Shear Flow Interaction Between a Tube and the Surrounding Matrix

In this study, we derive the exact solution for the distribution of flow velocities in a tube and the surrounding porous media, with the pressure gradient being parallel to the wall. Analysis using the solution leads to a conclusion that for a tube with radius at the order of pore size or smaller, tube flow arises dominantly from the Beavers–Joseph condition. For an infinite fine tube, the average velocity approaches the specific flux in the matrix. This paper theoretically reveals the existence of a hyporheic zone in the extreme case of no boudinage, and thickness of the zone is quantified using the intrusion depth of tube water into the matrix.