Pressure jump interface law for the Stokes-Darcy coupling: Confirmation by direct numerical simulations

It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers-Joseph slip law. To the contrary, interface law for the effective stress has been a subject of controversy. Recently, a pressure jump interface law has been rigorously derived by Marciniak-Czochra and Mikeli\'c. In this paper, we provide a confirmation of the analytical result using direct numerical simulation of the flow at the microscopic level.Comment: 25 pages, preprin

Kinetics of Gravity-Driven Water Channels Under Steady Rainfall

We investigate the formation of fingered flow in dry granular media under simulated rainfall using a quasi-2D experimental set-up composed of a random close packing of mono-disperse glass beads. Using controlled experiments, we analyze the finger instabilities that develop from the wetting front as a function of fundamental granular (particle size) and fluid properties (rainfall, viscosity).These finger instabilities act as precursors for water channels, which serve as outlets for water drainage. We look into the characteristics of the homogeneous wetting front and channel size as well as estimate relevant time scales involved in the instability formation and the velocity of the channel finger tip. We compare our experimental results with that of the well-known prediction developed by Parlange and Hill [1976]. This model is based on linear stability analysis of the growth of perturbations arising at the interface between two immiscible fluids. Results show that in terms of morphology, experiments agree with the proposed model. However, in terms of kinetics we nevertheless account for another term that describes the homogenization of the wetting front. This result shows that the manner we introduce the fluid to a porous medium can also influence the formation of finger instabilities.Comment: 13 pages, 7 figure

Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients

Improved micro-continuum approach for capillary-dominated multiphase flow with reduced spurious velocity

A diverse range of multiphase flow and transport occurs in multiscale porous media. The multiphase micro-continuum Darcy-Brinkmann-Stokes (DBS) model has been developed to simulate the multiphase flow at both the pore and continuum scales via single-field equations. However, the unacceptable spurious velocities produced by the conventional micro-continuum DBS model present challenges to the modeling of capillary-dominated flow dynamics. This study improves the micro-continuum DBS model to mitigate these spurious velocities at the gas-liquid interface and contact-line regions. A hybrid interpolation scheme is proposed to improve the computational accuracy of the interface curvature and reduce the spurious velocity around the gas-liquid interface by 1-2 orders of magnitude. At the porous boundary, the normal to the gas-liquid interface is corrected, and the normal to the solid-fluid interface is smoothed to guarantee the prescribed wettability condition and decrease the spurious velocities at the contact-line region by an order of magnitude. A series of static and dynamic benchmark cases are investigated to demonstrate that the improved DBS model can simulate capillary-dominated multiphase flows with negligible spurious velocities at capillary numbers as low as 10-4 in both simple and complex geometries. The improved DBS model can combine X-ray computed micro-tomography images to perform multiscale simulations of capillary-dominated multiphase flow and understand the effect of sub-resolution porosity on fluid dynamics in naturally multiscale rocks