The fluid mechanics of fracture and other junctions

In connection with solute transfer in fracture networks, Hull and Koslow (1986) proposed proportional routing of streamlines through discontinuous fracture junctions (in which inlet and outlet branches alternate). We apply fluid mechanics to the problem and show that the errors of proportional routing may be unacceptably large when the two inlet discharges and the two outlet discharges both differ greatly in magnitude. In extreme cases one inlet flow is wholly excluded from one of the two outlets, and proportional routing is maximally incorrect. Solutions are established for arbitrary discharge patterns through four-way coplanar junctions: exact solutions for Laplace flows (Hele-Shaw flows and Darcy flows (fractures filled with porous material)) and approximate solutions for Stokes flows. The Laplace solutions apply also to a range of transport processes.