Blockage coefficient of cylindrical blocker and diffusion resistance of membrane channels

This study deals with potential flow of ideal fluid in an infinite cylindrical tube in the presence of a blocking object. The blockage effect of the object on the flow can be characterized by a lump parameter, blockage coefficient, which accounts for the object shape and size. For a cylindrical blocking object, analytical results for the blockage coefficient are known only in three limiting cases: for a long thin cylinder and for small and large blocking disks. We propose a simple analytical expression for the blockage coefficient of a cylindrical blocker of arbitrary length and radius that reduces to the known asymptotic results in the corresponding limits.