## Thermodynamics of Irreversible Processes

### Description

*Thermodynamics of Irreversible Processes* provides a thorough treatment of the basic axioms of irreversible systems and deals with specific applications to diffusion of liquids and matter in flow. This volume is invaluable reading for anyone working in the field of irreversible phenomena.

### Contains

*Thermodynamics of Irreversible Processes* presents:

- A lucid review of classical thermodynamics.
- Rigorous derivations of the fundamental principles of irreversible thermodynamics.
- In-depth studies of multicomponent diffusion, with applications to non-ideal systems.
- Thorough treatments of relaxation phenomena and linear viscoelasticity.

Thermodynamics of irreversible Processes is the first advanced text dealing with the applications of irreversible thermodynamics to multicomponent diffusion and viscoelasticity. Gerard Kuiken has written a book which will appeal to students and researchers in chemistry, chemical technology, polymer and materials science, physics and rheology.

### Excerpts from Reviews

This is a serious work in the series designed for those who are engaged in practical research, in teaching and those who wish to learn about the role of theory in chemistry today. ... it provides a basis for describing a wide range of phenomena: the author defines the thermodynamics of irreversible processes (TIP) as describing within the framework of a continuum point of view all systems obeying linear constitutive equations of state. It thus unifies formulations of continuum theory used in many branches of physics and chemistry as mechanics, fluid dynamics, magnetohydrodynamics, mass transport and thermodynamics. Moreover, the results often apply to quasi-linear systems.

... Chap. 2. This chapter, which includes an elegant discussion of modelling theory and orders of magnitude, is accessible to undergraduate students, and it is unusually lucid and easy to follow. ... The Onsager-Casimir relations are introduced in Chapter 5. To this reviewer, who started examination of Dr. Kuiken's monograph with only very limited grasp of the origin of these famous relations, this chapter is the most interesting of the book. The author's development does not take Boltzmann's entropy identification for granted but derives the probability distribution from the Fokker-Planck equation for aged systems. In this way he shows that microscopic reversibility only yields the Onsager reciprocal relations if one starts with the Boltzmann distribution. This is the most lucid and authoritative treatment I have seen. ...

Chapter seven is the longest chapter in the book and includes extensive general discussions of relaxation phenomena as well specific examples on linear viscoelasticiy. These discussions are clearly for the specialists, and are not readily accesible to others. ...

The typography and figures are of high quality, and the secondary features are quite impressive. There are two extensive appendices, the first deriving Maxwell's electromagnetic field equations and the second summarizing vector and tensor notation. The nomenclature list is very helpful, and there are both author and subject indexes.

E.N. Lightfoot, Dept. Chem. Eng., Univ. Wisconsin, Madison WI.

Chem. Eng. Sci., vol. 50 (1995) pp. 2503-2504.

This book is a thorough and clear exposition of the underlying principles of the linear thermodynamics of irreversible processes (TIP). The monograph admirably satisfies the goals of the Wiley tutorial series in theoretical chemistry and although it is primarily aimed at undergraduate students it should also serve as an excellent reference textbook for research as well as teaching. ...

In Chapter 2 the fundamental concepts and laws of classical equilibrium thermodynamics are introduced and an interesting method of heat engine representation is provided via vector diagrams. I am also pleased to see the inclusion of Caratheodory's statement with the Clausius and Kelvin-Planck statements of the second law. ...

In Chapter 4 the author extends the topics of classical equilibrium and nonequilibrium thermodynamics to multicomponent fluids which do not possess internal 'hidden' variables. The material balance, diffusion equations, and electromagnetic balance equations are then developed (with regard to the latter topic it is also of interest to note that the author provides an excellent summary of the derivation of the electromagnetic field equations in Appendix A of the text). A rather complete analysis of the energy balance is also given and a number of representative forms are derived. At the end of this chapter the author derives the entropy dissipation function and his emphasis on the concept of affinity, particularly in association with internal degrees of freedom which will later be a central theme of Chapter 7, is noted. ...

Chapter 6 is the first of the two most important chapters in the book. This chapter details the fundamental equations for the irreversible thermodynamics of vector processes with particular reference to diffusion. The author develops both the phenomenological and Maxwell-Stefan descriptions of the diffusion force/flux relations and provides a generalised set of Maxwell diffusion equations which are applicable to isotropic fluids. His analysis of the mass transport equations is clear and to the point and I agree strongly with his conclusion that the Maxwell-Stefan representation of the diffusion equations is the preferred form for an unambiguous analysis of diffusion. An excellent and very readable analysis of the flux equations for binary mixtures is provided emphasising the distinction between the Fickian diffusivity usually reported in the literature and the Maxwell-Stefan diffusivity. ...

The last chapter in the book, which develops the second major theme of the text, is an excellent introduction to linear, nonequilibrium phenomena in rheology. The introductory sections to the chapter clearly define the rheological models based on the four properties elasticity, anelasticity, viscosity, and plasticity. ...

