Adsorption-diffusion model

E. Adsorption-diffusion model of interfacial mass transfer 201... 

E. Adsorption-Diffusion Model of Interfacial Mass Transfer... 

The rate of contaminant adsorption onto activated carixm particles is controlled by two parallel diffusion mechanisms of pore and surface diffusion, which operate in different manners and extents depending upon adsorption temperature and adsorbate concentration. The present study showed that two mechanisms are separated successfully using a stepwise linearization technique incorporated with adsorption diffusion model. Surface and pore diffiisivities were obtained based on kinetic data in two types of adsorbers and isothermal data attained from batch bottle technique. Furthermore, intraparticle diffiisivities onto activated carbon particles were estimated by traditional breakthrough curve method and final results were compared with those obtained by more rigorous stepwise linearization technique. 

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

The differences in the rate of adsorption are primarily attributable to the differences in the equilibrium capacity at the various pHs, and the pore diffusion model simulated our data satisfactorily. 

The Diffusion Model. The uptake of a solute by a sorbent can be analyzed by a diffusion model, which has been used successfully to model adsorption rates onto activated carbon (74, 75), ion exchangers (72), heterogeneous catalysts (76), and soil columns (77). For the purpose of illustration, we can consider the diffusion of a compound into a spherical sorbent grain under conditions of linear sorption and no exterior mass transfer limitations (73), which is described by... 

Three kinetic models were applied to adsorption kinetic data in order to investigate the behavior of adsorption process of adsorbates catechol and resorcinol onto ACC. These models are the pseudo-first-order, the pseudo-second-order and the intraparticle diffusion models. Linear form of pseudo-first-order model can be formulated as... 

Kinetic data of adsorption of catechol and resorcinol were also tested according to intraparticle diffusion model which can be formrrlated as... 

In this Section we introduce a stochastic alternative model for surface reactions. As an application we will focus on the formation of NH3 which is described below, equations (9.1.72) to (9.1.76). It is expected that these stochastic systems are well-suited for the description via master equations using the Markovian behaviour of the systems under study. In such a representation an infinite set of master equations for the distribution functions describing the state of the surface and of pairs of surface sites (and so on) arises. As it was told earlier, this set cannot be solved analytically and must be truncated at a certain level. The resulting equations can be solved exactly in a small region and can be connected to a mean-field solution for large distances from a reference point. This procedure is well-suited for the description of surface reaction systems which includes such elementary steps as adsorption, diffusion, reaction and desorption.The numerical part needs only a very small amount of computer time compared to MC or CA simulations. 

The observation by Price and co-workers (Booth et al. 1978 Price et al. 1982 Teo et al. 1986) of a loss of copolymer during elution through a GPC column was ascribed to adsorption of copolymer by the gel in the column. Spacek (1986) proposed the alternative explanation that some of the micelles, formed inside the gel particles, cannot leave narrow pores permeable only for the unimer. A simplified diffusion model was used to estimate the time needed for the formation of micelles under the conditions of the GPC experiment. The value obtained was in reasonable agreement with results from a stopped-flow experiment (Bednar et al. 1988). On the other hand, the experimental fact that the major part of the... 

A mathematical model has been developed to describe the kinetics of multicomponent adsorption. The model takes into account diffusional processes in both the solid and fluid phases, and nonlinear adsorption equilibrium. Comparison of model predictions with binary rate data indicates that the model predictions are in excellent for solutes with comparable diffusion rate characteristics. For solutes with markedly different diffusion rate constants, solute-solute interactions appear to affect the diffusional flows. In all cases, the total mixture concentration profiles predicted compares well with experimental data. 

Using these relations in equation (18), and applying the LRC model to predict the loadings and heats of adsorption, the model for "surface 1 diffusion of the i-th component in a multi-component mixture becomes ... 

Smith, E.H. 1991. Modified solution of homogeneous surface diffusion model for adsorption. J Environ. Eng-ASCE 117(3) 320-338. 

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). 

The non-equilibrium problem is even more complicated. The large particles can have surface binding energy much larger than kT and in this case they neither diffuse nor desorb from the surface. The Random Sequential Adsorption (RSA) model [9] assumes that a particle, which arrives at a random location on a surface, is adsorbed only if there is... 

Lombardo and Bell (1991) reviewed stochastic models of the description of rate processes on the catalyst surface, such as adsorption, diffusion, desorption, and surface reaction, which make it possible to account for surface structure of crystallites, spatial inhomogeneities, and local fluctuations of concentrations. Comparison of dynamic MC and mean-field (effective) description of the problem of diffusion and reaction in zeolites has been made by Coppens et al. (1999). Gracia and Wolf (2004) present results of recent MC simulations of CO oxidation on Pt-supported catalysts. 

Cantwell and co-workers submitted the second genuine electrostatic model the theory is reviewed in Reference 29 and described as a surface adsorption, diffuse layer ion exchange double layer model. The description of the electrical double layer adopted the Stem-Gouy-Chapman (SGC) version of the theory [30]. The role of the diffuse part of the double layer in enhancing retention was emphasized by assigning a stoichiometric constant for the exchange of the solute ion between the bulk of the mobile phase and the diffuse layer. However, the impact of the diffuse layer on organic ion retention was danonstrated to be residual [19],... 

Identification of the effective diffusion coefficient with the mathematical model of hatch adsorption. The model assumes that the carbon particles are spherical and porous (gp- voids fraction). Using c (kg A/m fluid inside the pores) and q (kg A/kg adsorbent) to express the concentration of the transferable species through the pores and through the particle respectively, we can write the following expression for transport flux ... 

Abuzaid, N. S. and G. Nakhla (1997). Predictability of the homogeneous surface diffusion model for activated carbon adsorption kinetics formulation of a new mathematical model, J. Environment. Science Health, Part A Environment. Eng. Toxic Hazardous Substance Control. 32, 7, 1945-1961. 

Qualitatively, the zeroth-order Stern layer (flg. 3.20a) differs from the purely diffuse model in that the screening is poorer. Higher potentials are needed to obtain a certain surface charge. When there is specific adsorption (figs. 3.20b and c) a new feature emerges the non-electrostatlc contribution to the (Gibbs) energy of adsorption of counterions leads to an additional contribution to AG . It is recalled from sec. 3.2 that double layers form only because of non-electrostatlc affinities of ions for a surface. 

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