the range of stable operating regimes. This effect is felt most strongly through incorporation of the anisotropic shear viscosity, although the anisotropic extensional viscosity also contributes. The changes to the rheology induced by the presence of the fibres therefore significantly alter the dynamics of the system, and hence should not be neglected.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Centre for Scientific Computing | ||||||||
Library of Congress Subject Headings (LCSH): | Taylor vortices | ||||||||
Journal or Publication Title: | Proceedings of the Royal Society A : mathematical, physical and engineering sciences | ||||||||
Publisher: | The Royal Society Publishing | ||||||||
ISSN: | 1364-5021 | ||||||||
Official Date: | 13 May 2015 | ||||||||
Dates: |
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Volume: | 471 | ||||||||
Number: | 2178 | ||||||||
Number of Pages: | 13 | ||||||||
Page Range: | pp. 1-13 | ||||||||
Article Number: | 20150141 | ||||||||
DOI: | 10.1098/rspa.2015.0141 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 29 December 2015 | ||||||||
Date of first compliant Open Access: | 29 December 2015 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), University of Birmingham, Higher Education Funding Council for England (HEFCE) | ||||||||
Grant number: | EP/J500367/1 |
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