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Oscillatory motion of a viscoelastic fluid within a spherical cavity

Published online by Cambridge University Press:  21 September 2011

Julia Meskauskas ,
Rodolfo Repetto  and
Jennifer H. Siggers
Julia Meskauskas
Affiliation:
Department of Engineering of Structures, Water and Soil, University of L’Aquila, Strada provinciale per Monticchio, Monticchio, 67100 L’Aquila, Italy
Rodolfo Repetto*
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
Jennifer H. Siggers
Affiliation:
Department of Bioengineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

We study the motion of a viscoelastic fluid within a rigid spherical cavity with the aim of improving understanding of the motion of the vitreous humour in the human eye. The flow of vitreous humour leads to traction on the retina, which, once the retina is torn or damaged, can cause it to detach from the choroid, leading to loss of sight if left untreated. In the first part of the paper we investigate the relaxation behaviour of the fluid, the transient flow that would be observed in the stationary sphere starting from non-stationary initial conditions. For a general viscoelastic fluid we calculate the growth rates and eigenfunctions associated with the system, and we discuss two particular rheological models of the vitreous humour taken from the literature. In the second part of the paper we consider forced oscillations of the fluid, due to small-amplitude rotations of the sphere about a diameter, representing saccades of the eyeball. We conclude with a discussion of the possible occurrence of resonant phenomena and their clinical relevance.

JFM classification

Biological Fluid Dynamics: Biomedical flows Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 1 - 22
Copyright
Copyright © Cambridge University Press 2011

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