Multiple adsorption

Such characteristic horizontal bands, as shown in Figure 5.43, might be termed adsorption multiplicity since they arise primarily from the interactions of external film heat and mass transfer resistances with the adsorption resistance. For smaller adsorption resistance, the horizontal bands disappear giving way to the more familiar multiplicity regions, arising from the interactions of physical transport and surface reaction resistances. 

P lGURE 5.52 Effect of Thiele modulus on adsorption multiplicity. Unimolecular reaction fi = fij-. 

Molecular adsorbates usually cover a substrate with a single layer, after which the surface becomes passive with respect to fiirther adsorption. The actual saturation coverage varies from system to system, and is often detenumed by the strength of the repulsive interactions between neighbouring adsorbates. Some molecules will remain intact upon adsorption, while others will adsorb dissociatively. This is often a frinction of the surface temperature and composition. There are also often multiple adsorption states, in which the stronger, more tightly bound states fill first, and the more weakly bound states fill last. The factors that control adsorbate behaviour depend on the complex interactions between adsorbates and the substrate, and between the adsorbates themselves. 

Another limitation of tire Langmuir model is that it does not account for multilayer adsorption. The Braunauer, Ennnett and Teller (BET) model is a refinement of Langmuir adsorption in which multiple layers of adsorbates are allowed [29, 31]. In the BET model, the particles in each layer act as the adsorption sites for the subsequent layers. There are many refinements to this approach, in which parameters such as sticking coefficient, activation energy, etc, are considered to be different for each layer. 

The nature of electrode processes can, of course, be more complex and also involve phase fonnation, homogeneous chemical reactions, adsorption or multiple electron transfer [1, 2, 3 and 4],... 

Although most appHcations of fixed bed have multiple adsorber beds to treat continuous streams, batch operation using a single adsorber bed is an alternative. For purification appHcations, where one vessel can contain enough adsorbent to provide treatment for days, weeks, or even months, the cost savings and simplicity often justify the inconvenience of stopping adsorption treatment periodically for a short regeneration. 

Mechanisms of Leukocyte Adsorption. The exact mechanism of leukocyte adhesion to filter media is not yet fuUy understood. Multiple mechanisms simultaneously contribute to the adhesion of cells to biomaterials, however, physical and biological mechanisms have been distinguished. Physical mechanisms include barrier phenomenon, surface tension, and electrostatic charge biological mechanisms include cell activation and cell to cell binding. 

There are seven commercial processes in operation six operate in the vapor phase. The Universal Oil Products process operates in the Hquid phase and is unique in the simulation of a moving bed. The adsorption unit consists of one vessel segmented into sections with multiple inlet and oudet ports. Flow to the various segments is accompHshed by means of a rotary valve which allows each bed segment to proceed sequentially through all the adsorption/desorption steps. 

The adsorbed layer at G—L or S—L surfaces ia practical surfactant systems may have a complex composition. The adsorbed molecules or ions may be close-packed forming almost a condensed film with solvent molecules virtually excluded from the surface, or widely spaced and behave somewhat like a two-dimensional gas. The adsorbed film may be multilayer rather than monolayer. Counterions are sometimes present with the surfactant ia the adsorbed layer. Mixed moaolayers are known that iavolve molecular complexes, eg, oae-to-oae complexes of fatty alcohol sulfates with fatty alcohols (10), as well as complexes betweea fatty acids and fatty acid soaps (11). Competitive or preferential adsorption between multiple solutes at G—L and L—L iaterfaces is an important effect ia foaming, foam stabiLizatioa, and defoaming (see Defoamers). 

In the physical separation process, a molecular sieve adsorbent is used as in the Union Carbide Olefins Siv process (88—90). Linear butenes are selectively adsorbed, and the isobutylene effluent is distilled to obtain a polymer-grade product. The adsorbent is a synthetic 2eohte, Type 5A in the calcium cation exchanged form (91). UOP also offers an adsorption process, the Sorbutene process (92). The UOP process utilizes ahquid B—B stream, and uses a proprietary rotary valve containing multiple ports, which direct the flow of Hquid to various sections of the adsorber (93,94). The cis- and trans-isomers are alkylated and used in the gasoline blending pool. 

Adsorption and ion exchange share so many common features in regard to apphcation in batch and fixed-bed processes that they can be grouped together as sorption for a unified treatment. These processes involve the transfer and resulting equilibrium distribution of one or more solutes between a fluid phase and particles. The partitioning of a single solute between fluid and sorbed phases or the selectivity of a sorbent towards multiple solutes makes it possible to separate solutes from a bulk fluid phase or from one another. 

FIG. 16-50 Multiple hearth furnace for carhon reactivation. (Reprinted with permission of EPA. Reference EPA, Process Design Manual for Carhon Adsorption, U.S. Envir Protect. Agency., Cincinnati, 1.973.)... 

With regard to the line 1, the development eould be noted for the following methods those, where peroxide derivatives of earboxylie aeids are used methods of multiple-wavelength speetrophotometrie analysis methods of quantitative aeeounting of a priori information methods of liquid ehromatography (a Unified adsorption eenter model and a Mobile phase effeetive eoneentration eoneeption an applieation of mieellar ehromatography standardization of TLC-plates). 

Often (adsorption, reconstruction) the periodicity at the surface is larger than expected for a bulk-truncated surface of the given crystal this leads to additional (superstructure) spots in the LEED pattern for which fractional indices are used. The lattice vectors bi and b2 of such superstructures can be expressed as multiples of the (1 X 1) lattice vectors ai and Zx. ... 

Length of tune required for the regeneration should be as short as possible. If continuous adsorption and recovery are required, multiple sys- terns have to be installed. 

Finally, let us discuss the adsorption isotherms. The chemical potential is more difficult to evaluate adequately from integral equations than the structural properties. It appears, however, that the ROZ-PY theory reflects trends observed in simulation perfectly well. The results for the adsorption isotherms for a hard sphere fluid in permeable multiple membranes, following from the ROZ-PY theory and simulations for a matrix at p = 0.6, are shown in Fig. 4. The agreement between the theoretical results and compu-... 

Our main focus in this chapter has been on the applications of the replica Ornstein-Zernike equations designed by Given and Stell [17-19] for quenched-annealed systems. This theory has been shown to yield interesting results for adsorption of a hard sphere fluid mimicking colloidal suspension, for a system of multiple permeable membranes and for a hard sphere fluid in a matrix of chain molecules. Much room remains to explore even simple quenched-annealed models either in the framework of theoretical approaches or by computer simulation. 

The transfer matrix method extends rather straightforwardly to more than one dimension, systems with multiple interactions, more than one adsorption site per unit cell, and more than one species, by enlarging the basis in which the transfer matrix is defined. 

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