Gravity flow in rock fractures with substrate and edge drainage

We investigate the influence of fluid rheology on flow in a finite rock fracture with vertically varying aperture and subject to competing drainage mechanisms due permeable substrate draining edge. The is release volume fluid, either Newtonian, Ostwald–deWaele, or Herschel–Bulkley. Hele–Shaw analogy between lubrication seepage flows allows extending our results porous medium permeability porosity vertical direction. general solution numerical, except for self-similar derived Newtonian fluids constant another Ostwald–deWaele without drainage. Results profile current remaining within fracture, drained at edge, depend dimensionless parameter λ incorporating rheology, geometry, ambient depth; times exhibit order magnitude variations depending λ. A second parameter, λ′, intervenes Herschel–Bulkley fluids, λ′→∞ fluids. theoretical model validated series experiments conducted novel experimental apparatus, accurately reproducing condition allowing determination λ′. agreement theory both configurations V-shaped quite good, considering approximations uncertainties. present analysis shows how domain anisotropy, though simply schematized, are relevant correct estimation all integral variables, such as residual function time.