Modified Darcy s law

The modified Darcy s law for non-Newtonian fluid through porous medium is... 

On the other hand, the v values of the 7.5 and 10.0 wt % silica suspensions are more negatively deviated from that predicted by the modified Darcy s law with an increase in the silica concentration. They tend to approach a plateau value with an increase in Vp, This means that the finger velocities of... 

The physical process of melt ascent during two-phase flow models is typically based on the separation of melt and solid described by Darcy s Law modified for a buoyancy driving force. The melt velocity depends on the permeability and pressure gradients but the actual microscopic distribution of the melt (on grain boundaries or in veins) is left unspecified. The creation of disequilibria only requires movement of the fluid relative to the solid. 

The traditional, continuum-based approach uses Darcy s law, modified for partially saturated porous media, to quantify the flux of water ... 

Analyze the linear stability of the fluid layer. The analysis is similar to the classical Rayleigh-Benard problem, but simpler because the Navier-Stokes equations are replaced with Darcy s law. It can be solved analytically. In place of the Rayleigh number, you should find that the stability depends on a modified Rayleigh number,... 

Based on the principle of mass conservation and Darcy s law, a modified form of Biot s (1955) equation for flow through deformable porous media is written tensorially as (Guvanasen and Chan 2000) ... 

Unsaturated flow formulation is necessary here as far as suction has to be known. The flow model used is based on works in relation with the problem of nuclear waste disposal (Collin et al. 2002a). For each fluid (Water and oil), balance equations and state equations are written. In partial saturation conditions, the permeability and the storage law have to be modified a generalised Darcy s law defines the fluid motion (Bear 1972). Numerous couplings existing between mechanics and flows are considered. 

The filter cake concentration profile relative to actual height from the medium can be obtained from the above if the superficial filtrate flow rate through the medium q has been measured via a modified form of Darcy s law Equation (2.47) ... 

Lloyd and Dodds [1972] calculated the flow of liquid firomthe cake by application of Darcy s law to elemental sections of the cake using a relative permeability model Wakeman [1979] extended this approach by incorporating a pore distribidion function in the relationship between saturation and capillary pressure. Ihe model involves a con q)utation of liquid and gas flow by a simultaneous solutions of Darcy s law. The relative permeability values used are obtained from a pore size disbibotian index X which relates the average reduced saturation of the cake to the ratio of the modified thrediold pressure Pb to the capillary pressure Pc. The equations are ... 

In macrolevel analysis, capillary number can be modified while retaining Darcy s law to describe the bulk impregnation of the resin into the fiber preforms. It is useful to point out that the anisotropic nature of the fiber preforms will now appear in the permeability tensor and we can expect some directionality of the capillary pressure influence, which is not necessary in almost all other research areas, where capillary pressure is used. Thus... 

A number of different approaches are proposed and used in modeling flow through porous media. Some of the most popular approaches include (i) Darcy s law, (ii) Brinkman equation, and (iii) a modified Navier-Stokes equation. In the absence of the bulk fluid motion or advection transport, the reaction gas species can only transport through the GDL and CL by the diffusion mechanisms, which we will discuss in a later section. 

The modified Navier-Stokes equation reduces to Brinkman s equahon when the inertia force term is dropped and it reduces to Darcy s law when both inertia and viscous force terms are dropped. 

Permeability Description in Hydrogeology In hydrogeological practice, a modified version of Darcy s law is frequently applied. Water flow q is referenced to the hydraulic gradient... 

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