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Low-Reynolds-number flow through two-dimensional shunts

Published online by Cambridge University Press:  16 April 2013

A. Setchi ,
A. J. Mestel ,
K. H. Parker  and
J. H. Siggers
A. Setchi*
Affiliation:
Department of Bioengineering, Imperial College London, London SW7 2AZ, UK
A. J. Mestel
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
K. H. Parker
Affiliation:
Department of Bioengineering, Imperial College London, London SW7 2AZ, UK
J. H. Siggers
Affiliation:
Department of Bioengineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: asetchi@imperial.ac.uk
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Abstract

Motivated by numerous biological and industrial applications relating to bypasses, mixing and leakage, we consider low-Reynolds-number flow through a shunt between two channels. An analytical solution for the streamfunction is found by matching biorthogonal expansions of Papkovich–Fadle eigenfunctions in rectangular subregions. The general solution can be adapted to model a variety of interesting problems of flow through two-dimensional shunts by imposing different inlet and outlet flux distributions. We present several such flow profiles but the majority of results relate to the particular problem of a side-to-side anastomosis in the small intestine. We consider different flux fractions through the shunt with particular emphasis on the pressure and recirculating regions, which are important factors in estimating health risks pertaining to this surgical procedure.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 21 - 39
Copyright
©2013 Cambridge University Press 

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