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Solute dispersion in bifurcating networks

Published online by Cambridge University Press:  27 August 2020

Robert A. Zimmerman  and
Daniel M. Tartakovsky Open the ORCID record for Daniel M. Tartakovsky [Opens in a new window]
Robert A. Zimmerman
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM87545, USA
Daniel M. Tartakovsky*
Affiliation:
Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA94305, USA
*
†Email address for correspondence: tartakovsky@stanford.edu
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Abstract

Advective–diffusive transport of passive scalars in confined environments (e.g. vessels and channels) within a network is of fundamental importance in a plethora of biological and geophysical phenomena. We conduct a leading-order analysis, consistent with the theory of hydrodynamic dispersion, which averages out the radial variability within a vessel. One-dimensional solutions for individual vessels (edges of a network), obtained for arbitrary (undefined) transient Dirichlet boundary conditions, serve as a building block for a network model. A network transport solution is developed by iteratively linking single-vessel solutions to each other in a bifurcating fractal tree model, i.e. at nodes of the network. We find transport behaviour to be strongly affected by the network geometry and daughter vessels to significantly impact the rate of transport in the upstream parent vessels.

JFM classification

Biological Fluid Dynamics: Biomedical flows Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A24
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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