Irreversible thermodynamics transport properties

In contrast to thermodynamic properties, transport properties are classified as irreversible processes because they are always associated with the creation of entropy. The most classical example concerns thermal conductance. As a consequence of the second principle of thermodynamics, heat spontaneously moves from higher to lower temperatures. Thus the transfer of AH from temperature to T2 creates a positive amount of entropy ... 

The production of species i (number of moles per unit volume and time) is the velocity of reaction,. In the same sense, one understands the molar flux, jh of particles / per unit cross section and unit time. In a linear theory, the rate and the deviation from equilibrium are proportional to each other. The factors of proportionality are called reaction rate constants and transport coefficients respectively. They are state properties and thus depend only on the (local) thermodynamic state variables and not on their derivatives. They can be rationalized by crystal dynamics and atomic kinetics with the help of statistical theories. Irreversible thermodynamics is the theory of the rates of chemical processes in both spatially homogeneous systems (homogeneous reactions) and inhomogeneous systems (transport processes). If transport processes occur in multiphase systems, one is dealing with heterogeneous reactions. Heterogeneous systems stop reacting once one or more of the reactants are consumed and the systems became nonvariant. 

Fortunately, several simplifications can be made (Nye, 1957). Transport phenomena, for example, are processes whereby systems transition from a state of nonequilibrium to a state of equilibrium. Thus, they fall within the realm of irreversible or nonequilibrium thermodynamics. Onsager s theorem, which is central to nonequilibrium thermodynamics, dictates that as a consequence of time-reversible symmetry, the off-diagonal elements of a transport property tensor are symmetrical (i.e., xy = X/,-). This is known as a reciprocal relation. The Norwegian physical chemist Lars Onsager (1903-1976) was awarded the 1968 Nobel Prize in Chemistry for reciprocal relations. Thus, the tensor above can be rewritten as... 

Other examples of transport properties include electrical and thermal conductivity. Transport of a physical quantity along a determined direction due to a gradient is an irreversible process by which a system transitions from a nonequilibrium state to an equilibrium state (e.g., compositional or thermal homogeneity). Therefore, it is outside the realm of equilibrium thermodynamics. (For this reason, equilibrium thermodynamics is more appropriately termed thermostatics.) Transport processes must be studied by irreversible thermodynamics. 

A variety of RO membrane models exist that describe the transport properties of the skin layer. The solution-diffusion model( ) is widely accepted in desalination where the feed solution is relatively dilute on a mole-fraction basis. However, models based on irreversible thermodynamics usually describe membrane behavior more accurately where concentrated solutions are involved.( ) Since high concentrations will be encountered in ethanol enrichment, our present treatment adopts the irreversible thermodynamics model introduced by Kedem and Katchalsky.(7.)... 

Cation, anion, and water transport in ion-exchange membranes have been described by several phenomenological solution-diffusion models and electrokinetic pore-flow theories. Phenomenological models based on irreversible thermodynamics have been applied to cation-exchange membranes, including DuPont s Nafion perfluorosulfonic acid membranes [147, 148]. These models view the membrane as a black box and membrane properties such as ionic fluxes, water transport, and electric potential are related to one another without specifying the membrane structure and molecular-level mechanism for ion and solvent permeation. For a four-component system (one mobile cation, one mobile anion, water, and membrane fixed-charge sites), there are three independent flux equations (for cations, anions, and solvent species) of the form... 

Thus, from the point of view of modem phenomenological thermodynamics, the current outputs of classical equilibrium thermodynamics (e.g. the description of thermochemistry of mixtures) and the tasks of irreversible thermodynamics, like the description of linear transport phenomena and nonlinear chemical kinetics, are valid much more generally, e.g. even when all these processes mn simultaneously. As we noted above, these properties are not expected to be valid in any material models in some models the local equilibrium may not be valid, reaction rates may depend not only on concentrations and temperature, etc. 

Just as in the case of equilibrium thermodynamics, thermodynamics of irreversible processes yields phenomenological equations which in principle are independent of the molecular nature of the system. In contrast, statistical mechanics derives transport properties from the microscopic picture of the solution. Considerable progress has been made in this latter type of approach during recent years. 

Several approaches have been followed to understand the transport phenomena occurring in perfluoropolymeric membranes, and these include irreversible thermodynamics, use of the Nemst-Planck transport equation (Eq.l3), and various descriptions (e.g., free-volume model, lattice model, quasi-crystalline model) coupling the morphological and chemical properties of the membranes. The reader is referred to the references and citations in the reviews [81-87] for more details related to these models. 

The Nemst-Planck equation is often employed by practitioners because of its similarity to Pick s law and its convenient separation of diffusion and migratiOTi terms. It should be borne in mind, however, that the theory is inconsistent with the basic requirements of irreversible thermodynamics [6, 7]. Nemst-Planck theory uses n + k properties to characterize transport in an isothermal, isobaric n-species system containing... 

