Porous solids, diffusion through

Aside from cavitation, the enhanced mass transfer rates in acoustic fields can be attributed to plug flow of capillary liquid as well as to enhanced dispersion of the liquid and vapor moisture due to alternating compression and expansion cycles, which result in reduced viscosity of the liquid-vapor mixture. In fact, a substantial increase in the amount of liquid diffusing through porous solids has been noted in the presence of ultrasound (Fairbanks and Chen, 1969 Woodford and Morrison, 1969 Kuznetsov and Subbotina, 1965). The enhanced diffusion appears to be of the directional type since mass transfer was hindered when ultrasound irradiation was opposed to the direction of diffusive flow (Kuznetsov and Subbotina, 1965). 

The first example cited is one in which the solid is totally consumed, whereas the second and third examples involve the formation of a new solid product which might be either a desired product, as in the second case, or a waste product (the gangue) as in the third example. Despite such fundamental differences from catalytic reactions, there are many similarities. In each case, chemisorption, surface chemical reaction emd diffusion through porous media occurs which is in common with heterogeneous chemical reactions. Hence, models representing the dynamics of these non-catalytic gas—solid processess incoporate the same principles of chemical reaction concomitant with diffusion and reaction in heterogeneous catalysts. 

In connection with multiphase diffusion another poorly understood topic should be mentioned—namely, the diffusion through porous media. This topic is of importance in connection with the drying of solids, the diffusion in catalyst pellets, and the recovery of petroleum. It is quite common to use Fick s laws to describe diffusion through porous media fJ14). However, the mass transfer is possibly taking place partly by gaseous diffusion and partially by liquid-phase diffusion along the surface of the capillary tubes if the pores are sufficiently small, Knudsen gas flow may prevail (W7, Bl). 

In ion exchange equipment, cations or anions from the fluid deposit in the solid and displace equivalent amounts of other ions from the solid. Suitable solids are not necessarily porous the ions are able to diffuse through the solid material. A typical exchange is that of H + or OH ions from the solid for some undesirable ions in the solution, such as Ca++or SOa. Eventually all of the ions in the solid are replaced, but the activity is restored by contacting the exhausted solid with a high concentration of the desired ion. for example, a strong acid to replace lost hydrogen ions. 

Section III is concerned with moisture movement through porous solids. The general theory of moisture distribution and the rate of moisture movement inside porous media is reviewed. The three theories of condensation— diffusion, capillarity, and vaporization—are discussed. The roles of various mechanisms causing liquid movement in solids are assessed. 

POROUS SOLIDS AND FLOW BY CAPILLARITY. The flow of liquid through porous solids does not conform to the solution to the diffusion equation given by Eq. (24.16). This may be seen by comparing the moisture distribution in a solid of this type during drying with that for diffusion. A typical moisture-distribution curve for a porous solid is shown in Fig. 24.7. A point of inflection divides the... 

Moisture flows through porous solids by capillarity - - and to some extent by surface diffusion (see Chap. 25, p. 826). A porous material contains a complicated network of interconnecting pores and channels, the cross sections of which vary greatly. At the surface are the mouths of pores of various sizes. As water is removed by vaporization, a meniscus across each pore is formed, which sets up capillary forces by the interfacial tension between the water and the solid. The capillary forces possess components in the direction perpendicular to the surface of the solid. It is these forces that provide the driving force for the movement of water through the pores toward the surface. 

Calculate fluxes through porous solids when both molecular and Knudsen diffusion are important. 

The rate of diffusion of the solute through the solid and solvent to the surface of the solid is often the controlling resistance in the overall leaching process and can depend on a number of different factors. If the solid is made up of an inert porous solid structure with the solute and solvent in the pores in the solid, the diffusion through the porous solid can be described by an effective diffusivity. The void fraction and tortuosity are needed. This is described in Section 6.5C for diffusion in porous solids. 

The diffusion rates of fluids, particularly gases, through porous solid materials are of particttlar interest becMise of the common practice of using porous solids as ctealysts and adsorbents. Diffiidonal transport rates within the pores may limit the rates which such processes occur. 

Penman, H. L. 1940. Gas and vapor movements in the soil 1. The diffusion of vapours through porous solids. Journal of Agricultural Science 30 436 62. 

Unsteady-State Diffusion Through a Porous Solid... 

This problem illustrates the solution approach to a one-dimensional, nonsteady-state, diffusional problem, as demonstrated in the simulation examples, DRY and ENZDYN. The system is represented in Fig. 4.2. Water diffuses through a porous solid, to the surface, where it evaporates into the atmosphere. It is required to determine the water concentration profile in the solid, under drying conditions. The quantity of water is limited and, therefore, the solid will eventually dry out and the drying rate will reduce to zero. 

Figure 4.2. Unsteady-state diffusion through a porous solid.

If this reaction is implemented at temperatures where the iron yielded is a solid, a sectioned, fractionally reacted iron oxide might appear as shown in Figure 3.26. As shown, for the hydrogen to reach the iron oxide with which it reacts, it has to diffuse through a layer of iron (mostly porous). In addition, the water vapour produced as a consequence of the reaction must be transported away from the iron-iron oxide interface by diffusion. Failing this, there will be accumulation of water vapour at the interface which will permit equilibrium point to be attained and the reaction ceases from further occurring. 

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