Porous solids models

Feng, C., V. V. Kostrov and W. E. Stewart. 1974. Multicomponent diffusion of gases in porous solids. Models and experiments. Ind. Eng. Chem. Fundam. 13(1) 5-9. 

In a somewhat similar paper, diffusion through a 2D porous solid modeled by a regular array of hard disks was evaluated [65] using non-equilibrium molecular dynamics. It was found that Pick s law is not obeyed in this system unless one takes different diffusion constants for different regions in the flow system. Other non-equilibrium molecular dynamics simulations of diffusion for gases within a membrane have been presented [66]. The membrane was modeled as a randomly... 

Fitzer E, Fritz W, Schoch G (1991) The chemical vapor impregnation of porous solids, modeling of the CVI-process. J de Physique IV 2 C-2-143-150... 

THE MAIN PRINCIPLES OP MODELLING OP POROUS SOLIDS. MODELS OP SYSTEMS WITH NEEDLE-LIKE PARTICLES... 

As the result of analysis of literature and development of some new ideas the main principles of porous solids modelling are presented. Two models of the systems with needle-like particles are discribed. Special attention is paid to the problem of network modelling. 

The adsorption branch of isotherms for porous solids has been variously modeled. Again, the DR equation (Eq. XVII-75) and related forms have been used [186,194]. With respect to desorption, the variety of shapes of loops of the closed variety that may be observed in practice is illustrated in Fig. XVII-29 (see also Refs. 195 and 197). 

Any interpretation of the Type I isotherm must account for the fact that the uptake does not increase continuously as in the Type II isotherm, but comes to a limiting value manifested in the plateau BC (Fig. 4.1). According to the earlier, classical view, this limit exists because the pores are so narrow that they cannot accommodate more than a single molecular layer on their walls the plateau thus corresponds to the completion of the monolayer. The shape of the isotherm was explained in terms of the Langmuir model, even though this had initially been set up for an open surface, i.e. a non-porous solid. The Type I isotherm was therefore assumed to conform to the Langmuir equation already referred to, viz. 

Diffusion within the largest cavities of a porous medium is assumed to be similar to ordinary or bulk diffusion except that it is hindered by the pore walls (see Eq. 5-236). The tortuosity T that expresses this hindrance has been estimated from geometric arguments. Unfortunately, measured values are often an order of magnitude greater than those estimates. Thus, the effective diffusivity D f (and hence t) is normally determined by comparing a diffusion model to experimental measurements. The normal range of tortuosities for sihca gel, alumina, and other porous solids is 2 < T < 6, but for activated carbon, 5 < T < 65. 

Table 6.2 summarizes the low pressure intercept of observed shock-velocity versus particle-velocity relations for a number of powder samples as a function of initial relative density. The characteristic response of an unusually low wavespeed is universally observed, and is in agreement with considerations of Herrmann s P-a model [69H02] for compression of porous solids. Fits to data of porous iron are shown in Fig. 6.4. The first order features of wave-speed are controlled by density, not material. This material-independent, density-dependent behavior is an extremely important feature of highly porous materials. 

Use of the term mean-bulk temperature is to define the model from which temperatures are computed. In shock-compression modeling, especially in porous solids, temperatures computed are model dependent and are without definition unless specification of assumptions used in the calculations is given. The term mean-bulk temperature describes a model calculation in which the compressional energy is uniformly distributed throughout the sample without an attempt to specify local effects. In the energy localization case, it is well known that the computed temperatures can vary by an order of magnitude depending on the assumptions used in the calculation. 

The use of FOSS polyhedra as models for silica surfaces or as secondary building units in inorganic materials such as zeolites or other porous solids is likely to increase rapidly as more is understood about the mechanisms by which the polyhedra may be constructed. It will be of particular interest to see if the larger structures such as TeoHeo or T240H240 or their derivatives (Section VII.C) and analogous to carbon structures such as Cgo or nanotubes, can be prepared. 

Models of atmospheric phenomena are similar to those of combustion and involve the coupling of exceedingly complex chemistry and physics with three-dimensional hydrodynamics. The distribution and transport of chemicals introduced into groundwater also involve a coupling of chemical reactions and transports through porous solid media. The development of groundwater models is critical to understanding the effects of land disposal of toxic waste (see Chapter 7). 

Strictly speaking, the validity of the shrinking unreacted core model is limited to those fluid-solid reactions where the reactant solid is nonporous and the reaction occurs at a well-defined, sharp reaction interface. Because of the simplicity of the model it is tempting to attempt to apply it to reactions involving porous solids also, but this can lead to incorrect analyses of experimental data. In a porous solid the chemical reaction occurs over a diffuse zone rather than at a sharp interface, and the model can be made use of only in the case of diffusion-controlled reactions. 

In Figure 9.1(c), the opposite extreme case of a very porous solid B is shown. In this case, there is no internal diffusional resistance, all parts of the interior of B are equally accessible to A, and reaction occurs uniformly (but not instantaneously) throughout the particle. The concentration profiles are flat with respect to radial position, but cB decreases with respect to time, as indicated by the arrow. This model may be called a uniform-reaction model (URM). Its use is equivalent to that of a homogeneous model, in which the rate is a function of the intrinsic reactivity of B (Section 9.3), and we do not pursue it fiirther here. 

Unsupported, or bulk cobalt catalysts are commonly used as model systems to avoid the influence of support interactions. Bulk cobalt (also known as cobalt black) is typically produced by reduction of Co304, leading to a porous solid with a low... 

General Problems of Porous Solids Texture Modeling.293... 

GENERAL PROBLEMS OF POROUS SOLIDS TEXTURE MODELING... 

Morphology of Porous Solids and Problems with Modeling... 

Model of a granule of a porous solid as a lattice (labyrinth) of pores and particles, which takes into account the average values of coordination number of bonds and distribution of sites and bonds over the characteristic sizes. 

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