Constitutive equation Darcy

Due to the infinitesimal dimension of the pore sizes, Equation (3.3) is often inapplicable to porous media. Therefore, the momentum conservation for the fluid flow through the porous electrodes is often substituted by the phenomenologically derived constitutive equations, such as Darcy s law given by... 

Both MTPM and DGM share the Darcy s constitutive equation governing the permeation molar flux intensity of the z th component Nf,... 

Combining the spatial Darcy and constitutive equations and integrating across the cake with limits of (0, L) on X and (0, Ap ) on p yields ... 

Relationship of superficial liquid flow rate q to liquid pressure gradient, Darcy s law. Empirical constitutive equations relating permeability K, specific resisfance a, and soli-dosify (vol fraction of solids) e, to the effective pressure. 

Balance of momentum for dissolved species and for fluid phases are reduced to constitutive equations (Pick s law and Darcy s law). 

At small deflection from equilibrium is observed linear correlation between action of individual forces F. and the rate V. of flows they form. Such linear correlation forms the foundation of many laws (Darcy, Pick, Fourier, etc.) and is called phenomenological correlation or constitutive equation. That is why, if the migration rate of component i depends simultaneously on the action of several different forces j, it may be expressed as a sum of linear function ... 

Hence dU represents that part of the plastic work which is not dissipated into heat. Returning to (65), it is observed that the non-negativity of the dissipation Op leads to Darcy s law as the constitutive equation of flow, which is defined for the isotropac case as ... 

Compressible Single Phase Flow Single phase flow is of theoretical and practical importance. In this simpler model there is only one phase so that a single balance law, for phase-A say, and a single constitutive equation, the classical Darcy s law... 

From equation (14)i we could obtain the Darcy s law, if we neglect the inertial terms and the mass exchange and make suitable constitutive hypotheses on fields m,bf and Tf. The equation of balance (15)i for the volume fraction generalize the classical Langmuir s evolution equation, while the balance (15)2 for the microstretch Us includes the Wilmanski s porosity balance as well as the equation which rules the changes of internal surfaces area of the pores (see [8, 11, 1], respectively). The energy balance equations do not appear at all because the process is assumed to be isothermal. 

As discussed in Section 1, the absolute permeability is a constitutive macroscopic property which arises in the local volume-averaged momentum balance, which is Darcy s law (Eq. (2)). It is interesting that, while the porosity can be defined independently of the equation of continuity, the permeability is... 

To calculate the pore pressure response due to a volume source we use the Green s function based on the effective Biot theory. We write the coupled system of equations directly from the constitutive relations given by Biot (1962). These are the total stress of the isotropic porous medium, the stress in the porous fluid, the momentum balance equation for total stress, and the generalized Darcy s law. Following Parra (1991) and Boutin et al. (1987), the coupled system of differential equations in the... 

The material balance equations for the water vapor and the inert gas are given by Equations 12.10 and 12.11, and the constitutive expressions for and N-a, are obtained from Equations 12.12 and 12.13. Equation 12.17 represents one possible form for the rate expression of the removal of bound water (see Section 12.2.2), and this equation (or its simpler form, as discussed above) could be used to describe the change in the concentration of sorbed water with time. The total mass flux Nf through the porous dried layer is obtained from Darcy s law, and is given by Equation 12.16. 

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