Penetration into Porous Solids

We now consider application of percolation theory to describing mercury intrusion into porous solids. First we briefly recall the main physical principles of mercury porosimetry (in particular, the Washburn equation). These principles are treated in detail in many textbooks [e.g., Lowell and Shields 49)]. The following discussions (Sections IV,B and IV,C) introduce general equations describing mercury penetration and demonstrate the effect of various factors characterizing the pore structure on this process. Mercury extrusion from porous solids is briefly discussed in Section IV,D. 

The method of mercury porosimetry requires evacuation of the sample and subsequent pressurization to force mercury into the pores 49). This technique was originally developed to enable pore sizes to be determined in the macropore range, where the gas adsorption method breaks down for practical reasons (6). Application of mercury porosimetry is based on the Washburn equation 62,63), 

During mercury intrusion, a given void or neck with r rp can be filled by mercury only if it is connected with the outer surface by a chain of voids and necks with r rp. Thus, mercury intrusion into porous solids is equivalent to the bond problem in percolation theory [Androutsopoulos and Mann (35), Wall and Brown (14), Chatzis and Dullien (36), Lane et al. (37), Zhdanov and Fenelonov (38), Tsakiroglou and P atakes (39-41), Day et al. (42), and Park and Ihm (43)]. The equivalence is based on the identification of network sites with voids, and bonds with necks. A bond is considered to be unblocked if the neck radius r rp. 

To describe mercury intrusion, one can use the same approaches as were employed in Section III for simulating condensate desorption from porous solids. In particular, if the pore volume is concentrated in voids (this model, shown in Fig. 2, has been analyzed in Refs. 14,37-41), the fraction of pore volume filled by mercury, C/in(rp), can be represented as (cf. Section III,D or Ref. 38) 

Pore Radius as a Function of Applied Pressure for Mercury Intrusion 

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During the past decade, percolation theory has been successfully used to analyze condensate desorption from porous solids (14-34), mercury penetration into porous solids (35 -43), and the kinetics of catalytic deactivation... 

SCFs have relatively low viscosity and high diffusivity, and they can penetrate into porous solid materials more effectively than liquid solvents and may render much faster mass transfer resulting in faster extractions. In SFE, a fresh fluid is continuously forced to flow through the samples therefore, it can provide quantitative or complete extraction [38, 51]. Moreover, SFE may allow direct coupling with a chromatographic method, which can be a useful to extract and directly quantify the desired compounds. 

Equations (90) and (91) can be used to approximate diffusion into porous solids like chunks of asphalt or soil and sediment grains. For example, assume that an HOP is diffusing into a soil grain with Dapp=10 5 m2 s 1 and a=10 3 m. Equation (90) can then be solved to yield the concentration profiles shown in Fig. 6 (where C0[Pg.21]

Here the problem is very much simpler, mainly because the surface areas of particulate or porous solids are much higher than the available areas of liquid/vapour interfaces. If no component of the solution penetrates into the solid (or), then rf = 0 and equation (A111.5) can be written, for a binary solution, in the form... 

The reaction would occur only on the outer surface of the solid particle if the solid is non-porous and A carmot penetrate into the solid. A model called shrinking core model (SCM) proposed for non-porous solid particles is widely used for the design of gas-solid reactors. The SCM is discussed in detail in the following section. 

However, evaluation of the surface energy of pure protein with contact-angle methods is not trivial. It is arguably impossible to determine a relevant value of ypy by measiuing contact angles on a prepared solid protein surface. For example, hquid penetration into a solid protein surface would probably be unavoidable as such, a surface would probably be both porous and hygroscopic. In this work, the value of ypy was approximated by... 

Fillers are added to emulsion adhesives to reduce cost by replacing resin solids without decreasing total solids, to reduce penetration into porous substrate, and to change the rheology of the compound. Depending on their individual properties, fillers can also add stiffness and strength or decrease tack and blocking. Un-... 

