Sorption modeling

Sorption Modeling. Pesticide sorption is characterized by describing sorption isotherms using the Freundhch equation, S = Kj, where S is the pesticide sorbed concentration, C is the pesticide solution concentration after equdibration, and fy and N are constants. Although other equations have been used, the Freundhch has satisfactodly described experimental sorption results for a wide range of pesticides in a variety of sods. The value of N is usually <1 and between 0.75 and 0.95, which indicates that pesticides are proportionally more sorbed at low solution concentration than at high solution concentration. 

The basic assumption for a mass transport limited model is that diffusion of water vapor thorugh air provides the major resistance to moisture sorption on hygroscopic materials. The boundary conditions for the mass transport limited sorption model are that at the surface of the condensed film the partial pressure of water is given by the vapor pressure above a saturated solution of the salt (Ps) and at the edge of the diffusion boundary layer the vapor pressure is experimentally fixed to be Pc. The problem involves setting up a mass balance and solving the differential equation according to the boundary conditions (see Fig. 10). 

The sorption data of Cd2+ and Pb2+ by B. subtilis and E. coli were well described by a one-site complexation model (r2 > 0.9) with Cd2+ showing somewhat lower sorption affinities than Pb2+ (Kulczycki et al. 2002). A two-site sorption model yielded an improved fit but only for the E. coli data. The stability constants for the high- and low-affinity sorption sites differed by several orders of magnitude. The total metal sorption capacity of E. coli increased, and moved closer to the value of B. subtilis when the presence of low-affinity sorption sites was allowed. Ngwenya et al. (2003) used potentiometric titrations to assess the different types of sites present... 

A speciation calculation including one of the sorption models described above, or a combination of two or more sorption models, can be evaluated numerically following a procedure that parallels the technique described in Chapter 4. We begin as before by identifying the nonlinear portion of the problem to form the reduced basis,... 

The basis includes an entry Ap for each sorption model considered, except for the K( and Freundlich models, which require no special entry. 

The parameters of the three sorption models can be determined by linear regression of the experimental observations. The reaction K( model (Eqn. 9.2) holds that,... 

The parameters determined in this manner for the three sorption models are,... 

Sorption of species from solution, as we noted in the previous chapter (Chapter 9), controls the mobility of certain species in solution, especially environmental contaminants. An accurate description of sorption, therefore, is a critical component of many geochemical models. The sorption models presented in the previous chapter are, however, too simplistic to be incorporated into a geochemical model intended for use under general conditions, such as across a range in pH. 

These results differ sharply from the behavior predicted by the distribution coefficient (K( ) approach. This approach, despite being broadly acknowledged as too simplistic to describe the behavior of heavy metals, is nonetheless the sorption model most commonly applied in studying aquifer remediation. 

Escher, B. I., Schwarzenbach, R. P. and Westall, J. C. (2000). Evaluation of liposome-water partitioning of organic acids and bases 1. Development of a sorption model, Environ. Sci. Technol., 34, 3954-3961. 

Figure 4. Distribution coefficients predicted from the two-phase sorption model.

Another widely used sorption model is the Langmuir equation. It was developed by Irving Langmuir [140] to describe the adsorption of gas molecules on a planar surface. It was first applied to soils by Fried and Shapiro [ 141 ] and Olsen and Watanabe [142] to describe phosphate sorption on soils. Since that time, it has been heavily employed in many environmental fields to describe sorption on various solid surfaces [19,65]. The general Langmuir model is... 

Fig. 12. Isotherm sorption models for bottom ash solid waste, representing Langmuir (C/Cs vs C), Freundlich (logCs vs log C), and Linear (Csvs C) models...

Many models have been developed that deal with the sorption properties of wood in the presence of moisture these have been discussed in a number of works (e.g. Skaar, 1972 Siau, 1984). They can be approximately divided into sorption models, such as the Brunauer-Emmett-Teller (BET) model, or solution models (such as the Hailwood-Horrobin, H-H, model). The sigmoidal shapes of sorption or desorption isotherms can be deconvoluted into two components. These are often taken to represent a monomolecular water layer (associated with the primary sorption sites, OH groups), and a multilayer component where the cell wall bound water molecules are less intimately associated with the fixed cell wall OH groups. 

Bradbury, M. H. Baeyens, B. 2000. A generalised sorption model for the concentration dependent uptake of caesium by argillaceous rocks. Journal of Contaminant Hydrology, 42, 141-163. 

Turner, D. R. Sassman, S. A. 1996. Approaches to sorption modeling for high-level waste performance assessment. Journal of Contaminant Hydrology, 21, 311-332. 

Figure 7.12 Adsorption of water by skim milk and sorption isotherms predicted by the Braunauer-Emmett-Teller (BET), Kuhn and Guggenheim-Andersson-De Boer (GAB) sorption models (from Roos, 1997).

The radial diffusion model and the linear sorption model are compared in Fig. 18.76. Since according to Eq. 19-76 the total mass of the chemical associated with the particle aggregate, (M(r), and the macroscopic solid-water distribution ratio, Kd(t), are linearly related ... 

Figure 19.19 Comparison of the solution of the linear sorption model with the radial diffusion model. Numbers on curves show y defined in Eq. 19-86. Y is the fraction of the chemical taken up by the sphere when equilibrium is reached. After Wu and Gschwend (1988).

Explain the difference between the two types of curves shown in Fig. 19.19, which are labeled radial diffusion model and sorption model, respectively. 

In the performance data of various polyamide and related membranes published to date there should be valuable information for molecular design of more excellent barrier materials. But at present a means for their evaluation and optimization is still not clear. One of the reasons may at least come from the competitive flood of proposals for the detailed mechanisms of reverse osmosis, e.g. the solution-diffusion model, the sieve model, the preferential sorption model and so on. 109)... 

The sorption and diffusion behaviour of gas mixtures is of particular interest from the point of view of membrane gas separation, which is steadily gaining in importance by virtue of its low energy requirements. On the basis of the dual mode sorption model, one may reasonably expect that sorption of a binary gas mixture A, B in the polymer matrix will exhibit little gas-gas interaction and hence will tend to occur essentially additively. In the Langmuir-like mode of sorption, on the other hand, there will be competition between A and B for the limited number of available sites. These considerations led 67) to the following reformulation of Eqs. (8) and (9)... 

Application of dual mode sorption models to low affinity ionic species has been reported. Pertinent examples are mentioned here to illustrate the variety of models... 

NR and — CO groups, measured after prior washing of the resin with water 85), was well represented by a Langmuir + Nernst dual mode sorption model at salt concentrations not exceeding 0.2 mol dm 3. A detailed physical interpretation of the relevant parameters was not given, however, neither was the dual mode concept utilized in a corresponding diffusion study 86). 

In considering an organic-rich slurry wall additive, the governing sorption mechanism is often considered to be hydrophobic partitioning and the effects of solution chemistry (pH, ionic strength, etc.) are considered secondary. The specification ofthe appropriate sorption model requires several choices ... 

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