Steady streaming of a viscoelastic fluid within a periodically rotating sphere
File(s)
Published version
Author(s)
Siggers, JH
Repetto, R
Meskauskas, J
Type
Journal Article
Abstract
Motivated by understanding mass transport processes occurring in the vitreous chamber of the eye, we consider the steady streaming component of the flow generated in a viscoelastic fluid contained within a hollow, rigid sphere performing small-amplitude, periodic, torsional oscillations about an axis passing through its centre. The problem is solved semi-analytically, assuming that the amplitude of the oscillations is small. The paper extends the work by Repetto et al. (J. Fluid Mech., vol. 608, 2008, pp. 71–80), in which the case of a purely viscous fluid was analysed. However, in reality, in young and healthy subjects, the vitreous humour has complex rheological properties, and so here we model it as a viscoelastic fluid. A similar problem was studied by Nikolakis (Eine Theorie für stationäre Drifterscheinungen viskoelastischer Flüssigkeiten, 1992, VDI). In the present model, the steady streaming flow is governed by four dimensionless parameters. We show that, when we account for the viscoelasticity of the fluid, there is a considerably more complex set of possible flow regimes than was found in the purely viscous case, and the flows can be classified into five qualitatively different types. Whereas there was only one circulation cell in each hemisphere in the viscous case, accounting for viscoelasticity it is possible have either one, two or three circulation cells, with different senses of rotation, depending on the parameter values.
Date Issued
2014-11-25
Citation
Journal of Fluid Mechanics, 2014, 761, pp.329-347
ISSN
1469-7645
Publisher
Cambridge University Press (CUP)
Start Page
329
End Page
347
Journal / Book Title
Journal of Fluid Mechanics
Volume
761
Copyright Statement
© 2014 Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9439982&fileId=S0022112014005461
Publication Status
Published