Journal of Engineering Mathematics

, Volume 64, Issue 4, pp 353-365

First online:

Flow in a multi-branching 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 compliant-walled channel which branches into two or more daughters is considered with the aim of understanding blood flow through arterio-venous malformations (AVMs) in the brain. The outer walls of the channel are assumed for definiteness to behave as spring-back 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 flow-structure interaction problem using a complex variable method. The flow shows markedly different qualitative features downstream of the branching, depending on the wall stiffness.


Branching channel Compliant walls Inviscid fluid flow Matching