Adsorbents film diffusion

Film diffusion Diffusion of azo dyes through the boundary layer to the surface of the adsorbent... 

Zogorski et al. [125] indicate that external transport is the rate-limiting step in systems having poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent, and a high affinity of adsorbate for adsorbent. Some experiments conducted at low concentrations have shown that film diffusion solely controls the adsorption kinetics of low molecular weight substances [81,85]. 

The importance of adsorbent non-isothermality during the measurement of sorption kinetics has been recognized in recent years. Several mathematical models to describe the non-isothermal sorption kinetics have been formulated [1-9]. Of particular interest are the models describing the uptake during a differential sorption test because they provide relatively simple analytical solutions for data analysis [6-9]. These models assume that mass transfer can be described by the Fickian diffusion model and heat transfer from the solid is controlled by a film resistance outside the adsorbent particle. Diffusion of adsorbed molecules inside the adsorbent and gas diffusion in the interparticle voids have been considered as the controlling mechanism for mass transfer. 

Due to the fact that protein adsorption in fluidized beds is accomplished by binding of macromolecules to the internal surface of porous particles, the primary mass transport limitations found in packed beds of porous matrices remain valid. Protein transport takes place from the bulk fluid to the outer adsorbent surface commonly described by a film diffusion model, and within the pores to the internal surface known as pore diffusion. The diffusion coefficient D of proteins may be estimated by the semi-empirical correlation of Poison [65] from the absolute temperature T, the solution viscosity rj, and the molecular weight of the protein MA as denoted in Eq. (16). 

Also, in the late 1950s and 1960s some particularly seminal papers on ion exchange kinetics appeared by Helfferich (1962b, 1963, 1965) that are classics in the field. In this research it was definitively shown that the rate-limiting steps in ion exchange phenomena were film diffusion (FD) and/ or particle diffusion (PD). Additionally, the Nernst-Planck theories were explored and applied to an array of adsorbents (Chapter 5). 

The analyte may interact two-dimensionally with the sorbent surface through adsorption due to intermolecular forces such as van der Waals or dipole-dipole interactions [53]. Surface interactions may result in displacement of water or other solvent molecules by the analyte. In the adsorption process, analytes may compete for sites therefore, adsorbents have limited capacity. Three steps occur during the adsorption process on porous sorbents film diffusion (when the analyte passes through a surface film to the solid-phase surface), pore diffusion (when the analyte passes through the pores of the solid-phase), and adsorptive reaction (when the analyte binds, associates, or interacts with the sorbent surface) [54]. 

This point can be appreciated more quantitatively after consideration of an important (but simple) model of transport-controlled adsorption kinetics, the film diffusion process.34 35 This process involves the movement of an adsorptive species from a bulk aqueous-solution phase through a quiescent boundary layer ( Nemst film ) to an adsorbent surface. The thickness of the boundary layer, 5, will be largest for adsorbents that adsorb water strongly and smallest for aqueous solution phases that are well stirred. If j is the rate at which an... 

The film diffusion process provides a supply of adsorptive molecules at the adsorbent surface to engage in a chemical reaction leading to adsorption (Eq. 4.3). The rate law for this reaction is developed, for example, in conjunction with the adsorption step in the sequential reaction schemes that appear in Eqs. 3.46, 3.56, and 4.51. Prototypical expressions are in Eqs. 3.47, 3.57, and 4.52a a generic rate law for reaction-controlled adsorption is in Eq. 4.17. For the present example the rate of adsorption can be described by the equation... 

The film diffusion process assumes that reactive surface groups are exposed directly to the aqueous-solution phase and that the transport barrier to adsorption involves only the healing of a uniform concentration gradient across a quiescent adsorbent surface boundary layer. If instead the adsorbent exhibits significant microporosity at its periphery, such that aqueous solution can effectively enter and adsorptives must therefore traverse sinuous microgrottos in order to reach reactive adsorbent surface sites, then the transport control of adsorption involves intraparticle diffusion.3538 A simple mathematical description of this process based on the Fick rate law can be developed by generalizing Eq. 4.62 to the partial differential expression36... 

The heterogeneous catalyst particles in the reactor are surrounded by a boundary layer of gas or liquid, which can be considered as a static him around the particle. A reactant molecule has to diffuse through this boundary layer via film diffusion (1). As most catalysts have pores, the reactant molecule also has to diffuse through the pores in order to approach the active site, the pore diffusion process (2). Inside the pores, the reactant molecules adsorb at or near the active center and react (3, 4). The resulting product molecules desorb (5) and return back into the fluid phase via pore diffusion (6) and film diffusion (7). Further details on this can be found in general textbooks [1-3]. 

Figure 4.1.1 Delineation of the steps of a catalyzed chemical reaction. In an ideal case, the reactant molecule diffuses through the boundary layer and the pores. Near the active center, it adsorbs, reacts, and desorbs and is the being transported back via pore and film diffusion.

Simulations of a number of dynamical processes in adsorbed films have been reported. These begin with the motions of individual molecules such as reorientation, either of the entire molecule or, for long chains, internal rotations. Of course, all these motions are affected by the torques exerted on a molecule due to its interactions either with neighboring adsorbate molecules or with the solid adsorbent. Other types of dynamics involve the translations that give rise to self-(or tracer) diffusion and to viscous flow in capillaries. Finally, simulations can be used to study the mechanism of lubrication by films between two closely spaced surfiices. Each of these topics will be discussed briefly here. 

The second step is diffusive transport of the solute molecule through the film layer which is called film diffusion (2). Transport of the solute molecules towards the adsorption centers inside the pore system of the adsorbent particles is the third step of the adsorption process. This step can follow two different transport mechanisms, which can occur separately or parallel to each other pore diffusion (3a) and surface diffusion (3b). 

Three main types of mass transfer resistances are recognized film diffusion (which occnrs at the external surface of the adsorbent), intraparticle diffusion (which occnrs within the pores or amorphous structure of the adsorbent), and adsorption/desorption kinetics (which occnrs at the internal surface of the adsorbent). 

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