Sorption equation

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.

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... 

T. Matsui, M. Fukamachi, M. Shimoda and Y. Osajima, Derivation of thermodynamic sorption equation of flavors with packaging films 1, J. Agric. Food Chem., 42 (1994) 2889-2892. 

Table 4.2 summarizes the isotherm equations discnssed so far pins some others, added for comparison. The first four have been discussed earlier in the text. The Guggenheim-Anderson-de Boer isotherm (GAB) is a multilayer sorption equation, a modified form of the BET equation that has found wide application in food science and technology (Timmermann 2003 and references therein). Basically, it does not consider the layers beyond the first as the liquid adsorbate but as an intermediate... 

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). 

Given this practical importance, it is obviously awkward that the equilibrium constants of the dual mode sorption equations cannot be correlated with the properties of the polymer and of the permeant. Such correlations are reasonably successful in the rubbery state. Owing to.the effects of mechanical and thermal history of the glass on the incidence and effective surface area of the voids, a reliable generalized correlation for prior estimations of the three constants for gas sorption in glassy polymers may never be possible. 

Reduced sorption equations. Because the first term in the above series is dominant, for large times, Eq. 11.66 can be reduced to... 

The assumptions in his model do not allow for the complexity of the moisture sorption isotherm and the sorption kinetics of fibers. Scientists presented two mathematical models to simulate the interaction between moisture sorption by fiber and moisture flux through the air spaces of a fabric. In the first model, they considered diffusion within the fiber to be so rapid that the fiber moisture content is always in equilibrium with the adjacent air. In the second model, they assumed that the sorption kinetics of the fiber follows Fickian diffusion. Their model neglected the effect of heat of sorption behavior of the fiber. Scientists developed a new sorption equation that takes into account the two-stage sorption kinetics of wool fibers, and incorporated this with more realistic boundary conditions to simulate the sorption behavior of wool fabrics. They assumed that water vapor uptake rate of fiber consists of a two components associated with the two stages of sorption identified by researchers. 

Equilibrium sorption and desorption behavior in natural soil systems are often nonlinear, and conunonly modeled well by the Freundlich sorption equation ... 

The above equations, based on the conservation of mass for chemical transport, yield the convection-dispersion-sorption equation CDSE (Eq. 3.41 and its variations), which is widely used in industrial applications, including dyeing. Many researchers call the term (D d ddx ) in Eq. 3.41b either dispersion or diffusion, and D is usually treated as a constant. In the context of this analysis, dispersion is used to describe this phenomenon, and the diffusion is considered a special case of dispersion when the velocity of the fluid is zero. 

One can use the above equation to discretise a partial difference equation (PDE) and implement a numerical method to solve the PDE. For example, if it is required to calculate numerical solutions of the convection-dispersion-sorption equation (CDSE, see Eq. 3.41b, also shown below) ... 

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