Viscous flow over outflow slits covered by an anisotropic Brinkman medium: A model of flow above interendothelial cell clefts

An analytic series solution is presented for the shear driven flow of a viscous fluid over an infinite series of outflow slits covered by a Brinkman medium with an anisotropic Darcy permeability. The solution is used to model the cellular scale flow of water over and within the endothelial glycocalyx, when the transmural water flux through the vascular endothelium is only allowed to pass via interendothelial cell clefts. Results are presented illustrating the effect of both the glycocalyx properties and the applied shearing rate (imposed by vascular scale fluid dynamics) on several relevant measures of the velocity field, including the wall normal velocity and the shear rate evaluated at the luminal surface of the glycocalyx.

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