Journal of Engineering Mathematics
, Volume 64, Issue 4, pp 353365
First online:
Flow in a multibranching vessel with compliant walls
 J. E. F. GreenAffiliated withDepartment of Mathematics, University College LondonMathematical Biosciences Institute, The Ohio State University Email author
 , F. T. SmithAffiliated withDepartment of Mathematics, University College London
 , N. C. OvendenAffiliated withDepartment of Mathematics, University College London
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The problem of fluid flow in a compliantwalled channel which branches into two or more daughters is considered with the aim of understanding blood flow through arteriovenous malformations (AVMs) in the brain. The outer walls of the channel are assumed for definiteness to behave as springback plates, whilst the divider is taken as rigid. The fluid is assumed to be incompressible and inviscid. When the Strouhal number is small (as occurs in practice in the brain), there are two main axial length scales, one much longer than the vessel width and the other comparable with the vessel width. Also, in the case of small wall displacements, one can analyse the local flowstructure interaction problem using a complex variable method. The flow shows markedly different qualitative features downstream of the branching, depending on the wall stiffness.
Keywords
Branching channel Compliant walls Inviscid fluid flow Matching Title
 Flow in a multibranching vessel with compliant walls
 Journal

Journal of Engineering Mathematics
Volume 64, Issue 4 , pp 353365
 Cover Date
 200908
 DOI
 10.1007/s106650099285z
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Branching channel
 Compliant walls
 Inviscid fluid flow
 Matching
 Industry Sectors
 Authors

 J. E. F. Green ^{(1)} ^{(2)}
 F. T. Smith ^{(1)}
 N. C. Ovenden ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
 2. Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, 43210, USA