Over the past decade, since it was first observed in vivo, there has been an explosion in interest in the thin (∼500 nm), gel-like endothelial glycocalyx layer (EGL) that coats the luminal surface of blood vessels. In this review, we examine the mechanical and biochemical properties of the EGL and the latest studies on the interactions of this layer with red and white blood cells. This includes its deformation owing to fluid shear stress, its penetration by leukocyte microvilli, and its restorative response after the passage of a white cell in a tightly fitting capillary. We also examine recently discovered functions of the EGL in modulating the oncotic forces that regulate the exchange of water in microvessels and the role of the EGL in transducing fluid shear stress into the intracellular cytoskeleton of endothelial cells, in the initiation of intracellular signaling, and in the inflammatory response.

https://www.annualreviews.org/doi/pdf/10.1146/annurev.bioeng.9.060906.151959

The Structure and Function of the Endothelial Glycocalyx Layer

http://people.bu.edu/edamiano/Damiano_&_Stace02.pdf

A Mechano-Electrochemical Model of Radial Deformation of the Capillary Glycocalyx

We examine the effects of capillarity and gravity in a model of one-dimensional imbibition of an incompressible liquid into a deformable porous material. We focus primarily on a capillary rise problem but also discuss a capillary/gravitational drainage configuration in which capillary and gravity forces act in the same direction. Models in both cases can be formulated as nonlinear free-boundary problems. In the capillary rise problem, we identify time-dependent solutions numerically and compare them in the long time limit to analytically obtain equilibrium or steady state solutions. A basic feature of the capillary rise model is that, after an early time regime governed by zero gravity dynamics, the liquid rises to a finite, equilibrium height and the porous material deforms into an equilibrium configuration. We explore the details of these solutions and their dependence on system parameters such as the capillary pressure and the solid to liquid density ratio. We quantify both net, or global, deformation of the material and local deformation that may occur even in the case of zero net deformation. In the model for the draining problem, we identify numerical solutions that quantify the effects of gravity, capillarity, and solid to liquid density ratio on the time required for a finite volume of fluid to drain into the deformable porous material. In the Appendix, experiments on capillary rise of water into a deformable sponge are described and the measured capillary rise height and sponge deformation are compared with the theoretical predictions. For early times, the experimental data and theoretical predictions for these interface dynamics are in general agreement. On the other hand, the long time equilibrium predicted theoretically is not observed in our experimental data.

/pdf/capillary-rise-of-a-liquid-into-a-deformable-porous-material-m958nwtiqz.pdf

Capillary rise of a liquid into a deformable porous material

The hydrodynamic influence of deformable porous surface layers on the motion of a rigid sphere falling in a narrow cylindrical tube filled with a stationary Newtonian fluid is studied using lubrication theory. The porous layers on both the surface of the tube and the sphere are modelled as binary mixtures of solid and liquid components. The sphere is placed at an arbitrary position in the tube and is free to rotate. Effects of the clearance between the sphere and the tube, the eccentricity of the position of the sphere and the properties of the surface layers on the velocity and rotation of the sphere are studied. It is found that, when the lengthscale on which the velocity varies within the porous layer is much smaller than the clearance, the effects of the porous layer can be represented by an equivalent slip boundary condition, the slip velocity at the boundary being proportional to the local shear rate. The slip velocities have a strong influence on the motion of the sphere when the clearance is small. For a given clearance and slip parameters, both the falling and rotation velocities of the sphere increase with the sphere eccentricity. The shear stresses on the surfaces of both the tube and the sphere are greatly reduced when slip boundary conditions are applied, as is the pressure gradient in the region between the sphere and the tube wall. This work could have some relevance to the creeping motion of blood cells in the microcirculation where the glycocalyx, a polysaccharide-rich layer, covers the external surfaces of both endothelial and red blood cells.

The effect of deformable porous surface layers on the motion of a sphere in a narrow cylindrical tube

Flow-induced deformation from pressurized cavities in absorbing porous tissues.

The flow of a viscous fluid over a thin, deformable porous layer fixed to the solid wall of a channel is considered. The coupled equations for the fluid velocity and the infinitesimal deformation of the solid matrix within the porous layer are developed using binary mixture theory, Darcy's law and the assumption of linear elasticity. The case of pure shear is solved analytically for the displacement of the solid matrix, the fluid velocity both in the porous medium and the fluid above it. For a thin porous layer the boundary condition for the fluid velocity at the fluid-matrix interface is derived. This condition replaces the usual no slip condition and can be applied without solving for the flow in the porous layer.

G. K. Aldis

Papers

Fluid flow over a thin deformable porous layer