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A boundary-integral representation for biphasic mixture theory, with application to the post-capillary glycocalyx.

Sumets PP, Cater JE, Long DS, Clarke RJ - Proc. Math. Phys. Eng. Sci. (2015)

Bottom Line: We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic-mobility problems using boundary element methods.We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer.This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL).

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Science , University of Auckland , Auckland 1142, New Zealand.

ABSTRACT

We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic-mobility problems using boundary element methods. We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer. This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL). In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.

No MeSH data available.


Related in: MedlinePlus

Sinuous vessels ((a–d) cases V–VIII and (e) X, respectively): elastic displacements and shear stresses exerted by the solid phase, the magnitudes of which are indicated by the colour bar. The region inside the dashed box in (d) is shown magnified in figure 18.
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RSPA20140955F15: Sinuous vessels ((a–d) cases V–VIII and (e) X, respectively): elastic displacements and shear stresses exerted by the solid phase, the magnitudes of which are indicated by the colour bar. The region inside the dashed box in (d) is shown magnified in figure 18.

Mentions: Let us now briefly examine the changes which occur when the vessel is sinuous (Φ=π/2). We first note from figures 14 and 15 that the magnitudes of the stresses on the walls and the cell, from both the fluid and solid phases, are comparable with those observed in the varicose case. As the vessel does not expand and contract with downstream distance in the manner of the varicose vessel, the FSSs on the wall have a greater tendency to stay positive. For example, see figure 16, which compares the flow shear stress on the upper wall when xc=(−1,0), for both Φ=0 (case II) and Φ=π/2 (case VI). We see that the region of negative FSS disappears.Figure 14.


A boundary-integral representation for biphasic mixture theory, with application to the post-capillary glycocalyx.

Sumets PP, Cater JE, Long DS, Clarke RJ - Proc. Math. Phys. Eng. Sci. (2015)

Sinuous vessels ((a–d) cases V–VIII and (e) X, respectively): elastic displacements and shear stresses exerted by the solid phase, the magnitudes of which are indicated by the colour bar. The region inside the dashed box in (d) is shown magnified in figure 18.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4528650&req=5

RSPA20140955F15: Sinuous vessels ((a–d) cases V–VIII and (e) X, respectively): elastic displacements and shear stresses exerted by the solid phase, the magnitudes of which are indicated by the colour bar. The region inside the dashed box in (d) is shown magnified in figure 18.
Mentions: Let us now briefly examine the changes which occur when the vessel is sinuous (Φ=π/2). We first note from figures 14 and 15 that the magnitudes of the stresses on the walls and the cell, from both the fluid and solid phases, are comparable with those observed in the varicose case. As the vessel does not expand and contract with downstream distance in the manner of the varicose vessel, the FSSs on the wall have a greater tendency to stay positive. For example, see figure 16, which compares the flow shear stress on the upper wall when xc=(−1,0), for both Φ=0 (case II) and Φ=π/2 (case VI). We see that the region of negative FSS disappears.Figure 14.

Bottom Line: We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic-mobility problems using boundary element methods.We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer.This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL).

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Science , University of Auckland , Auckland 1142, New Zealand.

ABSTRACT

We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic-mobility problems using boundary element methods. We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer. This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL). In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.

No MeSH data available.


Related in: MedlinePlus