Porous solids description

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

To complete the mechanical response description in this book, the phenomena of viscoelasticity, spall (dynamic tensile behavior), melting, and compression of porous solids are briefly considered. 

The illustrations shown are just a portion of a variety of textures of real porous solids, also used as adsorbents and catalysts. It is obvious that when one goes from descriptions to quantitative... 

Voronoi-Delaunay Method for Description of Corpuscular and Sponge-Like Porous Solids... 

Abstract A simplified quintuple model for the description of freezing and thawing processes in gas and liquid saturated porous materials is investigated by using a continuum mechanical approach based on the Theory of Porous Media (TPM). The porous solid consists of two phases, namely a granular or structured porous matrix and an ice phase. The liquid phase is divided in bulk water in the macro pores and gel water in the micro pores. In contrast to the bulk water the gel water is substantially affected by the surface of the solid. This phenomenon is already apparent by the fact that this water is frozen by homogeneous nucleation. 

Herein, cl and cG are parameters responding to the capillary forces which has an effect between the solid and gas phase and between the liquid and gas phase, respectively. They depend on the form and nature of the pores and of the surface tensions between the phases. This new approach to the interaction forces allows the description of capillary motion in porous solids, see de Boer Didwania [6]. 

From this description it becomes obvious that a mechanical tension must develop in the surface film, because the atoms will tend to assume a closer packing. Hence any adsorbed molecule or atom which can improve the screening of the solid will decrease their state of tension and cause the surface film to expand and release some of the pressure which it exerted upon the subjacent layers. Adsorption of screeners, even of inert gas atoms such as argon, causes many porous solids to expand. 

Frequently we define a porous medium as a solid material that contains voids and pores. The notion of pore requires some observations for an accurate description and characterization. If we consider the connection between two faces of a porous body we can have opened and closed or blind pores between these two faces we can have pores which are not interconnected or with simple or multiple connections with respect to other pores placed in their neighborhood. In terms of manufacturing a porous solid, certain pores can be obtained without special preparation of the raw materials whereas designed pores require special material synthesis and processing technology. We frequently characterize a porous structure by simplified models (Darcy s law model for example) where parameters such as volumetric pore fraction, mean pore size or distribution of pore radius are obtained experimentally. Some porous synthetic structures such as zeolites have an apparently random internal arrangement where we can easily identify one or more cavities the connection between these cavities gives a trajectory for the flow inside the porous body (see Fig. 4.30). 

The diameter or the radius of the pores is one of the most important geometric characteristic of porous solids. In terms of lUPAC nomenclature, we can have macropores (mean pore size greater than 5 x 10 m), mesopores (between 5 x 10 and 2 x 10 m) and micropores (less than 2 x 10 m). The analysis of species transport inside the porous structure is very important for the detailed description of many unit operations or applications among them we can mention suspension filtration, solid drying and humidification, membrane processes (dialysis, osmosis, gaseous permeation. ), flow in catalytic beds, ion exchange, adsorp-... 

For pores smaller than 10 m, a molecular sieving effect can be present and the movement of one or more species inside the porous solid occurs due to the molecular interactions between the species and the network of the porous body here, for the description of species displacement, the theory of molecular dynamics is frequently used. The affinity between the network and the species is the force that controls the molecular motion at the same time, the affinity particularities, which appear when two or more species are in motion inside the porous structure, explain the separation capacity of those solids. We can use a diffusive characterisation of species motion inside a porous solid by using the notion of conformational diffusion. 

In the modern chemical and biochemical research porous materials play an irreplaceable role. The mass transport resistance in the pore structure of the porous solids significantly affects rates of transport processes, which take place inside the porous material (Keil [1], Haugaard and Livbjerg [2], Capek and Seidel-Morgernstern [3]). Inclusion of transport processes into the description of the whole process is essential when reliable simulations/predictions have to be made. 

One method for the characterization of porous solids bases on the concept of the adsorption integral equation [1,2]. It requires to access the local isotherms for a wide range of pore widths. Because experiments cannot provide local isotherms of well-defined pores, a big demand results for suitable theoretical descriptions of the physical adsorption. 

Equations 7.6 and 7.7 can be used to describe diffusion down a straight cylindrical pore. A porous solid does not consist of straight cylindrical pores, each having the same length and radius. Models for pore structure have been proposed that describe the pore size distribution and orientation as a function of location within the pellet [2]. These microscopic descriptions can be used to predict the porosity, pore size distribution, pore volume and pore area, all of which can be measured experimentally. 

By applying an appropriate perturbation to a relevant parameter of a system under equilibrium, various frequency modulation methods have been used to obtain kinetic parameters of chemical reactions, adsorption-desorption constants on surfaces, effective diffusivities and heat transfer within porous solid materials, etc., in continuous flow or batch systems [1-24]. In principle, it is possible to use the FR technique to discriminate between all of the kinetic mechanisms and to estimate the kinetic parameters of the dynamic processes occurring concurrently in heterogeneous catalytic systems as long as a wide enough frequency range of the perturbation can be accessed experimentally and the theoretical descriptions which properly account for the coupling of all of the dynamic processes can be derived. 

The rest of the book is dedicated to adsorption kinetics. We start with the detailed description of diffusion and adsorption in porous solids, and this is done in Chapter 7. Various simple devices used to measure diffusivity are presented, and the various modes of transport of molecules in porous media are described. The simplest transport is the Knudsen flow, where the transport is dictated by the collision between molecules and surfaces of the pore wall. Other transports are viscous flow, continuum diffusion and surface diffusion. The combination of these transports is possible for a given system, and this chapter will address this in some detail. 

Since an analysis of the charge regulation problem is intimately related to certain parameters used to characterize the porous structure of solids, it is useful to start with an elementary description, outlining the most common experimental routines used for characterization of porous solids and elucidating the involved model assumptions and limitations. For more details on the subject, the reader is referred to special monographs. Refs. 6-8. 

PARSIM is a simulation package written in Fortran for the dynamic onedimensional description of the reactions in a porous solid particle. Different... 

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