In the materials processing industry, size reduction or comminution is usually carried out in order to increase the surface area because, in most reactions involving solid particles, the rate of reactions is directly proportional to the area of contact with a second phase. Thus the rate of combustion of solid particles is proportional to the area presented to the gas, though a number of secondary factors may also be involved. For example, the free flow of gas may be impeded because of the higher resistance to flow of a bed of small particles. In leaching, not only is the rate of extraction increased by virtue of the increased area of contact between the solvent and the solid, but the distance the solvent has to penetrate into the particles in order to gain access to the more remote pockets of solute is also reduced. This factor is also important in the drying of porous solids, where reduction in size causes both an increase in area and a reduction in the distance... 

When a liquid is placed in contact with a surface of a porous solid the question arises as to whether it will penetrate into the pores. The answer must be pursued in the realm of capillarity which deals with the equilibrium geometries of liquid-solid interfaces and the angle of contact between the liquid and the pore wall. 

Fillers are added to emulsion adhesives to build the total solids content, to reduce penetration into a porous substrate, and to lower costs. 

This situation is caused by the coafs insolubility. Most coals are nearly insoluble in nearly everything. Although selective solvents may dissolve as much as 20-25% of some coals without reaction, the bulk of the material remains insoluble. Thus the reagent must penetrate the coal to reach the reactive group. The fact that coals are highly porous certainly helps. We will return to this point later. Now our concern is with reagent transport into the solid material as distinguished from transport in the pore system. The character of the solid material will control that diffusion rate. 

Water absorption by porous solids depends on the water-solid contact angle and on the liquid surface tension. The spreading of water in fabrics is the result of wetting the fiber surface, penetration into the fibers, and capillary pressure [20], The wetting of yarns depends on their surface energy and the interfiber space. 

Absorption I) The ability of a porous solid to hold a liquid by cohesion and capillary action 2) Action similar to that of a sponge or blotter in soaking up a liquid 3) As applied to solids, absorption refers to a more or less uniform penetration throughout a solid by any particular component, as distinguished from the existence of a higher concentration of the component at a surface or interface as found in adsorption-, 4) The penetration of liquid or vapor into the solid structure that is, it could be considered a solution with the solid acting as the solvent. 

Porosity and Gas Physisotption The term adsorption described originally the condensation of gas on a free surface as opposed to its penetration into the bulk of a solid, that is, absorption. This distinction between the two processes has tended to disappear, and today the uptake of a gas by a porous material is commonly referred to as adsorption (or simply sorption), regardless which actual physical mechanism takes place (25). 

Cryochemically synthesized PPX films containing metal or semiconductor nanocrystals have a fine porous structure caused by features of solid-state polymerization. Due to this structure, molecules of gaseous substances readily penetrate into polymer film from the environment. Synthesized composite films demonstrate valuable strong sensor effects resulting from a marked influence of some low-molecular-weight molecules, diffusing into the polymer and adsorbed onto nanocrystals, on the film conductivity [4, 30, 62-64]. Such effects are characteristic of films whose conductivity is governed by electron transfer between nanoparticles. 

It is important that the nomenclature is clear and in this article the following is used the volume of the column that is filled up with the ion exchange material and the liquid phase is divided into the solid phase, the resin phase, and the electrolyte phase. The solid phase is the part of the column to which the liquid cannot penetrate. The resin phase is the part of the column to which the liquid can penetrate but is stagnant in a chromatographic process. For a porous ion exchange material this phase mainly consists of the pore volume. The external electrolyte phase is the part of the column that is filled by the electrolyte and at the same time can be associated with a flow velocity in a chromatographic process. 

Additionally, pure SCFs have no interfacial tension (since no vapor-liquid interface exists), so penetration into and removal from solid porous structures is facilitated. Note, however, that an SCF-swollen polymeric fluid will exhibit an interfacial tension with an SCF phase. 

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