Flow in a wavy-walled channel lined with a poroelastic layer

H. H. Wei*, S. L. Waters, Shu Qian Liu, J. B. Grotberg

*Corresponding author for this work

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Motivated by physiological flows in capillaries, venules and the pleural space, the pressure-driven flow of a Newtonian fluid in a two-dimensional wavy-walled channel is investigated theoretically. The sinusoidal wavy shape is due to the configuration of underlying cells, their nuclei and intercellular junctions or clefts. The walls are lined with a thin poroelastic layer that models the glycocalyx coating of the cell surface. The upper and lower wavy walls are offset axially by the phase angle Φ, where Φ = 0 (π) yields an antisymmetric (symmetric) channel. Biphasic theory is employed for the poroelastic layer and the flow is solved by a lubrication approximation using a small parameter, δ ≪ 1, where δ is the channel width/wavelength ratio. The velocity fields in the core and layer are determined as perturbation expansions in 2 and finite-Reynolds-number effects occur at O(δ2 ) assuming δ2 Re ≪ 1. When the hydraulic resistivity, α, the ratio of the channel width to the Darcy permeability, is sufficiently large and Φ is near enough to π, the flow develops a trapped recirculation eddy within the glycocalyx layer near the widest part of the channel. This can be of significance to transport through the cellular boundary, since that location corresponds to intercellular clefts through which important fluid and solute exchange occurs. Increasing Φ - π diminishes the recirculation region. Increasing the Reynolds number moves the recirculation slightly upstream. Both layer velocity and wall shear stresses decrease as α increases and support the appearance of flow recirculation. Further, the wavy geometry allows a portion of the flow to enter and exit the layer, which provides a mechanism for convective transport between these two regions that otherwise have only diffusive interactions. The relevant Péclet number is Pe = V*n b/D where D is molecular diffusivity and V*n is the normal velocity to the glycocalyx layer. For large molecules, Pe = O(102) or higher, so the convective transport is important. The solid displacement, dictated by the layer flow field, increases as α increases.

Original languageEnglish (US)
Pages (from-to)23-45
Number of pages23
JournalJournal of fluid Mechanics
Issue number492
DOIs
StatePublished - Oct 10 2003

Fingerprint

Reynolds number
Fluids
Lubrication
Shear stress
Flow fields
Hydraulics
Coatings
Wavelength
Molecules
Geometry
Newtonian fluids
lubrication
cells
hydraulics
upstream
shear stress
diffusivity
flow distribution
permeability
solutes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Wei, H. H. ; Waters, S. L. ; Liu, Shu Qian ; Grotberg, J. B. / Flow in a wavy-walled channel lined with a poroelastic layer. In: Journal of fluid Mechanics. 2003 ; No. 492. pp. 23-45.
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title = "Flow in a wavy-walled channel lined with a poroelastic layer",
abstract = "Motivated by physiological flows in capillaries, venules and the pleural space, the pressure-driven flow of a Newtonian fluid in a two-dimensional wavy-walled channel is investigated theoretically. The sinusoidal wavy shape is due to the configuration of underlying cells, their nuclei and intercellular junctions or clefts. The walls are lined with a thin poroelastic layer that models the glycocalyx coating of the cell surface. The upper and lower wavy walls are offset axially by the phase angle Φ, where Φ = 0 (π) yields an antisymmetric (symmetric) channel. Biphasic theory is employed for the poroelastic layer and the flow is solved by a lubrication approximation using a small parameter, δ ≪ 1, where δ is the channel width/wavelength ratio. The velocity fields in the core and layer are determined as perturbation expansions in 2 and finite-Reynolds-number effects occur at O(δ2 ) assuming δ2 Re ≪ 1. When the hydraulic resistivity, α, the ratio of the channel width to the Darcy permeability, is sufficiently large and Φ is near enough to π, the flow develops a trapped recirculation eddy within the glycocalyx layer near the widest part of the channel. This can be of significance to transport through the cellular boundary, since that location corresponds to intercellular clefts through which important fluid and solute exchange occurs. Increasing Φ - π diminishes the recirculation region. Increasing the Reynolds number moves the recirculation slightly upstream. Both layer velocity and wall shear stresses decrease as α increases and support the appearance of flow recirculation. Further, the wavy geometry allows a portion of the flow to enter and exit the layer, which provides a mechanism for convective transport between these two regions that otherwise have only diffusive interactions. The relevant P{\'e}clet number is Pe = V*n b/D where D is molecular diffusivity and V*n is the normal velocity to the glycocalyx layer. For large molecules, Pe = O(102) or higher, so the convective transport is important. The solid displacement, dictated by the layer flow field, increases as α increases.",
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Flow in a wavy-walled channel lined with a poroelastic layer. / Wei, H. H.; Waters, S. L.; Liu, Shu Qian; Grotberg, J. B.

