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SELF-EXCITED OSCILLATIONS IN A COLLAPSIBLE CHANNEL WITH APPLICATIONS TO RETINAL VENOUS PULSATION

Part of: Biological fluid mechanics

Published online by Cambridge University Press:  15 August 2019

PETER S. STEWART Open the ORCID record for PETER S. STEWART [Opens in a new window]  and
ALEXANDER J. E. FOSS Open the ORCID record for ALEXANDER J. E. FOSS [Opens in a new window]
PETER S. STEWART*
Affiliation:
School of Mathematics and Statistics, The Mathematics and Statistics Building, University Place, University of Glasgow, Glasgow G12 8SQ, UK email peter.stewart@glasgow.ac.uk
ALEXANDER J. E. FOSS
Affiliation:
Department of Ophthalmology, Queen’s Medical Centre, Nottingham NG7 2UH, UK email alexaner.foss@nottingham.ac.uk
*
✉peter.stewart@glasgow.ac.uk
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Abstract

We consider a theoretical model for the flow of Newtonian fluid through a long flexible-walled channel which is formed from four compliant and rigid compartments arranged alternately in series. We drive the flow using a fixed upstream flux and derive a spatially one-dimensional model using a flow profile assumption. The compliant compartments of the channel are assumed subject to a large external pressure, so the system admits a highly collapsed steady state. Using both a global (linear) stability eigensolver and fully nonlinear simulations, we show that these highly collapsed steady states admit a primary global oscillatory instability similar to observations in a single channel. We also show that in some regions of the parameter space the system admits a secondary mode of instability which can interact with the primary mode and lead to significant changes in the structure of the neutral stability curves. Finally, we apply the predictions of this model to the flow of blood through the central retinal vein and examine the conditions required for the onset of self-excited oscillation. We show that the neutral stability curve of the primary mode of instability discussed above agrees well with canine experimental measurements of the onset of retinal venous pulsation, although there is a large discrepancy in the oscillation frequency.

Keywords

self-excited oscillationsflexible-walled channel

MSC classification

Primary: 76Z05: Physiological flows
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 3 , July 2019 , pp. 320 - 348
Copyright
© 2019 Australian Mathematical Society 

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