No abstract

No abstract

A mathematical model is presented for steady fluid flow across microvessel walls through a serial pathway consisting of the endothelial surface glycocalyx and the intercellular cleft between adjacent endothelial cells, with junction strands and their discontinuous gaps. The three-dimensional flow through the pathway from the vessel lumen to the tissue space has been computed numerically based on a Brinkman equation with appropriate values of the Darcy permeability. The predicted values of the hydraulic conductivity L p , defined as the ratio of the flow rate per unit surface area of the vessel wall to the pressure drop across it, are close to experimental measurements for rat mesentery microvessels. If the values of the Darcy permeability for the surface glycocalyx are determined based on the regular arrangements of fibres with 6 nm radius and 8 nm spacing proposed recently from the detailed structural measurements, then the present study suggests that the surface glycocalyx could be much less resistant to flow compared to previous estimates by the one-dimensional flow analyses, and the intercellular cleft could be a major determinant of the hydraulic conductivity of the microvessel wall.

Interactions of wakes in a ow past a row of square bars, which is placed across a uniform ow, are investigated by numerical simulations and experiments on the assumption that the ow is two-dimensional and incompressible. At small Reynolds numbers the ow is steady and symmetric with respect not only to streamwise lines through the center of each square bar but also to streamwise centerlines between adjacent square bars. However, the steady symmetric ow becomes unstable at larger Reynolds numbers and make a transition to a steady asymmetric ow with respect to the centerlines between adjacent square bars in some cases or to an oscillatory ow in other cases. It is found that vortices are shed synchronously from adjacent square bars in the same phase or in anti-phase depending upon the distance between the bars when the ow is oscillatory. The origin of the transition to the steady asymmetric ow is identiÿed as a pitchfork bifurcation, while the oscillatory ows with synchronous shedding of vortices are clariÿed to originate from a Hopf bifurcation. The critical Reynolds numbers of the transitions are evaluated numerically and the bifurcation diagram of the ow is obtained.

No abstract