Flow in a porous non-axisymmetric annular conduit: Coupling wall compliance and peristalsis
Abstract
Coenen \textit{et al.}\ (\textit{J. Fluid Mech.}, vol.~921, 2021, p.~R2) developed a reduced-order model of peristaltic pumping in non-axisymmetric annular conduits with rigid walls, in the context of periarterial space (PAS) flows. \textit{In vivo} studies show that the PAS's outer wall undergoes significant displacement due to flow within and that the penetrating PASs form a porous pathway. To account for these biomechanical aspects, we revisit the problem of flow in an eccentric annular conduit and incorporate porous drag and two-way-coupled fluid--structure interaction between the compliant outer wall and the cerebrospinal fluid flow within. A Darcy--Brinkman term in the axial momentum equation accounts for drag due to the porous medium. We account for changes in hydraulic resistance due to peristalsis and compliant-wall displacements perturbatively, thereby reducing the problem to a single nonlinear partial differential equation for the axial pressure. This reduced-order model allows us to build a mechanistic understanding of flow through a porous penetrating PAS and enables parametric studies. For small-amplitude peristaltic waves, analytical solutions are possible.
Versions
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BibTeX
@misc{surianarayanan2026flow,
title = {{Flow in a porous non-axisymmetric annular conduit: Coupling wall compliance and peristalsis}},
author = {Nishanth Surianarayanan and Ivan C. Christov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.15239},
eprint = {2607.15239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15239},
}
RIS
TY - UNPB
TI - Flow in a porous non-axisymmetric annular conduit: Coupling wall compliance and peristalsis
AU - Nishanth Surianarayanan
AU - Ivan C. Christov
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2607.15239
UR - https://arxiv.org/abs/2607.15239
AB - Coenen \textit{et al.}\ (\textit{J. Fluid Mech.}, vol.~921, 2021, p.~R2) developed a reduced-order model of peristaltic pumping in non-axisymmetric annular conduits with rigid walls, in the context of periarterial space (PAS) flows. \textit{In vivo} studies show that the PAS's outer wall undergoes significant displacement due to flow within and that the penetrating PASs form a porous pathway. To account for these biomechanical aspects, we revisit the problem of flow in an eccentric annular conduit and incorporate porous drag and two-way-coupled fluid--structure interaction between the compliant outer wall and the cerebrospinal fluid flow within. A Darcy--Brinkman term in the axial momentum equation accounts for drag due to the porous medium. We account for changes in hydraulic resistance due to peristalsis and compliant-wall displacements perturbatively, thereby reducing the problem to a single nonlinear partial differential equation for the axial pressure. This reduced-order model allows us to build a mechanistic understanding of flow through a porous penetrating PAS and enables parametric studies. For small-amplitude peristaltic waves, analytical solutions are possible.
ER -