Biporous

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

Figure 9.17 The basic schemes of (a) bidisperse (biporous) porous solid structure 1, nonporous primary particles, 2, aggregates of primary particles (secondary particles), 3, porous solid (granule, grain, pallet, etc.) (b) a bed of granules in a catalytic reactor 4.

The concentration C(xy t) of a pulsed gas as a function of time and axial position in a bed packed with a bipore distribution solid can be obtained by solving the following set of equations with appropriate initial and boundary conditions (1,2)... 

By using the first two moments it is, therefore, possible to calculate the mass-transfer coefficients which characterize the diffusional resistances of a particle with a bipore system. To calculate these moments it is necessary to integrate the experimental values of C(L, t) as a function of time at different values of U. 

Physical adsorption at a surface is extremely rapid, and the kinetics of physical adsorption are invariably controlled by mass or heat transfer rather than by the intrinsic rate of the surface process. Biporous adsorbents such as pelleted zeolites or carbon molecular sieves offer three distinct resistances to mass transfer the external resistance of the... 

FIGURE 4 Schematic diagram of a biporous adsorbent pellet showing the three resistances to mass transfer (external fluid film, macropore diffusion, and micropore diffusion). R9 pellet radius rc crystal radius. 

The definitions of the moments and their relationship to the system parameters for a biporous (macropore-micropore) adsorbent such as a commercial pelleted molecular sieve are given by the following equations(15,16) ... 

A third category comprises conducting polymers. The film-forming anodic polymerization of monomers, e.g., pyrrole, leads in the majority of cases to porous or even biporous [28] polymer layers, adhering to the substrate. The porosity can be improv at higher current densities, but the overoxidation limit must be considered. Another improvement is possible in terms of the application of graphite felt as a substrate [28, 58, 455]. Last but not least, the co-deposition of dispersed c.b.s in the electrolyte leads to composites with up to 65 wt% c.b. in the polymer layer for... 

In all but extreme climates, the upper portion of the soil profile is extensively occupied by plant roots, which remove both water and mineral nutrients. Plants and other biota (such as insects and small mammals) create extensive networks of voids often referred to as macropores, which result in a heterogeneous, biporous (i.e., there are two porosity values, for micro- and macropores), and structurally very complex material. Macropores (and pipes, which are larger, continuous macropores) can play a significant role in water transport, although the exact role of flow through macropores versus flow through the rest of the soil matrix is not completely understood. For an overview of the types and mechanisms of formation of macropores, the reader is referred to Beven and Germann (1982). 

One of the problems inherent to high-flow operation is increased back pressure, particularly when methanol is used in the mobile phase. This difficulty has been circumvented by the introduction of monolithic stationary phases, which employ a unique contiguous biporous structure prepared from sol-gel chemistry [90,91]. Reduced flow resistance is accomplished by throughpores (2 /zm), while smaller mesopores (13 nm) provide the surface-area capacity needed for adequate chromatographic separation. High flow rates can be employed with monolithic columns due to reduced back pressure and the ability for facile mass transfer. 

With the aid of a kinetic model for a biporous sorbent (144), Zolotarev et al. (143) described the diffusion and kinetics of sorption for water-silica gel systems. On the basis of this theoretical model, an explanation was given for the differences in the experimental kinetic curves for water-vapor sorption on biporous silica gels (143). The coefficients for the mass... 

Diffusion-convection sorbents are biporous materials with a network of wide pores providing convective transport connected to smaller diffusion pores that posses most of the surface area, and are responsible for retention [132-136]. An optimized arrangement of diffusion and convection pores results in enhanced mass transfer properties and shorter separation times for macromolecules. Sorbents in this category include superporous agarose beads [137,138], biporous monolithic or continuous bed... 

This technique may also be used to measure effective macropore diffusivities in biporous adsorbent pellets [13,14]. For such a system with a linear equilibrium isotherm and assuming rapid intracrystalhne diffusion, the governing diffusion equation is of the same form as for micropore control. The solution is identical to Eq. 1 except that R now refers to the particle radius and the diffusivity D is replaced by the effective diffusivity De = Dp p/(ep + (1 - p)fC). Since the equilibrium constant (K) is generally large and varies with temperature according to the van t Hoff equation (K = it is clear that a macropore-controlled system will gener-... 

Recent studies of SBA-15 materials have shown the existence of micropores within the pore walls of their mesoporous structure, thus confirming the biporous nature of these materials [102-105]. Figure 18 shows a schematic representation of a typical SBA-15 pore structure. According to the diagram these materials have an array of hexagonally ordered primary mesopores, but... 

Crystals of microporous materials must be formed into pellets of siutable dimensions, porosity and mechanical strength, or be formed into a membrane on the surface of support materials when used in practice. Such composite pellets or membranes offer a bidispersed porous structure, with macro-or mesopores between the crystals and micropores permeating the crystals. The overall rate of the transport in such systems depends on the interplay of various processes occurring within the pellets or membranes. Jordi and Do [24,46] have developed a general theoretical model and seven relevant degenerate models to analyse the frequency response spectra of a system containing bidispersed pore structure materials for slab, cylindrical and spherical macro- and micropore geometry. Sun et al. [47] also reported the theoretical models of the FR for non-isothermal adsorption in biporous sorbents. 

The overall characteristic functions 5in and 5out for a system involving biporous materials are [24]... 

When the macropore diffusion rate for a system involving biporous sorbents is by far faster than the micropore diffusion rate, i.e., 1, the overall... 

Studies on mass transport processes of sorbates in bidispersed porous solid materials, exhibiting macro- or mesopores between crystals and micropores inside the crystals, are of considerable importance in obtaining a better understanding of the separation and catalytic processes involved in the systems. Such systems have not, however, been studied in depth. As discussed in Sect. 3.2.5, the FR technique provides a realistic way to investigate the dynamics processes taking place in such biporous systems. 

The FR spectra when both micro- and macropore diffusion processes are rate-controlling in systems involving dispersed solid materials with biporous structures have not been observed as yet. However it should be possible by adjusting the crystal and pellet sizes, i.e., obtaining an appropriate e value in Eq. 25. 

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