Sorption coefficients, equation

Permeability P, can be expressed as the product of two terms. One, the diffusion coefficient, reflects the mobility of the individual molecules in the membrane material the other, the Henry s law sorption coefficient, reflects the number of molecules dissolved in the membrane material. Thus equation 9 can also be written as equation 10. 

Because many studies have shown a direct relationship between pesticide sorption and organic carbon content of sod, attempts have been made to develop a universal sorption coefficient based on sorption of the pesticide to sod organic carbon (44). Sorption based on sod organic carbon is expressed as C, where is pesticide sorbed per unit mass sod organic carbon, and C is pesticide solution concentration after equdibration. If. is the fraction of organic carbon, can be obtained from i in the equation. Assumptions in the use of this approach include... 

Indirect methods of estimating sorption have been used when actual measurement of sorption isotherm is impossible (44). For instance, sorption coefficients have been estimated from soil organic carbon and a specific surface of soil, and from semiempidcal equations using pesticide properties. 

Frequently it is convenient, when conducting sorption experiments, to use a cosolvent such as methanol to facilitate transfer of a volatile or insoluble solute. Equation 31 may be used to estimate the effect of the cosolvent on measured sorption coefficient. If fc equals 10- and a is conservatively chosen as unity, the methanol is predicted to decrease the sorption of anthracene (ac = 9.76 log Kow = 4.54 50) by 1% relative to the case of no cosolvent. The effect of the cosolvent should be smaller for solutes with smaller HSA (or KQW), which is consistent with the observed negligible impact of methanol at f. < 10 3.6 52). ... 

Estimate the site-specific sorption coefficient (Kd or Kf) from the estimated K(k and the organic carbon content of the soil or sediment, using Equation (3). 

Sorption is measured by recording sorption isotherms, which themselves are a way to express the amount of surfactant sorbed as function of the concentration of the compound in the solution. The Freundlich isotherm (Equation II) is a general sorption isotherm which describes sorption behavior and often is used in studies of surfactant sorption. KF is the Freundlich sorption coefficient which expresses the affinity of a surfactant for a given solid... 

Table 17.11 details the dependence of log KF on the number of carbon atoms (nC atoms) according to the Equation log KF = B + A n( aloma. A varies between 0.33 and 0.46 for LAS and AEs. The rather small variation in A indicates that the increase in sorptivity per added C-atom does not differ substantially between the two classes of surfactants. In addition, Hand and Williams (1987) observed that the sorption coefficient increased by a factor of two when the p-sulfophenyl moiety moved from a central position in the alkyl chain to the 2-position. 

Based on their data for sorption onto a lake sediment, Kiewiet et al. (1996) derived an equation predicting sorption coefficients of CnEOms as a functions of alkyl chain length and the number of oxyethylene units. Di Toro et al. (1990) proposed a model for description of sorption of anionic surfactants which includes sorbent properties (organic carbon content, cation exchange capacity, and particle concentration) and the CMC as a function of the solution properties (ionic strength, temperature). The CMC is used as a relative hydrophobicity parameter. Since the model takes the contribution of electrostatic as well as hydrophobic forces explicitly into account, it is an example of an attempt to model surfactant behavior on the basis of the underlying mechanisms. 

At this point the superscript G is introduced to denote the gas phase. For example yp, the activity of component i in the gas phase, and Kf, the sorption coefficient of component i between the gas and membrane phases [Equation (2.56)]. 

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... 

The sorption coefficients of gases in polymers remain relatively constant because sorption in polymers behaves as though the polymers were ideal fluids. Gas sorption in a polymer is expressed from Equation (2.57) as... 

By substituting for the sorption coefficient Kf from Equation (2.56), Equation (2.89) can be written as... 

Figure 2.26 Average sorption coefficients of simple gases in a family of 18 related polyimides plotted against the expected sorption in an ideal polymer calculated using Equation (2.97). Data from Tanaka el al. [23]...

The selectivity (amcm) of pervaporation membranes critically affects the overall separation obtained and depends on the membrane material. Therefore, membrane materials are tailored for particular separation problems. As with other solution-diffusion membranes, the permeability of a component is the product of the membrane sorption coefficient and the diffusion coefficient (mobility). The membrane selectivity term amem in Equation (9.11) can be written as... 

Sorption Prediction Equations. Equations predicting radioelement distribution coefficients, K s, as arithmetic functions of component concentrations were obtained for sorption of strontium, neptunium, plutonium, and americium on two Hanford sediments. These equations, presented in Table VH and derived from statistical fits of Box-Behnken experimental designs, were generated for strontium in terms of sodium ion, HEDTA, and EDTA concentrations. Prediction equations for neptunium and plutonium sorption were derived from NaOH, NaA102, HEDTA, and EDTA concentrations. Americium sorption prediction equations were based on NaOH, HEDTA, and EDTA concentrations. 

In the equations above, subscript i denotes a gas species, subscript j represents a specific step t denotes time z is bed axial distance c is gas phase mole fraction q denotes adsorbed phase mole fraction i is reaction stoichiometry for the species / , is the rate of reaction v is interstitial fluid velocity vq is inlet gas velocity Dz is dispersion coefficient k is LDF coefficient b is sorption coefficient e is bed voidage. For both the pressurization (j = 1) and the adsorp-... 

Drying kinetics was represented by a diffusive model. The models were completed with water sorption equilibrium equation, expressions for product and moist air properties, correlations for convective heat and mass transfer coefficients, and the kinetics of drying and of the selected quality changes in the product as functions of water content and temperature (Di Scala and Crapiste, 2005). Experimental data were obtained from Di Scala and Crapiste (2005) and Roura et al. (2001). 

The first stage is represented by Fickian diffusion with a constant coefficient. Second-stage sorption is much slower than the first and follows an exponential relationship. The relative contributions of the two stages to the total uptake vary with the sorption stage and the initial regain of the fibers. Thus, the sorption rate equation can be written as ... 

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