Irreversible thermodynamics membrane process

The transport of both solute and solvent can be described by an alternative approach that is based on the laws of irreversible thermodynamics. The fundamental concepts and equations for biological systems were described by Kedem and Katchalsky [6] and those for artificial membranes by Ginsburg and Katchal-sky [7], In this approach the transport process is defined in terms of three phenomenological coefficients, namely, the filtration coefficient LP, the reflection coefficient o, and the solute permeability coefficient to. 

For membrane processes involving liquids the mass transport mechanisms can be more involved. This is because the nature of liquid mixtures currently separated by membranes is also significantly more complex they include emulsions, suspensions of solid particles, proteins, and microorganisms, and multi-component solutions of polymers, salts, acids or bases. The interactions between the species present in such liquid mixtures and the membrane materials could include not only adsorption phenomena but also electric, electrostatic, polarization, and Donnan effects. When an aqueous solution/suspension phase is treated by a MF or UF process it is generally accepted, for example, that convection and particle sieving phenomena are coupled with one or more of the phenomena noted previously. In nanofiltration processes, which typically utilize microporous membranes, the interactions with the membrane surfaces are more prevalent, and the importance of electrostatic and other effects is more significant. The conventional models utilized until now to describe liquid phase filtration are based on irreversible thermodynamics good reviews about such models have been reported in the technical literature [1.1, 1.3, 1.4]. 

There are three basic concepts that explain membrane phenomena the Nemst-Planck flux equation, the theory of absolute reaction rate processes, and the principle of irreversible thermodynamics. Explanations based on the theory of absolute reaction rate processes provide similar equations to those of the Nemst-Planck flux equation. The Nemst-Planck flux equation is based on the hypothesis that cations and anions independently migrate in the solution and membrane matrix. However, interaction among different ions and solvent is considered in irreversible thermodynamics. Consequently, an explanation of membrane phenomena based on irreversible thermodynamics is thought to be more reasonable. Nonequilibrium thermodynamics in membrane systems is covered in excellent books1 and reviews,2 to which the reader is referred. The present book aims to explain not theory but practical aspects, such as preparation, modification and application, of ion exchange membranes. In this chapter, a theoretical explanation of only the basic properties of ion exchange membranes is given.3,4... 

The thermodynamics of irreversible processes are very useful for understanding and quantifying coupling phenomena. However, structure-related membrane models are more useful than the irreversible thermodynamic approach for developing specific membranes. A number of such transport models have been developed, partly based on the principles of the thermodynamics of irreversible processes, both for porous and nonporous membranes. Again, two types of structure will be considered here porous membranes, as found in microfUtration/uItrafiltration, and nonporous membranes of the type used in pervaporation/gas separation. 

Physically, the proton should overcome the voltage barrier — g, which separates the potentials of the membrane and carbon phases. Here is the cathode half-cell open-circuit voltage. However, the irreversible dissipation of energy occurs only when the proton acquires the voltage g required to reach the potential Further transport of the proton with the potential to the Pt particle is a thermodynamically reversible process. 

In the second chapter of this book, we shall represent and discuss a few examples of physical or chemical models for biological phenomena like transport across membranes, membrane excitation, control of metabolism, and population dynamic interaction between different species. All these models will be of the type of a reaction kinetic model, i.e., the model processes are chemical reactions and diffusion of molecules or may at least be interpreted like that. Thus, the physical background of the various models is irreversible thermodynamics of reactions and diffusion. 

In this Section, it is implicitly assumed that the mass transport resistance at the fluid-membrane interface on either side of the membrane is negligible. Also the following is information that is made available publicly by the membrane manufacturers, when not otherwise noted. As in technical processes, mass transport across semipermeable medical membranes is conveniently related to the concentration and pressme driving forces according to irreversible thermodynamics. Hence, for a two-component mixture the solute and solvent capacity to permeate a semipermeable membrane under an applied pressure and concentration gradient across the membrane can be expressed in terms of the following three parameters Lp, hydraulic permeability Pm, diffusive permeability and a, Staverman reflection coefficient (Kedem and Katchalski, 1958). All of them are more accurately measured experimentally because a limited knowledge of membrane stmcture means that theoretical models provide rather inaccurate predictions. 

For example, thermodynamic calculations will provide a value for the maximum voltage of a storage battery—that is, the voltage that is obtained when no current is drawn. When current is drawn, we can predict that the voltage will be less than the maximum value, but we cannot predict how much less. Similarly, we can calculate the maximum amount of heat that can be transferred from a cold environment into a building by the expenditure of a certain amount of work in a heat pump, but the actual performance will be less satisfactory. Given a nonequilibrium distribution of ions across a cell membrane, we can calculate the minimum work required to maintain such a distribution. However, the actual process that occurs in the cell requires much more work than the calculated value because the process is carried out irreversibly. 

Example 4.9 Entropy production in separation process Distillation Distillation columns generally operate far from their thermodynamically optimum conditions. In absorption, desorption, membrane separation, and rectification, the major irreversibility is due to mass transfer. The analysis of a sieve tray distillation column reveals that the irreversibility on the tray is mostly due to bubble-liquid interaction on the tray, and mass transfer is the largest contributor to the irreversibility. 

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. 

Thermodynamics of irreversible processes discussed above by itself cannot give an insight into the mechanism of gaseous transport through membranes. The molecular kinetic theory can be used with advantage for this purpose. 

We shall first outline the theory of electro-osmosis and streaming potential based on thermodynamics of irreversible processes [9-14], Let us consider two chambers separated by a very thin membrane, so that it merely serves as a dividing surface which we need not consider as a separate phase. 

The case of ammonia represents a raerabrane process based on physical permeation since acmonia is soluble in the membrane phase If a solute is insoluble, a complex-forming compound (carrier agent) has to be introduced there to provide facilitated transport. Since the reaction of the solute with the carrier agent has to be reversible, reaction equilibrium will apply at both surfaces. The process will thus be thermodynamically controlled unless a reactive compound is introduced into the internal phase to remove the solute from the system by an irreversible reaction. 

The purpose of this chapter is to underline the importance of transport phenomena and mathematical modelling in biomedical applications where a thermodynamic system, not in an equilibrium condition, undergoes a spontaneous irreversible transformation, as in classic drug delivery systems. The irreversibility of thermodynamic processes was thoroughly investigated from a mathematical point of view, using phenomenological and kinetic approaches. Three biomedical examples were analysed in detail membranes... 

The most serious obstacle to the study of models of the uptake of metal cations, in spite of the lively experimental activity, is probably the theoretical difficulties in energetics and molecular structure at the cellular barrier membranes, the chemistry of which seems to be unexpectedly complex. In principle, the uptake of metal cations is divided into the passive, physicochemical phase and an active phase that depends on metabolic sources of energy. The active uptake has been adequately demonstrated and the sites of input for different groups of cations have been revealed by competitive experiments. In spite of many attempts, however, the active carriers of cations have not been found. It is an appropriate time for new experimental and/or theoretical ideas. For example, the new, developing thermodynamics of irreversible processes has energetically outlined some very interesting possibilities of the stationary state for the coupling of the processes which are worthy of closer experimentation. 

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