Porous media interface

Compared with the use of arbitrary grid interfaces in combination with reduced-order flow models, the porous medium approach allows one to deal with an even larger multitude of micro channels. Furthermore, for comparatively simple geometries with only a limited number of channels, it represents a simple way to provide qualitative estimates of the flow distribution. However, as a coarse-grained description it does not reach the level of accuracy as reduced-order models. Compared with the macromodel approach as propagated by Commenge et al, the porous medium approach has a broader scope of applicability and can also be applied when recirculation zones appear in the flow distribution chamber. However, the macromodel approach is computationally less expensive and can ideally be used for optimization studies. 

In order to simplify the situation, we assume that our porous sample under investigation covers the bottom of an open straight-walled can and fills it to a height d (Figure 1). Such a sample will exhibit the same areal exhalation rate as a free semi-infinite sample of thickness 2d, as long as the walls and the bottom of the can are impermeable and non-absorbant for radon. A one-dimensional analysis of the diffusion of radon from the sample is perfectly adequate under these conditions. To idealize the conditions a bit further we assume that diffusion is the only transport mechanism of radon out from the sample, and that this diffusive transport is governed by Fick s first law. Fick s law applied to a porous medium says that the areal exhalation rate is proportional to the (radon) concentration gradient in the pores at the sample-air interface... 

Soft biological structures exhibit finite strains and nonlinear anisotropic material response. The hydrated tissue can be viewed as a fluid-saturated porous medium or a continuum mixture of incompressible solid (s), mobile incompressible fluid (f), and three (or an arbitrary number) mobile charged species a, (3 = p,m, b). A mixed Electro-Mechano-Chemical-Porous-Media-Transport or EMCPMT theory (previously denoted as the LMPHETS theory) is presented with (a) primary fields (continuous at material interfaces) displacements, Ui and generalized potentials, ifi ( , r/ = /, e, to, b) and (b) secondary fields (discontinuous) pore fluid pressure, pf electrical potential, /7e and species concentration (molarity), ca = dna/dVf or apparent concentration, ca = nca and c = Jnca = dna/dVo. The porosity, n = 1 — J-1(l — no) and no = no(Xi) = dVj/dVo for a fluid-saturated solid. Fixed charge density (FCD) in the solid is defined as cF = dnF/dV , cF = ncF, and cF = cF (Xf = JncF = dnF/d o. 

Abstract When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials. 

Amorphous silicas play an important role in many different fields, since siliceous materials are used as adsorbents, catalysts, nanomaterial supports, chromatographic stationary phases, in ultrafiltration membrane synthesis, and other large-surface, and porosity-related applications [16,150-156], The common factor linking the different forms of silica are the tetrahedral silicon-oxygen blocks if the tetrahedra are randomly packed, with a nonperiodic structure, various forms of amorphous silica result [16]. This random association of tetrahedra shapes the complexity of the nanoscale and mesoscale morphologies of amorphous silica pore systems. Any porous medium can be described as a three-dimensional arrangement of matter and empty space where matter and empty space are divided by an interface, which in the case of amorphous silica have a virtually unlimited complexity [158],... 

In spatially evolving multiphase media (e.g., during dissolution of a porous medium, or phase separation in a polymer blend), the mean curvature of the interface between two phases is of interest. Curvature is a sensitive indicator of morphological transitions such as the transition from spherical to rod-like micelles in an emulsion, or the degree of sintering in a porous ceramic material. Furthermore, important physicochemical parameters such as capillary pressure (from the Young-Laplace equation) are curvature-dependent. The local value of the mean curvature K — (1 /R + 1 /Ri) of an interface of phase i with principal radii of curvature Rx and R2 can be calculated as the divergence of the interface normal vector ,... 

The conducting properties of a liquid in a porous medium can provide information on the pore geometry and the pore surface area [17]. Indeed, both the motion of free carriers and the polarization of the pore interfaces contribute to the total conductivity. Polymer foams are three-dimensional solids with an ultramacropore network, through which ionic species can migrate depending on the network structure. Based on previous works on water-saturated rocks and glasses, we have extracted information about the three-dimensional structure of the freeze-dried foams from the dielectric response. Let be d and the dielectric constant and the conductivity, respectively. Dielectric properties are usually expressed by the frequency-dependent real and imaginary components of the complex dielectric permittivity ... 

Bergman, D. J., and Dunn, K.-J. (1995). Self-diffusion in a periodic porous medium with interface absorption. Phys. Rev. E 51, 3401-3416. 

P7-28i An understanding of bactoria transport in porous media is vital to the efficient operation of the watar flooding of petroleum reservoirs. Bacteria can have both beneficial and harmful effects on the reservoir. In enhanced microbial oil recovery, EMOR, bacteria are injected to secrete surfactants to reduce the interfacia] tension at the oil-water interface so that the oil will flow out more easily. However, under some circumstances the bacteria can be harmful, by plugging the pore space and thereby block the flow of water and oil. One bacteria that has been studied, Leuconostoc mesentroides, has the unusual behavior that when it is injected into a porous medium and fed sucrose, it greatly... 

