Adsorptive reactions, nonlinear isotherms

Distributed Reactivity Model. Isotherm relationships observed for natural systems may well be expected to reflect composite sorption behavior resulting from a series of different local isotherms, including linear and nonlinear adsorption reactions. For example, an observed near-linear isotherm might result from a series of linear and near-linear local sorption isotherms on m different components of soft soil organic matter and p different mineral matter surfaces. The resulting series of sorption reactions, because they are nearly linear, can be approximated in terms of a bulk linear partition coefficient, KDr that is... 

You saw how the equations governing energy transfer, mass transfer, and fluid flow were similar, and examples were given for one-drmensional problems. Examples included heat conduction, both steady and transient, reaction and diffusion in a catalyst pellet, flow in pipes and between flat plates of Newtonian or non-Newtonian fluids. The last two examples illustrated an adsorption column, in one case with a linear isotherm and slow mass transfer and in the other case with a nonlinear isotherm and fast mass transfer. Specific techniques you demonstrated included parametric solutions when the solution was desired for several values of one parameter, and the use of artificial diffusion to smooth time-dependent solutions which had steep fronts and large gradients. 

First a simple precipitation/dissolution reaction without carbon speciation and acid-based chemistry is considered (cf. Boudreau, 1997) using an approach similar to nonlinear adsorption/desorption (Langmuir isotherm). As shown above, the component A(jq) released by DOC biodegradation consuming a given electron acceptor can be buffered or precipitated by a precipitation/dissolution reaction... 

In this chapter, it is shown how to simulate the adsorption of a substance, not taking into account any electrochemical reactions the substance may undergo. That is, only the adsorption itself is dealt with here. In Chap. 2, Sect. 2.5, some theory is presented, laying the groundwork for the simulation. It is noted there that adsorption may be controlled by transport and the adsorption isotherm, in which case there is equilibrium at all times between the solution and surface phases or that the adsorption step itself may limit the rate of adsorption. In this latter case, there are rate constants whose values must be known. In both cases, for isotherms more complicated than the Henry isotherm (2.104), nonlinear terms will enter the equations to be solved in a simulation. 

Fluhler and Selim (1986) investigating F adsorption on an acid loam soil, found that a two-site Langmuir isotherm was required to describe observed F BTC. The transport model used by these authors considered nonlinear adsorption on two types of sites with chemical reactions on these sites governed by first-order kinetic expressions (Fluhler and Jury, 1983). The various ionic species of F (i.e., F , Al-F, etc.) were thought to exhibit different adsorption/dcsorption kinetics due to differences in their abilities to penetrate the various layers of mineral surfaces. 

Sample reaction or chemisorption on the adsorbent bed (3) is generally associated with the strong adsorption sites or small pores which are responsible for isotherm nonlinearity (1) and excessively large sample retention volumes (2). The use of adsorbent deactivation or homogeneous surface adsorbents hence serves as a simultaneous answer to all three problems (1-3). Adsorbent standardization (4) is still a significant problem in both GSC and LSC, but much progress has been made recently (see Section 6-3). Once a satisfactory GSC column has been prepared, moreover, its lifetime will generally exceed that of a GLC column many times over. 

If one of the phases is a solid, the distribution is more appropriately described in terms of adsorption. Such adsorption can be a combination of unspecific adsorption of the environmental chemical to the solid smface, electrostatic interactions between the charged chemical and oppositely charged sitrface sites, and the covalent reaction of the chemical with reactive sites at the surface. Quantitative expressions rely again on concentration ratios, but equihbrium adsorption coefficients are less likely to be constant over wide concentration ranges. These relationships thus need to be characterized by nonlinear adsorption isotherms, such as those formulated by Langmuir and Freimdhch. 

Nonlinearity of mathematical model equations results from reactions with orders higher than tmity or particular boundary terms (e.g., adsorption isotherms). 

Two ideas have been considered to derive valid lumped models for systems with nonlinear kinetics. The first is the use of cooperative kinetics,which is applicable to catalytic reactions governed by Langmuir isotherm adsorption, and can be extended to other models if there is uniform catalytic surface coverage. The second is a transformation of the coordinates (such as nonlinear stretching of the time coordinate). ... 

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