We present an efficient and accurate characteristic method for the solution of the unsteady-state advection-diffusion transport equations, which arise in the mathematical models for flow and transport processes in porous media. The advantages of this method include symmetrizing the governing transport equation, treating boundary conditions naturally in the formulation, and conserving mass. More...

We derive from kinetic theory, fluid mechanics and thermodynamics the minimal continuum-level equations governing the flow of a binary, non-electrolytic mixture in an isotropic porous medium with osmotic effects. For dilute mixtures, these equations are linear and in this limit provide a theoretical basis for the widely used semi-empirical relations of Kedem & Katchalsky (Kedem & Katchalsky 195...

The dispersion of passive scalar by Stokes flow through a dilute suspension of solid spheres fixed at random points in space is a basic model of mixing and transport in an unconsolidated porous medium. Earlier investigators have used a general theory of macroscopic transport to calculate the Lagrangian velocity autocorrelation function and the effective diffusivity of this system. If the tracer...

Barometric pumping plays a crucial role in the release of trace gases from fractured porous media to the atmosphere, and it requires a rigorous and complete modeling in order to go beyond the approximate schemes available in the literature. Therefore, a coupled set of convection and convection-diffusion equations for a slightly compressible fluid in unsteady conditions should be solved. The num...

We develop a model for the propagation of a fluid-filled crack in a porous medium. The problem is motivated by the mechanism whereby drainage networks may form in partially molten rock below the Earth‘s lithosphere. Other applications include the propagation of hydraulic fractures in jointed rocks and in oil drilling operations, and the formation of dessication cracks in soils. Motivated by the...

The purpose of the present paper is to study an unsteady laminar flow of an incompressible conducting viscous dusty fluid between two infinitely non-conducting parallel plates, where above plate is bounded by porous medium. The flow is influenced by pulsatile pressure gradient, uniform magnetic field which is applied perpendicular to the plates and due to oscillations of the plates under the ef...

A novel discrete singular convolution (DSC)  formulation  is  presented for the seepage analysis in irregular geometric porous media. The DSC is a new promising numerical approach which has been recently applied to solve several engineering problems. For a medium with regular geometry, realizing of the DSC for the seepage analysis is straight forward. But DSC implementation for a medium with ir...

Porous medium vacuum drying is a complicated heat and mass transfer process. Based on the theory of heat and mass transfer, a coupled model for the porous medium vacuum drying process is constructed. The model is implemented and solved using COMSOL software. The water evaporation rate is determined using a nonequilibrium method with the rate constant parameter Kr. Kr values of 1, 10, 1000, and ...

The thin film and quantum drift diffusion equations belong to a fourth-order family of evolution equations proposed in [21] to be analogous to the (second-order) porous medium family. They are 2Wasserstein (= d2) gradient flows of the generalized Fisher information I(v) just as the porous medium family was shown to be the d2 gradient flow of the generalized entropy E(v) by Otto [40]. The identi...

the heat and mass transfer analysis for mhd casson fluid boundary layer flow over a permeable stretching sheet through a porous medium is carried out. the effect of non-uniform heat generation/absorption and chemical reaction are considered in heat and mass transport equations correspondingly. the heat transfer analysis has been carried out for two different heating processes namely; the prescr...