Mass transfer irreversible thermodynamics model

Section 15.6 describes the deficiencies in the Fickian model and points out why an alternative model (the fourth) is needed for some situations. The alternative Maxwell-Stefan model of mass transfer and diffusivity is explored in Section 15.7. The Maxwell-Stefan model has advantages for nonideal systems and multicomponent mass transfer but is more difficult to couple to the mass balances when designing separators. The fifth model of mass transfer, the irreversible thermodynamics model fde Groot and Mazur. 1984 Ghorayeb and Firoozabadi. 2QQQ Haase. 1990T is useful in regions where phases are unstable and can split into two phases, but it is beyond the scope of this introductory treatment. The... 

Finite-time thermodynamics is an extension to traditional thermodynamics in order to obtain more realistic limits to the performance of real processes, and to deal with processes or devices with finitetime characteristics. Finite-time thermodynamics is a method for the modeling and optimization of real devices that owe their thermodynamic imperfection to heat transfer, mass transfer, and fluid flow irreversibility. 

We have emphasized the proper modeling of thermodynamic nonideality both with regard to molecular diffusion and interphase mass transfer. The benefits of adopting the irreversible thermodynamic approach are particularly apparent here it would not be possible otherwise to explain the peculiar behavior of the Fick diffusivities. The practical implications of this behavior in the design of separation equipment operating close to the phase transition or critical point (e.g., crystallization, supercritical extraction, and zone refining) are yet to be explored. In any case, the theoretical tools are available to us. 

The model, based on Hnear, irreversible thermodynamics, constitutes a more general phenomenological approach, appHcable to systems with either class of membranes, multiple solutes, and driving forces involved. It includes component and overall mass balances, mass-transfer rates, local equilibrium relations, and electroneutrahty constraints. 

The models based on the irreversible process thermodynamics show that the cell membrane (plasma lemma) represents the major resistance to mass transfer. This is contradicted by findings of Raoult-Wack et al. [46-48], who showed that membranes are not necessary for osmotic dehydration and merely diffusive properties of the material are responsible for high water flux with only marginal sugar penetration. These authors suggest the following mechanism. 

Transport in OSN membranes occurs by mechanisms similar to those in membranes used for aqueous separations. Most theoretical analyses rely on either irreversible thermodynamics, the pore-flow model and the extended Nemst-Planck equation, or the solution-diffusion model [135]. To account for coupling between solute and solvent transport (i.e., convective mass transfer effects), the Stefan-Maxwell equations commonly are used. The solution-diffusion model appears to provide a better description of mixed-solvent transport and allow prediction of mixture transport rates from pure component measurements [136]. Experimental transport measurements may depend significantly on membrane preconditioning due to strong solvent-membrane interactions that lead to swelling or solvent phase separation in the membrane pore structure [137]. 

Banki, R. Hoteit, H. Firoozabadi, A. (2008). Mathematical Formulation and Numerical Modeling of Wax Deposition in Pipelines from Enthalpy-Porosity Approach and Irreversible Thermodynamics. International Journal of Heat Mass Transfer, Vol.51, No.13-14, pp.3387-3398, ISSN 0017-9310... 

The capacitive elements and fields in the model represent equilibrium thermodynamics part of the model. As the simulation proceeds, the matter inside the control volume represented by these elements changes reversibly from one equilibrium state to the next, i.e. the process is assumed to be quasi-static. The R-fields represent the non-equilibrium parts of the model, and they introduce the irreversibilities into the system. The R-field elements represented by MR in Fig. 10.4 introduce the irreversibility due to mass convection into the system (refer to Section 10.2.4). The R-field element represented by RS in Fig. 10.4 introduces the irreversibility due to the over-voltage phenomena (ohmic, concentration and activation losses). The other R-field elements introduce the irreversibilities due to the heat transfer phenomena. 

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