Sorption transport coefficients

From Fig. 19.3a-c, and as opposed to purely sorption controlled processes, it can be seen that during pervaporation both sorption and diffusion control the process performance because the membrane is a transport barrier. As a consequence, the flux 7i of solute i across the membrane is expressed as the product of both the sorption (partition) coefficient S, and the membrane diffusion coefficient Di, the so-called membrane permeability U, divided by the membrane thickness f and times the driving force, which maybe expressed as a gradient of partial pressures in place of chemical potentials [6] ... 

The transport coefficients of ethyl acetate, an aroma booster found in a large variety of aroma formulations, have been calculated from sorption of ethyl acetate in PLA experiments. The ethyl acetate permeability of PLA is 5.34 x 10 kg.m.m. s Pa at 30°C and 0.3 activity. It is higher than the one of PET but lower than those of PP and LDPE. However, the ethyl acetate solubility coefficient in PLA, equal to 6.17 xlfi kg.m. Pa at 30°C and 0.3 activity, is higher than the other polymers [140]. This result is comparable to the value reported by Colomines et al. for an amorphous PLA with 99% L-lactide content at 25°C and 0.5 activity [125]. Moreover, increasing the crystallinity of PDLLA provokes a decrease of the ethyl acetate solubility coefficient at 0.5 and 0.9 activity [125]. 

Volatilization causes contaminants to transfer from the dissolved phase to the gaseous phase. In general, factors affecting the volatilization of contaminants from ground water into soil gas include the contaminant concentration, the change in contaminant concentration with depth, the Henry s Law constant and diffusion coefficient of the compound, mass transport coefficients for the contaminant in both water and soil gas, sorption, and the temperature of the water. ... 

Consistent with the preceding discussion concerning sorption and flux reductions by relatively noninteracting penetrants, the data shown in Fig. 20.4-11 clearly illustrate the progressive exclusion of CO2 from Langmuir soiption sites in poly(methyl methaciylate) (PMMA) as ethylene partial pressure (Pb) increased in the presence of an essentially constant CO2 partial pressure of 3-05 7 0.13 atm. The tendency of the CO2 soiption shown in Fig. 20.4-11 to decrease monotonically with ethylene pressure provides impressive support for the competition concept on which E. . 4-17) and (20.4-18) are based. Pemreation data are not available for this stem to determine if changes in the values of Dp and Dh occur in the mixed gas situation. If offsettiiig increases in these transport coefficients do not occur in the presence of ethylene, the CO2 permeability will be depressed in the mixed gas peimeation situations. 

The transport of substituted benzenes through blends of thermoplastic polyurethane (TPU) and NR at 30, 50, and 70 °C was studied by A1 Minnath et al Results indicated that the equilibrium solvent uptake in the blends decreased with an increase in the concentration of TPU. The mechanism of diffusion of the solvents was found to deviate from the normal Fickian trend. The sorption data obtained were used to estimate the transport coefficient, and various sorption kinetic parameters. 

The linear response functions, presented above, are the result of linearization of the mathematical formalism, by assuming constant transport coefficients of water, kv and and using a linear approximation for the vapor sorption isotherm. The slopes mvE and mle represent linear effective resistances, analogous to ohmic resistances in electrical networks. 

The vaporization exchange model for water sorption and flux in Nafion-type PEMs has been modified and applied to treat transient water flux data (Rinaldo et al., 2011). A decisive modification was the inclusion of transport coefficients that depend on the water concentration or water content in the PEM. A simple form of this dependence is a step function change from slow to fast transport at a given transition concentration c. For this purpose, a hyperbolic tangent function was introduced ... 

The extracted parameters are vital for rationalizing mechanisms and amounts of water fluxes in PEFCs. The model could be applied for the analysis of sorption data at varying PEM thickness and equilibrium water content. Experiments running at varying T would provide activation energies of the vaporization-exchange rate constant and bulk transport coefficients. Similar modeling tools can be developed for the study of water sorption and fluxes in catalyst layers. They can be extended, furthermore,... 

