Liquid phase equilibrium sorption

Both adsorption from a supercritical fluid to an adsorbent and desorption from an adsorbent find applications in supercritical fluid processing. The extrapolation of classical sorption theory to supercritical conditions has merits. The supercritical conditions are believed to necessitate monolayer coverage and density dependent isotherms. Considerable success has been observed by the authors in working with an equation of state based upon the Toth isoterm. It is also important to note that the retrograde behavior observed for vapor-liquid phase equilibrium is experimentally observed and predicted for sorptive systems. 

Figure 15.3 (Brown et al, 1992) shows the equilibrium isotherms for the sorption of copper and cadmium ions onto peat at 20°C. The figure shows the amount of metal ion sorbed /umol/g) at the liquid phase equilibrium metal ion concentration (C mmol/dm ). The maximum saturation capacities for copper and cadmium ions on peat are 270 and 180 /umol/g respectively. These results indicate the considerable potential for peat in metal ion removal.

Walters and Guiseppe-Elle [108] studied the sorption of 2,3,7,8-tetrachlorodibenzo-p-dioxin to soils from aqueous methanol mixtures and evaluated the applicability of the cosolvent theory to such sorption. Sorption kinetics were influenced by the fraction of methanol in the liquid phase and the soil type. Linear equilibrium sorption isotherms were... 

Apparent hysteresis occurs mainly when complete equilibrium is not reached. Diffusion into the solid matrix or into micropores of aggregates is considered a main cause of apparent hysteresis. In a transitory state, sorption occurs concurrently with desorption and the concentration of contaminant in the liquid phase is erroneously low because some fraction is associated with sorption. 

Despite the fact that both normal and monomethyl-substituted paraffins readily enter the pores of ZSM-5 and ZSM-11, preferential sorption of the normal isomer is observed under thermodynamic equilibrium, non-kinetically controlled conditions. Whereas small-pore zeolites, such as 5A and erionite, totally exclude branched hydrocarbons, and large-pore zeolites exhibit little preference, the intermediate pore-size zeolites ZSM-5 and ZSM-11 show a marked preference for sorption of the linear paraffin, even under equilibrium conditions. Competitive liquid phase sorption studies at room temperature indicated selectivity factors greater than ten in favor of n-hexane relative to... 

However, the sorption coefficient in Equation (2.67) is a liquid-phase coefficient, whereas the sorption coefficient in Equation (2.72) is a gas-phase coefficient. The interconversion of these two coefficients can be handled by considering a hypothetical vapor in equilibrium with a feed solution. This vapor-liquid equilibrium can then be written... 

The sorption coefficient (K) in Equation (2.84) is the term linking the concentration of a component in the fluid phase with its concentration in the membrane polymer phase. Because sorption is an equilibrium term, conventional thermodynamics can be used to calculate solubilities of gases in polymers to within a factor of two or three. However, diffusion coefficients (D) are kinetic terms that reflect the effect of the surrounding environment on the molecular motion of permeating components. Calculation of diffusion coefficients in liquids and gases is possible, but calculation of diffusion coefficients in polymers is much more difficult. In the long term, the best hope for accurate predictions of diffusion in polymers is the molecular dynamics calculations described in an earlier section. However, this technique is still under development and is currently limited to calculations of the diffusion of small gas molecules in amorphous polymers the... 

In batch systems, the distribution or sorption coefficient (Xliquid phases. The X(j is commonly measured under equilibrium or at least steady-state conditions, unless the goal of the experiment is to examine the kinetics of sorption. It is defined as follows ... 

Vapor sorption measurements yield equilibrium composition and fugacity or chemical potential the isopiestic version (19) is used to determine the uptake of a pure vapor by a nonvolatile material. This technique determines equilibrium composition of a phase which cannot be separated quantitatively from the liquid phase in equilibrium with it. In our application, a nonvolatile crystalline surfactant specimen S is equilibrated with vapor of V, which is, in turn, at equilibrium with a system of S and V consisting of two phases, one rich in S, and one rich in V. At equilibrium, the Gibbs-Duhem relation guarantees. that the initial specimen of S takes up enough V from the vapor phase that the chemical potential of S, as well as of V, is the same as in the biphasic system, and so the composition of the phase formed by vapor sorption is the same as that of the S-rich phase. This composition is easily determined by weight measurement. If the temperature were a triple point, i.e. three phases at... 

Extraction—distribution between immiscible liquid phases Crystallization—melting point or solubility Adsorption—surface sorption Reverse osmosis—diflusivity and solubility Membrane gas separation—diflusivity and solubility Ultrafiltration—molecular size ion exchange—chemical reaction equilibrium Dwlysis—diflusivity... 

Non-equilibrium sorption/desorption. Can also be used for non-aqueous phase liquid dissolution). 

Extraction—distribution between immiscible liquid phases Crystallization-melting point or solubility Adsorption-surface sorption Reverse osmosis—diffiisivity and solubility Membrane gas separation—diffusivity and solubility Ultrafiltration—molecular size Ion exchange—chemical reaction equilibrium Dialysis—diffiisivity... 

The classical thermodynamic approach has been applied to liquid phase adsorption by Larionov and Myers and by Minka and Myers. It was shown that for sorption of carbon tetrachloride-isooctane and benzene-carbon tetrachloride on aerosil the adsorbed solutions show approximately ideal behavior whereas adsorbed mixtures of benzene, ethyl acetate, and cyclohexane on activated carbon showed appreciable deviations from ideality. However, it is shown that the activity coefficients and hence the adsorption equilibrium data for the ternary systems may be successfully predicted, by classical methods, from data for the constituent binaries. 

Pseudo-first-order kinetic model The sorption of organic molecules from a liquid phase to a solid phase can be considered as a reversible process with equilibrium being established between the solution and the solid phase. Assuming a non-dissociating molecular adsorption of adsorbates onto adsorbent particles, the sorption phenomenon can be described as the diffusion-controlled process (Fogler, 1998). 

Polymers are often polydisperse with respect to molecular weight. Whereas this is of minor importance for the solvent sorption in polymers (vapor-hquid equilibrium), this fact usually remarkably influences the polymer solubility (liquid-hquid equilibrium). Therefore, polydispersity needs to be accounted for in interpretation and modeling of experimental data. This can be done by applying continuous thermodynamics as well as by choosing a representative set of pseudocomponents. It was shown that a meaningful estimation of the phase boundary is possible when using only two or three pseudocomponents as soon as they reflect the important moments (Mn, Mw, Mz) of the molecular weight distribution. 

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