Porous media morphology

In order to be useful in practice, the effective transport coefficients have to be determined for a porous medium of given morphology. For this purpose, a broad class of methods is available (for an overview, see [191]). A very straightforward approach is to assume a periodic structure of the porous medium and to compute numerically the flow, concentration or temperature field in a unit cell [117]. Two very general and powerful methods are the effective-medium approximation (EMA) and the position-space renormalization group method. 

The capillary pressure response, a direct manifestation of the underlying pore morphology, can be evaluated from the two-phase LB drainage simulation and the corresponding transport relation as function of liquid water saturation can be devised as shown in Fig. 20 for the reconstructed CL micro structure.21 The overall shape of the capillary pressure curve agrees well with those reported in the literature for synthetic porous medium.55 The capillary... 

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 ,... 

Let us consider an isotropic porous medium under the reconstruction described by a pore phase function fgk r) in the /cth iteration step of the simulated annealing algorithm and let the actual statistical characteristics of this phase function, i.e., the two-point correlation function, be Rgk u). The distance of from the target morphological characteristics Rgtarset(u) of the... 

For a porous medium represented by the phase function /g(r), we define the covering radius rc(r) of the solid phase as the radius of the largest sphere (or disk in 2D porous media) placed entirely into the solid phase and covering the point with coordinates r. The value of rc is zero inside the pores. The covering radius rc can be found by the morphological operation called opening, i.e., the erosion followed by the dilatation. The dilatation of the solid-phase domain A by the spherical element Br with radius r is the set A B, covered by all translations of Br centered in A,... 

In catalytic systems morphological changes of the pore structure, brought upon by the reaction and sorption processes, typically result in a reduction of the available pore volume. In some instances the internal pore structure is eventually blocked and becomes completely inaccessible to transport and/or reaction. In the field of noncatalytic fluid-solid reactions and acid rock dissolution, on the other hand, the chemical reaction consumes the solid matrix of the porous medium leading eventually to fragmentation and... 

The filter coefficient, X, varies as deposited material changes the morphology of the porous medium and as conditions surrounding the collection sites change. It has been noted that the filtration coefficient increases as fines migrate through a clean filter bed the retained fines increase the specific surface area. This increase in X is short-lived, and the magnitude of the filter coefficient decreases as additional fines are retained. Since Iwasaki published his notes on filtration in 1937, numerous variations of the rate expression have been recorded (72). 

Figure 2. Effective medium approximations relating porous silicon porosity to refractive index for a wavelength of 1.55 /am. The differences arise from different assumptions made about the porous silicon morphology.

Perturbation theory cannot be applied to describe the effect of the strong roughness. An approach based on Brinkman s equation has been used instead to describe the hydrodynamics in the interfacial region [82]. The flow of a liquid through a nonuniform surface layer has been treated as the flow of a liquid through a porous medium [83-85]. The morphology of the interfacial layer of thickness, L, has been characterized by a local permeability, that depends on the effective porosity of the layer, (j). A number of equations for the permeability have been suggested. For instance, the empirical Kozeny-Carman equation [83] yields a relationship... 

D morphological analysis of the connectivity of a porous medium. Acta Stereai., 17, 107-112. 

Porous materials are classified within five types according to the relative positions of their site- and bond- size distributions. This leads to a better understanding of the morphological aspects of the porous medium as well as an assessment of the different mechanisms arising during capillary condensation and evaporation. For each one of these types of materials, relevant characteristics can be recognised in their hysteresis loops. 

The objective of this smdy is to be able to estimate the effective transport resistance of a porous medium by characterizing its void morphology by mercury porosimetry. A series of porous catalyst solids were obtained differing only in void morphology, overall porosity and pore sizes. We cahnilated the tortuosity by a dynamic experiment employing solid-gas chromato phy, SGC. Tortuosities of aU solids were very si ar, in the range of 5-25. Transport resistance is more easily related to overall volume porosity rather than specific network architectu features observable by porosimetry. 

There is currently no way to estimate the transport resistance of a porous medium without performing the transport experiment. While direct, this procedure provides no understanding of the relationship between morphology and transport resistance and therefore no intuition into how the void network could be manipulated to effect a desired result. In many practical situatians reliable sampling is not possible or the transport experiment is not feasible the transport resistance must be estimated fi om an empiricism. 

Characterization of the morphology of a porous medium is not an unambiguous problem. It generally involves some assumption regarding the architecture of the media before any data may be analyzed. For catalysts made firom random agglomeration and fusion of non rous microparticles, a useful and sufficiently general structure is the pore-throat model. In this visualization, it is assumed that internal void volume is distributed within channels which connect pores. Channels provide the connecting paths between pores and ultimately between transport boundaries. The properties that are sufficient to define this type of medium are ... 

In this work solid-gas chromatography is used to measure dynamic diffusion coefficients of argon in various porous solids. Mercury porosimetry is used to study the internal macroporosity and macro-morphology of these solids. Finally, an attempt is made to elucidate a relationship between the tortuosity measured from the transport experiment and the internal structure of the porous medium as characterized by porosimetry. 

We propose that this morphological variable would therefore related to a network variable (tortuosity) and perhaps may be directly applied to the evaluation of the transport resistance of the medium. It is the goal of this work to correlate tortuosity measured in dynamic transport experiments to retained mercury. This would be the first technique that may independently estimate the transport resistance of a porous medium by studying its moiphology alone. 

Once a spatially 2D or 3D image of the multiphase medium of interest has been obtained, it is desirable to characterize the image by a set of morphological descriptors, which can then be correlated with effective properties of the medium or their evolution followed in time when a structure-transformation process (e.g., dissolution) takes place in the medium. Let us now review some morphological descriptors most commonly used for the characterization of porous and multiphase media. 

In mathematical terms, given the porosity and suitable morphological characteristics, we want to construct the replica of the porous/multiphase medium... 

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