Capillary Pressure. Because of the small size of pores, the fluid-fluid interfaces within the porous medium are highly curved, and the pressure difference across the interface can be substantial. This local pressure difference across the fluid-fluid interface is called capillary pressure. In general, one of the two fluids preferentially wets the solid and is called the... 

Capillary Forces The interfacial forces acting among oil, water, and solid in a porous medium. These determine the pressure difference (capillary pressure) across an oil-water interface in a pore. Capillary forces are largely responsible for oil entrapment under typical reservoir conditions. 

Capillary Pressure The local pressure difference across the oil-water interface in a pore contained in a porous medium. One of the liquids usually... 

In a water-saturated porous medium, water movement occurs from areas of higher hydraulic head to areas of lower hydraulic head. The gauge water pressure at the water table (or at any other interface between free-standing water and the atmosphere, such as the water surface in a pond), is by defini-... 

Pore-radius distributions and ab-/ desorption isotherms are important structural characteristics of generic porous media [80, 88]. The absorption isotherm provides a relation for the liquid uptake of a porous medium under controlled external conditions, viz., the pressure of an external fluid. Within a bounded system, such as a cylindrical tube, a discontinuity of the pressure field across the interface between two fluid phases exists. The corresponding pressure difference is called capillary pressure, Pc. In the case of contact between gas phase, Pg, and liquid water phase, P1, the capillary pressure is given by... 

In membrane filtration, water-filled pores are frequently encountered and consequently the liquid-solid transition of water is often used for membrane pore size analysis. Other condensates can however also be used such as benzene, hexane, decane or potassium nitrate [68]. Due to the marked curvature of the solid-liquid interface within pores, a freezing (or melting) point depression of the water (or ice) occurs. Figure 4.9a illustrates schematically the freezing of a liquid (water) in a porous medium as a fimction of the pore size. Solidification within a capillary pore can occur either by a mechanism of nucleation or by a progressive penetration of the liquid-solid meniscus formed at the entrance of the pore (Figure 4.9b). 

The third problem is known as the Saffinan-Taylor instability of a fluid interface for motion of a pair of fluids with different viscosities in a porous medium. It is this instability that leads to the well-known and important phenomenon of viscous fingering. In this case, we first discuss Darcy s law for motion of a single-phase fluid in a porous medium, and then we discuss the instability that occurs because of the displacement of one fluid by another when there is a discontinuity in the viscosity and permeability across an interface. The analysis presented ignores surface-tension effects and is thus valid strictly for miscible displacement. ... 

A problem that is somewhat analogous to the instability of an accelerating interface occurs when two superposed viscous fluids are forced by gravity and an imposed pressure gradient through a porous medium. This problem was analyzed in a classic paper by Saffman and Taylor.16 If the steady state is one of uniform motion with velocity V vertically upwards and the interface is horizontal, then it can be shown that the interface is stable to infinitesimal perturbations if... 

In many applications, we may wish to describe the motion of two fluids, which may be miscible (i.e., the interfacial tension is zero, though the fluids may have different viscosities or other properties) or immiscible (oil and water, for example) in a porous medium. At the microscale, within the pores, there is a well-defined interface separating two immiscible... 

Knowledge of detailed liquid-vapor configurations enables separation of capillary and adsorptive contributions to the interfacial area as shown in Fig. 1-1 la (note the log-log scale). We denote liquid-vapor interfacial areas associated with menisci (curved interfaces at pore comers) as capillary contributions, and those associated with films as adsorptive contributions. The results in Fig. 1-1 la illustrate the dominant contribution of liquid films to the total liquid-vapor interfacial area of a partially saturated porous medium (Millville silt loam). Note that the flat region in Fig. 1-1 la (changes in SA with no change in p) reflects pore snap-off processes. 

The mosl important early work on interfacial instabilities is that of Saffman and Taylor (1958) who considered the stability of an interface between two immiscible fluids moving vertically through a porous medium. Wooding (1959,... 

Wooding, R.A. 1962b. The stability of an interface between miscible fluids in a porous medium. Z. Angew. Math. Phys. 13 255-265. 

Currently, the tortuosity, r, and the quotient, D/r, are assumed constant. However, r may depend on the habit and texture of the particular precipitated mineral. Also, the assumption is made that precipitation is uniform over the fluid-porous medium interface, rather than concentrated in small pores or in bottlenecks connecting large pores. However, non-uniform deposition may be expected in natural systeoLS. Both assumptions are first approximations and are subject to refinement when experimental data become available that provide more detailed information about effects of precipitation/dissolution on tortuosity and about uniformity of precipitation. 

Much of the recent research in combustion in porous media has focused on developing a porous burner as a radiant heater [7-13]. This is an attractive application because the porous solid is an efficient radiator while still permitting the use of a clean fuel such as methane. One design that has shown promise is a burner consisting of two sections of porous medium with different characteristics [2, 9, 10]. This design is based on the idea that the effective flame speed within the matrix is determined by the porous medium properties such as solid conductivity, porosity, and pore diameter. The interface between the two sections of porous media acts as a flame holder preventing flashback. 

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