Fluids in Porous Solids

Diffusion in porous solids is usually the most important factor controlling mass transfer in adsorption, ion exchange, drying, heterogeneous catalysis, leaching, and many other applications. Some of the applications of interest are outlined in Table 5-16. Applications of these equations are found in Secs. 16, 22, and 23. 

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. 5-249). The tortuosity x that expresses this hindrance has been estimated from geometric arguments. Unfortunately, 

In small pores and at low pressures, the mean free path i of the gas molecule (or atom) is significantly greater than the pore diameter dyrjy,. Its magnitude may be estimated from 

As a result, collisions with the wall occur more frequently than with other molecules. This is referred to as the Knudsen mode of diffusion and is contrasted with ordinary or bulk diffusion, which occurs by intermolecular collisions. At intermediate pressures, both ordinary diffusion and Knudsen diffusion may be important [see Eqs. (5-252) and (5-253)]. 

Bulk diffusion in pores D ff — X (5-249) Gases or liquids in large pores. NKn = /dpore 0.01 [33] 

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Magnetic resonance has been used extensively to study fluids in porous solids [13-15], including ceramics [16,17]. In recent years, we have applied NMR imaging... 

The movements of fluids in porous solids." J. Franklin Inst., 203 313-324. 

Callaghan, FT., Coy, A., MacGowan, D., Packer, K.J., and Zelaya, F.O. Diffraction-like effects in NMR diffusion studies of fluids in porous solids. Nature, 351, 467, 1991. 

Porous silicas are usually mesoporous materials and they can be made with a variety of pore dimensions. In particular, silica glasses can be made with well-defined pore diameters, typically in the range 30-250 A, using sol-gel methods. Such a system provides a good model for testing the models of relaxation behaviour of fluids in porous solids. It is normally found that the two-site fast-exchange model for relaxation described above for macroporous systems is still valid. For instance, H and relaxation times have been measured during both adsorption and desorption of water in a porous silica. Despite hysteresis in the observed adsorption isotherms, it was found that the relaxation times depended solely on water content.For deuterated water in some porous silicas, multicomponent relaxation behaviour for T2 and Tip has been observed, and this has been attributed to the fractal nature of the pore structure. 

The adsorption of dipolar fluids in porous solids induces modifications of their bulk properties. Quantitative estimates of these changes on the dielectric properties and spatial correlations of the DHS fluid adsorbed in uncharged or charged disordered or random matrices of immobile hard spheres have been obtained by grand canonical MC simulations [203,204] for different densities of the adsorbed fluids and porosities of the matrices. 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

Use of the proper diffusion coefficient Replace the molecular diffusion coefficient by the effective diffusion coefficient of fluid in the porous structure. Representative values for gases and liquids in porous solids are given by Weisz (1959). 

In porous solids made of larger elements such as fixed packed beds, where the characteristic dimension of the packing is d (for example the diameter of a packed solid), the frequency of the velocity change is a = v/d (after each flow through an element of the packed bed, the local fluid velocity v changes its direction). Now if we use this value of a in the dispersion coefficient, we obtain the famous relation Pe = (vd)/D = 2, which gives the value of the dispersion coefficient when a fluid flows through a packed bed [4.90]. 

The linear displacement of fluid through porous solid material by another fluid that is completely miscible in the first can have an efficiency approaching 100%. This linear displacement is in contrast to immiscible displacement (such as of oil by water) in which a significant fraction of the original fluid remains trapped in the pores. Thus, dense C02 has an inherent advantage over immiscible fluids, like water, in the recovery efficiencies that are possible with its use. 

Biot, M. A., Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid -- II. Higher Frequency Ranges, J. Acoust. Soc. Am., Vol. 28, 1956, 179. 

Biot M.A., 1956a. Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. Journal of the Acoustical Society of America 28 179-191... 

Richard D, Marty B, Chaussidon M, Arndt N (1996) Helium isotopie evidenee for a lower mantle component in depleted Archean komatiite. Science 273 93-95 Risen W (1980) Isotopic studies of the rare gases in igneous rooks Implioations for the mantle and atmosphere. PhD dissertation, Dept Physics, University of California, Berkeley Rubey WW, Hubbert MK (1959) Role of fluid pressure in meohanios of overthmsting faulting I. Mechanics of fluid-filled porous solids and its application to overthmsting faulting. Geol Soo Am Bull 70 115-166... 

In porous solids, several fluid phases can interact in terms of flow, gas solubility, altering saturations, phase changes, etc. 

Journal of Applied Physics, Vol.26, No.2, (February 1955), pp. 182-185, ISSN 0021-8979 Biot, M. A. (1956a). Theory of Prop>agation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range. Journal of the Acoustical Society of America, Vol.28, No.2, (March 1956), pp. 168-178, ISSN 0001 966 Biot, M A. (1956b). Theory of Prop>agation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range. Journal of the Acoustical Society of America, Vol.28, No.2, (March 1956), pp. 179-191, ISSN 0001 966... 

This section provides some Qqiical experimental values of interdiffiision coefficients in gases, in solutions of nonelectrolytes, electrolytes, and macromolecules, in solids, and for gases in porous solids. Theoretical and empirical correlations for predicting diffiisivities will also be discussed for use in those cases where estimates must be made because eiqierimental data are unavailable. A critical discussion of predicting diffiisivities in a fluid phase can be found in the book by Reid et al. 

Poisson s ratio has been calculated directly from tensile tests (v = 0.37-0.50) [10] and indirectly from torsional shear and confined compression creep data (v = 0.37-0.47) [6, 9]. More recently, the relationship between Poisson s ratio, n, aggregate modulus, Ha, and permeability, k, have been established for cartilage indentation testing based on biphasic (fluid and porous solid) constitutive theory [15]. Using a complex numerical solution and curve fitting scheme, Poisson s ratio can be extracted from indentation data, resulting in values of v = 0.00-0.30 [11, 12, 16]. However, care must be exercised in interpreting such indirect measures of Poisson s ratio as unexpected results can arise e.g. v = 0.0. 

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