In: Journal of fluid Mechanics, No. 492, 10.10.2003, p. 23-45.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Flow in a wavy-walled channel lined with a poroelastic layer

AU - Wei, H. H.

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N2 - Motivated by physiological flows in capillaries, venules and the pleural space, the pressure-driven flow of a Newtonian fluid in a two-dimensional wavy-walled channel is investigated theoretically. The sinusoidal wavy shape is due to the configuration of underlying cells, their nuclei and intercellular junctions or clefts. The walls are lined with a thin poroelastic layer that models the glycocalyx coating of the cell surface. The upper and lower wavy walls are offset axially by the phase angle Φ, where Φ = 0 (π) yields an antisymmetric (symmetric) channel. Biphasic theory is employed for the poroelastic layer and the flow is solved by a lubrication approximation using a small parameter, δ ≪ 1, where δ is the channel width/wavelength ratio. The velocity fields in the core and layer are determined as perturbation expansions in 2 and finite-Reynolds-number effects occur at O(δ2 ) assuming δ2 Re ≪ 1. When the hydraulic resistivity, α, the ratio of the channel width to the Darcy permeability, is sufficiently large and Φ is near enough to π, the flow develops a trapped recirculation eddy within the glycocalyx layer near the widest part of the channel. This can be of significance to transport through the cellular boundary, since that location corresponds to intercellular clefts through which important fluid and solute exchange occurs. Increasing Φ - π diminishes the recirculation region. Increasing the Reynolds number moves the recirculation slightly upstream. Both layer velocity and wall shear stresses decrease as α increases and support the appearance of flow recirculation. Further, the wavy geometry allows a portion of the flow to enter and exit the layer, which provides a mechanism for convective transport between these two regions that otherwise have only diffusive interactions. The relevant Péclet number is Pe = V*n b/D where D is molecular diffusivity and V*n is the normal velocity to the glycocalyx layer. For large molecules, Pe = O(102) or higher, so the convective transport is important. The solid displacement, dictated by the layer flow field, increases as α increases.

AB - Motivated by physiological flows in capillaries, venules and the pleural space, the pressure-driven flow of a Newtonian fluid in a two-dimensional wavy-walled channel is investigated theoretically. The sinusoidal wavy shape is due to the configuration of underlying cells, their nuclei and intercellular junctions or clefts. The walls are lined with a thin poroelastic layer that models the glycocalyx coating of the cell surface. The upper and lower wavy walls are offset axially by the phase angle Φ, where Φ = 0 (π) yields an antisymmetric (symmetric) channel. Biphasic theory is employed for the poroelastic layer and the flow is solved by a lubrication approximation using a small parameter, δ ≪ 1, where δ is the channel width/wavelength ratio. The velocity fields in the core and layer are determined as perturbation expansions in 2 and finite-Reynolds-number effects occur at O(δ2 ) assuming δ2 Re ≪ 1. When the hydraulic resistivity, α, the ratio of the channel width to the Darcy permeability, is sufficiently large and Φ is near enough to π, the flow develops a trapped recirculation eddy within the glycocalyx layer near the widest part of the channel. This can be of significance to transport through the cellular boundary, since that location corresponds to intercellular clefts through which important fluid and solute exchange occurs. Increasing Φ - π diminishes the recirculation region. Increasing the Reynolds number moves the recirculation slightly upstream. Both layer velocity and wall shear stresses decrease as α increases and support the appearance of flow recirculation. Further, the wavy geometry allows a portion of the flow to enter and exit the layer, which provides a mechanism for convective transport between these two regions that otherwise have only diffusive interactions. The relevant Péclet number is Pe = V*n b/D where D is molecular diffusivity and V*n is the normal velocity to the glycocalyx layer. For large molecules, Pe = O(102) or higher, so the convective transport is important. The solid displacement, dictated by the layer flow field, increases as α increases.

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