Stokes flow through a row of cylinders between parallel walls: model for the glomerular slit diaphragm

As a model for flow through the slit diaphragms which connect the epithelial foot processes of renal glomerular capillaries, finite element solutions of Stokes equations were obtained for flow perpendicular to a row of cylinders confined between parallel walls. A dimensionless "additional resistance" (f), defined as the increment in resistance above the Poiseuille flow value, was computed for L/W < or = 4 and 0.1 < or = R/L < or = 0.9, where L is half the distance between cylinder centers, W is half the distance between walls and R is the cylinder radius. Two factors contributed to f: the drag on the cylinders, and the incremental shear stresses on the walls of the channel. Of these two factors, the drag on the cylinders tended to be dominant. A more complex representation of the slit diaphragm, suggested in the literature, was also considered. The predicted hydraulic permeability of the slit diaphragm was compared with experimental values of the overall hydraulic permeability of the glomerular capillary wall.