Sandstone, granular media, bone, wood, and cell membranes are just a few examples of porous media that abound in Nature and in synthetic situations. Two important effective properties of fluid-saturated porous media that have been extensively studied are the trapping constant g and scalar fluid permeability k. Exact expressions for the “void” bounds on g and k for coated-spheres and coated-cyli...

In this paper, we consider the Cauchy problem for a porous medium equation in Fingero-imbibition phenomena arising in double phase flow through porous media during oil recovery process. Fingero-imbibition is a physical phenomenon which represents the simultaneous occurrence of two special phenomenon viz. fingering and imbibitions in a porous media. We obtain a series solution of porous medium e...

We show that chaotic advection is inherent to flow through all types of porous media, from granular and packed media to fractured and open networks. The basic topological complexity inherent to all porous media gives rise to chaotic flow dynamics under steady flow conditions, where fluid deformation local to stagnation points imparts a 3D fluid mechanical analog of the baker's map. The ubiquito...

In this article, we develop a set of partial differential equations describing the flow of a dusty fluid in variable porosity media. The developed equations take into account the effect of the porous microstructure on the flowing phases. We presented and overview of the equations governing the flow of a dusty gas in various type media, including that in naturally occurring porous media. Numeric...

An interconnected set of algorithms is presented for the simulation of two-phase ow in porous media achieving more than two orders of magnitudes acceleration. The accuracy and e ciency of the approach is demonstrated through 2D and 3D numerical experiments for a range of two-phase porous media problems involving single cracks, heterogeneous permeability, and hydrophobic and hydrophilic media

A new model for turbulent flows in porous media is developed. The spatialand time fluctuations in this new model are tied together and treated as a single quantity. This novel treatment of the fluctuations leads to a natural construction of the k and e type equations for rigid and isotropic porous media in which all the kinetic energy filtered in the averaging process is modeled. The same terms...

In this paper we discuss the formulation of the governing equations that describe ow of uids in porous media Various types of uid ow ranging from single phase ow to compositional ow are considered It is shown that all the di erential equations governing these types of ow can be e ectively rewritten in a fractional ow formulation i e in terms of a global pressure and saturation or saturations an...

A mesoscopic numerical tool has been developed in this study for predictions of the effective thermal conductivities for microscale random porous media. To solve the energy transport equation with complex multiphase porous geometries, a lattice Boltzmann algorithm has been introduced to tackle the conjugate heat transfer among different phases. With boundary conditions correctly chosen, the alg...

∗ In this chapter we uncover through numerical simulation the velocity and pressure fields inside a model porous medium composed of an infinitely extending array of staggered square rods. These microtransport simulations allow for the prediction of macrotransport parameters that are of value to the volume-averaged description of fluid motion in porous media. We focus on computing the macroscopi...

Biofilm growth occurs in a variety of random porous media in a range of industrial processes; prediction of its growth and subsequent influence on hydrodynamics is hence desirable. In this study, we present the first numerical 3D pore-scale model of biofilm growth in porous media, based on a lattice Boltzmann simulation platform complemented with an individual-based biofilm model (IbM). We use ...