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.