FIGURE 5.3 Modeling of transient water flux data for Nation 117. (a) The relaxation of the experimental outlet vapor pressure (open circle) for Nafion 117 in LE mode at 50°C, flow chamber volume V = 0.125 L, flow rate V = 0.1 L min membrane area A = 2 cm, and saturation vapor pressure = 12336.7 Pa. Plotted for comparison are model simulations for a slow transport coefficient (dash dot), fast transport coefficient (dash), and a concentration-dependent transport coefficient (gray), (b) Water concentration profiles calculated in the model at different time. (Reprinted from Electrochem. Commun. 13, Rinaldo, S. G. et al. Vaporization exchange model for dynamic water sorption in Nafion Transient solution, 5-7, Figures 1 and 2, Copyright (2011) Elsevier. With permission.)... 

There are a number of other models of transport of solvent and solute through a reverse osmosis membrane the Kedem-Katchalsky model, the Spiegler-Kedem model, the frictional model, the finely porous model, the preferential sorption-capUlary flow model, etc. Most of these models have heen reviewed and compared in great detail hy Soltanieh and GiU (1981). We will restrict ourselves in this hook to the solution-diffusion and solution-diffusion-imperfection flux expressions for a number of reasons. First, the form of the solution-diffusion equation is most commonly used and is also functionally equivalent to the preferential sorption-capiUary flow model. Secondly, the solution-diffusion-imperfection model is functionally representative of a number of more exact three-transport-coefficient models, even though the transport coefficients in this model are concentration-dependent... 

It appears that pesticides with solubiHties greater than 10 mg/L are mainly transported in the aqueous phase (48) as a result of the interaction of solution/sediment ratio in the mnoff and the pesticide sorption coefficient. For instance, on a silt loam soil with a steep slope (>12%), >80% of atra2ine transport occurs in the aqueous phase (49). In contrast, it has been found that total metolachlor losses in mnoff from plots with medium ground slopes (2—9%) were <1% of appHed chemical (50). Of the metolachlor in the mnoff, sediment carried 20 to 46% of the total transported pesticide over the monitoring period. 

The gas sorption and transport properties also depend on the bisphenol connector groups [210]. The permeability coefficients for all gases rank in the order ... 

For practical purposes, the mutual diffusion coefficient is the quantity commonly reported to characterize diffusional transport in pharmaceutical systems. It is thus the purpose of investigators to determine this quantity experimentally. To this end, both sorption and permeation methods are commonly used. 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

This relative importance of relaxation and diffusion has been quantified with the Deborah number, De [119,130-132], De is defined as the ratio of a characteristic relaxation time A. to a characteristic diffusion time 0 (0 = L2/D, where D is the diffusion coefficient over the characteristic length L) De = X/Q. Thus rubbers will have values of De less than 1 and glasses will have values of De greater than 1. If the value of De is either much greater or much less than 1, swelling kinetics can usually be correlated by Fick s law with the appropriate initial and boundary conditions. Such transport is variously referred to as diffusion-controlled, Fickian, or case I sorption. In the case of rubbery polymers well above Tg (De < c 1), substantial swelling may occur and... 

Modeling relaxation-influenced processes has been the subject of much theoretical work, which provides valuable insight into the physical process of solvent sorption [119], But these models are too complex to be useful in correlating data. However, in cases where the transport exponent is 0.5, it is simple to apply a diffusion analysis to the data. Such an analysis can usually fit such data well with a single parameter and provides dimensional scaling directly, plus the rate constant—the diffusion coefficient—has more intuitive significance than an empirical parameter like k. 

The dominant transport process from water is volatilization. Based on mathematical models developed by the EPA, the half-life for M-hexane in bodies of water with any degree of turbulent mixing (e.g., rivers) would be less than 3 hours. For standing bodies of water (e.g., small ponds), a half-life no longer than one week (6.8 days) is estimated (ASTER 1995 EPA 1987a). Based on the log octanol/water partition coefficient (i.e., log[Kow]) and the estimated log sorption coefficient (i.e., log[Koc]) (see Table 3-2), ii-hexane is not expected to become concentrated in biota (Swann et al. 1983). A calculated bioconcentration factor (BCF) of 453 for a fathead minnow (ASTER 1995) further suggests a low potential for -hcxanc to bioconcentrate or bioaccumulate in trophic food chains. 

The Mc term can be used to approximate initial sorption or desorption on the glass surface, and the kt1 2 term the longer-term diffusion transport into or out of the surface (3). As shown in Figure 2, the sorption term decreases and the diffusion term increases with temperature for the obsidian experiments. Tabulated values for Equation 1 are presented in Table 1 along with the regression coefficient, r2, for glass data. 

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