Water sorption equation

Water uptake of Nafion 117. (a) Isopiestic water sorption data (extracted from T. E. Springer et al. Journal of the Electrochemical Society 138 (1991) 2334-2342) fitted by Equation (6.7) (b) capillary isotherms (extracted from J. Divisek et al.. Journal of the Electrochemical Society 145 (1998) 2677-2683) fitted by Equation (6.8). 

The addition of a filler changes the kinetics of the water absorption by an epoxy binder, water absorption becoming a multistage process (Fig. 12). Crank and Park150) have given the equation for the kinetics of water sorption by a thin plate, as well as a solution of the Fickian diffusion differential Equation as ... 

Equation [1.5.38] is still fairly general. Except for the premises of localization, surface homogeneity and absence of lateral interaction, we only have the restriction that at given J there is only one type of subsystem, l.e. only one q(J). This generality implies that, for instance, [1.5.38] also applies to the three-dimensional analogue, like water sorption on a non-expanding gel. Furthermore, a number of models are compatible with this expression. 

Figure 4. Linear presentation of water sorption data at 293 K evaluation in terms of Equations 3 and 4...

Figure 6. Kinetics of water sorption mass action kinetics in terms of Equation 7 water rate analysis...

Gentry et al. (1976) have recently shown, on the basis of isotopic analyses, that uranium introduction may have occurred far more recently than was previously supposed. However, they find also that, in some instances, the uranium was introduced before coalification was complete since the haloes have been compressed with the coal as it increased in rank. These results are consistent with laboratory and field work by Szalay (1964) who showed that the insoluble humic acids in peat are capable of concentrating uranium from very dilute solutions in natural waters. Sorption occurs as uranyl humate , the process following the normal kinetics of the Langmuir adsorption equation. (Where uraninite occurs in association with peat or other carbonaceous matter, the uranium may thus have been initially sorbed as a uranyl compound which was later reduced to uraninite.)... 

The experimentally determined isotherm for water sorption by the membrane (see Fig. 9) was used to convert from water vapor activity in the gas phase at the interface to water content in the membrane at the surface and considering generation of water at the cathode, the water level in the membrane surface adjacent the cathode was assumed accordingly to be X = 14 (or somewhat above, see Ref. 36). The components of water flow considered within the membrane included electroosmotic drag and diffusion, whereas hydraulic flux was considered insignificant (i.e., very small hydraulic pressure drop across the membrane) [36]. Consequently, the basic equation describing the flux within the membrane becomes... 

Figure 3.3. Sorption equations fitted to experimental data for the sorption of water by wood at 40°C (Simpson, 1980). The Langmuir isotherm is parabolic, corresponding to the formation of a BET monolayer. Multilayer adsorption describes sorption behaviour better but sorption at the highest moisture contents, where capillary condensation occurs, is underestimated.

Water-sorption properties of various films were determined gravimetri-cally after storage of freeze-dried samples in vacuum desiccators at a relative humidity ranging from 11 to 86% at 25°C. Water-sorption behavior was modeled with the Guggenheim-Anderson-de Boer (GAB) Equation 24.1 in which water content is m, monolayer moisture content is wXm, water activity is flw/ arid K and C are constants. 

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). 

For true adsorption, several equations for adsorption isotherms have been derived, based on various theories. Such equations often are applied to water sorption isotherms of foods as well. However, one cannot speak of adsorption in the case of most foods, as mentioned above, because there is no (or a very limited) phase surface onto which water can adsorb. Moreover, most foods contain numerous components even if phase surfaces were present they must be very inhomogeneous. In the author s opinion, it therefore makes little sense to use such equations. Only for relatively simple and homogeneous systems, like pure starch granules, can some theories be more or less applicable, but not for real foods. Mathematical fitting of experimental data may be useful for practical purposes, and since the equations generally have three or four adjustable parameters, a reasonable fit can often be obtained. But one cannot attribute physical significance to the parameters derived in this way, such as a monolayer water content. ... 

That is, if water sorption occurs on two types of sites, a polymer site and a pol3rmer-water site, the influence of the former will predominate as P and the amount of sorbed water simultaneously approach zero. A plot of vs P with a slope of k] (the inverse of Equation 2), as shown in Figure 1, is tangent to the experimental Isotherm at the origin. The analysis outlined allows a unique specification of x interaction parameter, through use of the limiting (Henry s Law) approximation of the Flory-Hugglns theory ( 3). That is... 

Table 28 reports the maximum swelling coefficient Qmail, the time needed to reach this equilibrium state tmax, and the constants k and n that characterize the water sorption profiles according to the equation [166] ... 

Moisture Regain. The advantage of this method is that water vc r normally does not penetrate well-defined crystallites of cellulose (26). Thus the amount of moisture adsorbed a sample after conditioning at a i >ecific relative ve r pressure and tenf)erature can be used to estimate its accessibility and degree of order. In one method using water sorption (27), the fraction of amorf ous material (F ) has been calculated from the sorption ratio (SR) of the sanple using the equation... 

Hailwood and Horrobin ( ) develqped an equation for water sorption of cellulose based on a solution theory. It permits the calculation of the fraction of the san )le inaccessible to water vapor. However, Hailwood and Horrobin assumed in the development of their equation that an ideal solid solution of polymer, hydrated polymer and water is formed. This assutrption has laeen questioned in the general discussion following the presentation of their paper and also by McLaren and Rcwen (29). 

Water vapor at room temperature will not penetrate well-defined crystallites but will be adsorbed in the amorphous regions. Consequently, moisture sorption measured gravimetrically at a given relative vapor pressure and temperature has been used to determine order in cellulosic materials. In the case of Valentine [252] and Jeffries [253], the fraction of ordered material was obtained by correlating moisture sorption with values obtained by the deuterium oxide method. Hailwood and Horrobin [254] developed an equation for water sorption of cellulose based on a solution theory that allowed the calculation of the fraction of the sample inaccessible to water. 

Typically, the effect of water sorption on the T for an amorphous solid is estimated using the Gordon-Taylor equation [28a] ... 

Eq. 1). The data generated from the modified version of Eq. 1 were consequently expressed in a manner similar to the data obtained from Eq. 7 as the fraction of potential water sorption (Fuk) at time (t) (Ross et al., 2010b). This t3rpe of treatment is acceptable based on the S3rmmetry of the curves. The equations were given as follows ... 

At a water contents below the FSP the equilibrium molar fraction of water vapor in the gas phase is calculated due to the sorption equation of Moyne... 

Timmermann, E.O., and Chirife, J., The physical state of water sorbed at high activities in starch in terms of the GAB sorption equation, J. Food Eng., 13(3). 171-180 (1991). 

While several simplifying assumptions needed to be made so as to derive an analytical model, the model captures all relevant physical processes. Specifically, it employed thermodynamic equilibrium conditions for temperature, pressure, and chemical potential to derive the equation of state for water sorption by a single cylindrical PEM pore. This equation of state yields the pore radius or a volumetric pore swelling parameter as a function of environmental conditions. Constitutive relations for elastic modulus, dielectric constant, and wall charge density must be specified for the considered microscopic domain. In order to treat ensemble effects in equilibrium water sorption, dispersion in the aforementioned materials properties is accounted for. 

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