Single-Component Isotherms

The treatment here is restricted to the Langmuir or constant separation factor isotherm, single-component adsorption, dilute systems, isothermal behavior, and mass-transfer resistances acting alone. References to extensions are given below. Different isotherms have been considered, and the theory is well understood for general isotherms. 

Figure 12.29 Comparison of theoretical and experimental displacement separations of resorcinol and catechol by phenol. Calculations using the equilibrium-dispersive model, the LeVan- Vermeulen isotherm model, and single-component adsorption data. Experimental results on a 4.6x250 CIS Nucleosil 5 fim column, F = 0.4 carrier, water, Fj, = 0.2 mL/min, T = 20°C 1 1 mixture, = 0.5 mL displacer, 80 g/L phenol in water = 30%, Lf = 16.5%. (a) Calculation with LeVan-Vermeulen isotherm, (b) Calculation with quadratic isotherm, three floating parameters, (c) Calculation with competitive Langmuir isotherm, single-component isotherm parameters, (d) Calculation with Langmuir isotherm, best adjusted parameters. Reproduced with permission from. C. Bellot and J.S. Condoret, J. Chromatogr., 657 (1994) (Figs. 3c, 4c, 6c, 8c) 305.

Adsorption Models for Isothermal Single Component Systems... 

In the last section we have illustrated the essential behaviors of isothermal single component systems. In this section we will address the effect of heat release during the adsorption step or heat absorption during the desorption step on the adsorption kinetics. What we need is simply an extra equation to account for the heat balance around the particle. To make the analysis more general, we shall take adsorption isotherm being arbitrary. 

Adsorption models for isothermal single component systems 521... 

ISOTHERMAL SINGLE-COMPONENT SORPTION MICROPORE DIFFUSION CONTROL... 

A quantitative answer to above questions may be given through the theoretical modeling of non-isobaric, non-isothermal single component gas phase adsorption. External heat and mass transfer, intrapai ticle mass transport through Knudsen diffusion, Fickian diffusion, sorbed phase diffusion and viscous flow as well as intraparticle heat conduction are accounted for. Fig. 1 presents the underlying assumption on the combination of the different mass transport mechanisms in the pore system. It is shown elsewhere that the assumption of instantaneous... 

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

AH practical adsorbents have surfaces that are heterogeneous, both energetically and geometrically (not all pores are of uniform and constant dimensions). The degree of heterogeneity differs substantially from one adsorbent type to another. These heterogeneities are responsible for many nonlinearities, both in single component isotherms and in multicomponent adsorption selectivities. 

The working capacity of a sorbent depends on fluid concentrations and temperatures. Graphical depiction of soration equilibrium for single component adsorption or binary ion exchange (monovariance) is usually in the form of isotherms [n = /i,(cd or at constant T] or isosteres = pi(T) at constant /ij. Representative forms are shown in Fig. I6-I. An important dimensionless group dependent on adsorption equihbrium is the partition ratio (see Eq. 16-125), which is a measure of the relative affinities of the sorbea and fluid phases for solute. 

The isotacViic concentrations cl in the fully developed train are calculated directly from the single component isotherms using ... 

The intrinsic enantioselectivity of the micelles has been established based on single-component binding isotherms [73], resulting in a remarkably high value of 7.7. 

The Fowler-Guggenheim-Jovanovic model [3] assumes (as it was the earlier case also) the occurrence of intermolecular interactions among the molecules adsorbed as a monolayer but is based on the Jovanovic isotherm. The single-component isotherm is represented by the equation ... 

When the fluid being vaporised is a single component and the heating medium is steam (or another condensing vapour), both shell and tubes side processes will be isothermal and the mean temperature difference will be simply the difference between the saturation temperatures. If one side is not isothermal the logarithmic mean temperature difference should be used. If the temperature varies on both sides, the logarithmic temperature difference must be corrected for departures from true cross- or counter-current flow (see Section 12.6). 

Selectivity for C02 it represents the C02 uptake ratio to the adsorption of any other gas (typically nitrogen for post-combustion capture, and methane for natural gas). It is an essential evaluation criterion, and affects the purity of the adsorbed gas, which will significantly influence the sequestration of C02. The simplest method to estimate the selectivity factor is to use single-component adsorption isotherms of C02 and nitrogen. 

It has been shown by Harvey et al. (1989) that incorporation of palmitic acid into a monolayer spread from stearoylserine methyl ester (SSME) breaks up intermolecular SSME interactions. The palmitic acid acts as a two-dimensional diluent. Figures 52(A-C) give the Yl/A isotherms for mixtures of FE and SE C-15 6,6 -A with palmitic acid. Dilution of the monolayer cast from the second eluting isomer with 15 mol% palmitic acid separates the diacid molecules from one another on the water surface and perhaps allows for the expression of their stereochemically dependent conformations. The mixed film (15% palmitic acid/85% C-15 6,6 -A) expands at low II and behaves in much the same manner as the single-component monolayer (C-15 6,6 -A) behaves at 30°C. Addition of 15 mole% palmitic acid into a monolayer cast from the FE C-15 diacid has little effect on its energetics of compression, indicating a stronger intermolecular interaction afforded by its stereochemically dependent conformation at the air-water interface. 

When the feed mixture is infinitely diluted, the competitive Langmuir isotherms of the two component approach the respective non-competitive, linear, single-component isotherms (21) and the constraints on the nij parameters of the SMB unit reduce to the following set of decoupled inequalities ... 

Figure 2.31. Schematic representation of the P/T equilibria in a simple two-component system (forming continuous solid and liquid solutions). In (a) a perspective view of the P-T-X diagram is shown in (b) its projection on the P/T plane. Notice the two single-component systems represented, for instance, for the component B by the three lines SB/G (sublimation line of B representing the gas/so lid equilibrium), SB/LB (melting equilibrium of B) and the boiling line LB/G. The solid solution is indicated by a. Notice in (a) the isobaric and isothermal sections of the diagrams (compare with Fig. 2.1).

Single component system (SCS) adsorption models actually mean one pollutant component in aqueous system or in a SWM leachate [34]. Since water is simply assumed to be inert, and the pollutant/leachate adsorption is assumed to be unaffected by water, the system is treated as an SCS. To represent the equilibrium relation for SCS adsorption, a number of isotherm models reported in the literature are reviewed in the following. 

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