In this book we offer a coherent presentation of thermodynamics far from, and near to, equilibrium. We establish a thermodynamics of irreversible processes far from and near to equilibrium, including chemical reactions, transport properties, energy transfer processes and electrochemical systems. The focus is on processes proceeding to, and in non-equilibrium stationary states in systems with multiple stationary states and in issues of relative stability of multiple stationary states. We seek and find state functions, dependent on the irreversible processes, with simple physical interpretations and present methods for their measurements that yield the work available from these processes. The emphasis is on the development of a theory based on variables that can be measured in experiments to test the theory. The state functions of the theory become identical to the well-known state functions of equilibrium thermodynamics when the processes approach the equilibrium state. The range of interest is put in the form of a series of questions at the end of this chapter. 

Miller DG (1960) Certain transport properties of binary electrolyte solutions and their relation to the thermodynamics of irreversible processes. J Phys Chem 64 1598-1599... 

Modeling an electrochemical interface by the equivalent circuit (EC) representation approach has been exceptionally popular in studies of electrodes modified with polymer membranes, although an analytical approach based on transport equations derived from irreversible thermodynamics was also attempted [6,7]. ECs are typically composed of numerous ideal electrical components, which attempt to represent the redox electrochemistry of the polymer itself, its highly developed morphology, the interpenetration of the electrolyte solution and the polymer matrix, and the extended electrochemical double layer established between the solution and the polymer with variable localized properties (degree of oxidation, porosity, conductivity, etc.). 

Same as a peripheral microvessel, the wall of the BBB can be viewed as a membrane. The membrane transport properties are often described by Kedem-Katchalsky equations derived from the theory of irreversible thermodynamics [47] ... 

Perhaps the most elegant and exact but therefore the most limited approach to the transport properties is through a general equation such as the Boltzmann or Fokker-Planck equation describing the time-dependent distribution functions of the system. The results of the zeroth-order theories can be conveniently cast in the form of the friction constants of irreversible thermodynamics. 

All discussions of transport processes currently available in the literature are based on perturbation theory methods applied to kinetic pictures of micro-scattering processes within the macrosystem of interest. These methods do involve time-dependent hamiltonians in the sense that the interaction operates only during collisions, while the wave functions are known only before and after the collision. However these interactions are purely internal, and their time-dependence is essentially implicit the over-all hamiltonian of the entire system, such as the interaction term in Eq. (8-159) is not time-dependent, and such micro-scattering processes cannot lead to irreversible changes of thermodynamic (ensemble average) properties. 

In the formulation of the microscopic balance equations, the molecular nature of matter is ignored and the medium is viewed as a continuum. Specifically, the assumption is made that the mathematical points over which the balance field-equations hold are big enough to be characterized by property values that have been averaged over a large number of molecules, so that from point to point there are no discontinuities. Furthermore, local equilibrium is assumed. That is, although transport processes may be fast and irreversible (dissipative), from the thermodynamics point of view, the assumption is made that, locally, the molecules establish equilibrium very quickly. 

The theory treating near-equilibrium phenomena is called the linear nonequilibrium thermodynamics. It is based on the local equilibrium assumption in the system and phenomenological equations that linearly relate forces and flows of the processes of interest. Application of classical thermodynamics to nonequilibrium systems is valid for systems not too far from equilibrium. This condition does not prove excessively restrictive as many systems and phenomena can be found within the vicinity of equilibrium. Therefore equations for property changes between equilibrium states, such as the Gibbs relationship, can be utilized to express the entropy generation in nonequilibrium systems in terms of variables that are used in the transport and rate processes. The second law analysis determines the thermodynamic optimality of a physical process by determining the rate of entropy generation due to the irreversible process in the system for a required task. 

The main objective of performing kinetic theory analyzes is to explain physical phenomena that are measurable at the macroscopic level in a gas at- or near equilibrium in terms of the properties of the individual molecules and the intermolecular forces. For instance, one of the original aims of kinetic theory was to explain the experimental form of the ideal gas law from basic principles [65]. The kinetic theory of transport processes determines the transport coefficients (i.e., conductivity, diffusivity, and viscosity) and the mathematical form of the heat, mass and momentum fluxes. Nowadays the kinetic theory of gases originating in statistical mechanics is thus strongly linked with irreversible- or non-equilibrium thermodynamics which is a modern held in thermodynamics describing transport processes in systems that are not in global equilibrium. 

The product of thermodynamic forces and fiows yields the rate of entropy production in an irreversible process. The Gouy-Stodola theorem states that the lost available energy (work) is directly proportional to the entropy production in a nonequilibrium phenomenon. Transport phenomena and chemical reactions are nonequilibrium phenomena and are irreversible processes. Thermodynamics, fiuid mechanics, heat and mass transfer, kinetics, material properties, constraints, and geometry are required to establish the relationships... 

FIGURE 1.4 Illustration of basic fuel ceU processes and their relation to the thermodynamic properties of a cell. The electrical work performed by the cell, corresponds to the reaction enthalpy, — A//, minus the reversible heat due to entropy production, —TAS, and minus the sum of irreversible heat losses at finite load, Qi. These losses are caused by kinetic processes at electrochemical interfaces as well as by transport processes in diffusion and conduction media. 

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