The motion of a spherical particle suspended in an incompressible Newtonian fluid flowing longitudinally between hexagonally arranged circular cylinders has been numerically analysed by a finite-element method in the Stokes flow regime. The results are applied to study the diffusive and convective transport of spherical solutes across the vascular endothelial surface glycocalyx, based on the quasi-periodic ultrastructural model. The obtained values of diffusive permeability and reflection coefficient of the solutes show a reasonable agreement with experimental observations, and conform to the hypothesis that the endothelial surface glycocalyx forms the primary size selective structure to solutes in microvascular permeability.