Hall effects on an unsteady MHD flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes embedded in a porous medium have been studied. The governing equations have been solved analytically using the Laplace transform technique. The effects of rotation parameter, Hall parameter, Hartmann number and Darcy number have been conside...

The stability of buoyant flow in a vertical porous layer bounded by impermeable-isothermal boundaries is studied insofar as the variability fluid viscosity with temperature concerned. governed modified Darcy's law two different forms viscosity–temperature relationships namely, quadratic and exponential. modal analysis carried out velocity–temperature formulation governing equations for perturba...

We consider finite element methods for the Darcy equations that are designed to work with standard, low order C finite element spaces. Such spaces remain a popular choice in the engineering practice because they offer the convenience of simple and uniform data structures and reasonable accuracy. A consistently stabilized method [20] and a least-squares formulation [18] are compared with two new...

The Workshop was asked by Pall Corporation to consider ways in which membrane morphology may be characterized, and how such characterization can be used to assess filtration efficiency. The working group considered a variety of different (but related) approaches, which are outlined below but which will be described in more detail in the forthcoming report. 1 Darcy flow model In an effort to cha...

An implementation of a coupled Navier-Stokes/Darcy model based on different Dune discretization modules is presented. The Darcy model is taken from DuMux, the Navier-Stokes model is implemented on top of Dune-PDELab, and the coupling is done with help of Dune-MultiDomain together with some project-specific auxiliary code. The Navier-Stokes model features one fluid phase, the Darcy model two flu...

We present a numerical study of convection in horizontal layer comprising fluid-saturated porous bed overlain by an unconfined fluid layer. Convection is driven vertical, destabilising temperature difference applied across the whole system, as canonical Rayleigh-B\'enard problem. Numerical simulations are carried out using single-domain formulation two-layer problem based on Darcy-Brinkman equa...

We consider the homogenization limit of compressible barotropic Navier–Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. study regime particle sizes and distances such that volume fraction particles tends to zero but their resistance density infinity. Assuming Mach number is decreasing with certain rate, rescaled velocity pressure microsc...

We report on the reptation of vertically vibrated droplets of fine particles lying on a solid incline. On the one hand, time-resolved measurements show that the gas pressure in the gap between the droplet bottom and the solid surface can be accounted for by a Darcy law. The cumulative effect of the viscous drag is responsible for the droplet formation. On the other hand, we show that the gap pr...

We present a novel moving overset grid scheme for the accurate and efficient long-time simulation of an air bubble displacing a non-Newtonian fluid in the prototypical thin film device, the Hele–Shaw cell. We use a two-dimensional generalization of Darcy s law that accounts for shear thinning of a non-Newtonian fluid. In the limit of weak shear thinning, the pressure is found from a ladder of t...

Although hydrocarbon production from unconventional reservoirs, the so-called shale gas, has exploded recently, reliable predictions of resource availability and extraction are missing because conventional tools fail to account for their ultra-low permeability and complexity. Here, we use molecular simulation and statistical mechanics to show that continuum description--Darcy's law--fails to pr...