I believe Professor Kuiken has made a significant contribution in elucidating many of the principles of TIP in the last two core chapters of his monograph. ... it is a very well-written and readable text. The monograph should serve as an excellent text for an undergraduate course in materials science and engineering or as a comprehensive source for ideas in a variety of courses and research in chemical technology.

J.M.D. MacElroy, Chem. & Bioprocess Eng., Univ. Coll. Dublin, Dublin.

The Chem. Eng. J., vol. 60 (1996) pp. 179-180.

Kuiken provides a clear description of the continuum model and summarises the fundamental concepts of classical thermodynamics including a novel approach to the second law. The basic axioms of the of irreversible processes are discussed in Chapter 3 and used to derive the balance equations and the entropy equation for multicomponent fluids in Chapter 4. Stochastic processes are described in Chapter 5 and the Onsager reciprocal relations are derived using the solutions of the Fokker-Plank equations. This derivation is unusual in that it does not assume the Boltzmann hypothesis, that the entropy of a system is proportional to the logarithm of the probability of the corresponding state of the system, a priori, but demonstrates that the Boltzmann probability distribution is one possible distribution that yields the symmetry relations. These first five chapters provide an excellent account of the thermodynamics of irreversible processes in which the basic axioms are clearly explained as are the limitations of the theory.

The second half of the book consists of two chapters containing applications of the In the first of these, Chapter 6, Professor Kuiken addresses the problem of multi-component diffusion. The process rate in many real mass transfer processes is determined by the speed of the diffusion processes that can occur. The thermodynamics of irreversible processes is used to determine the Maxwell-Stefan equations for the description of diffusion. Chapter 7, which occupies almost one third of the book, is concerned with the application of rheology. Here we meet internal variables relaxation phenomena. Once again the author sets out the basic assumptions clearly and from, these formulates the constitutive relations for linear rheological materials. The book is well produced with a clear text, clearly drawn figures and few misprints. My only criticism is in the lack of hints or solutions to the exercises at the end of each chapter.

R.S. Jones, Dept. Math., Univ. Wales, Aberystwyth.

J. Non-Newtonian. Fluid Mech., 60 (1995) 359.

The thermodynamics of systems close to equilibrium underwent a remarkable development in the middle third of this century following the seminal work of Onsager on thermal transport coefficients. There emerged a class of continuum theories suitable for discussing diffusion, heat conduction, fluid flow and chemical reactions in which the large number of phenomenological transport coefficients was constrained and ordered by the Onsager-Casimir reciprocal relations, which reflected the underlying mechanical time-reversibility of these systems. The work of Prigogine, Meixner, de Groot and Mazur clarified the structure of these theories. Gerard Kuiken has written a monograph which surveys these developments and, with respect to diffusion and rheology, extends the classic exposition of de Groot and Mazur.

Kuiken aims to be accessible to students as well as to research workers, so he includes a detailed treatment of equilibrium thermodynamics as well as a summary of Maxwell's electromagnetic theory of polarizable media. He sets up the structure of non-equilibrium thermodynamics in an axiomatic way, stressing the role of invariance and covariance with respect to Galilean transformations. Separate chapters ...

While the first five chapters are quite accessible to a student, the last two chapters are characterized by a relentless complexity (there are nearly 500 numbered equations in the last chapter). These sections are not to be read as a textbook but will serve well as a reference work for those concerned with engineering applications of multi-component diffusion or visco-elasticity. For real systems such as fluids or colloidal dispersions, much modern research aims to derive the phenomenological coefficients from microscopic models studies analytically or computer simulation. Irreversible thermodynamics still plays a role in such microscopic models providing consistency checks on their predictions. This book is welcome both for exposition of the principles of non-equilibrium thermodynamics and for its treatment of diffusion and of viscoelastic systems. It would be a valuable addition to all science and engineering libraries.

R.B. Jones, J. Fluid Mech, vol. 316 (1996) p. 374.

...The representation of the items is more modern and concise than in the classical book (De Groot and Mazur, 1962), new insights about the derivation of Onsager reciprocal relations are discussed, multicomponent diffusion is described by use of Maxwell-Stefan diffusivities, and almost half of the book deals with rheology modelled along the lines of Kluitenberg's theory from 1962.

The book consists of 7 chapters... an author index citing 312 authors with more than 500 references, a list of symbols, and a lot of interesting historical hints close the book. Summaries and exercises belong to each chapter. ...

After a description of stochastic processes in the fifth chapter the Onsager-Casimir reciprocal relations (OCRR) are derived in a manner Kuiken developed in 1977: It turns out that the regression axiom and the assumption of microscopic reversibility are not sufficient to Onsager's symmetry relations, if Boltzmann's postulateS=k ln Wis not used. Taking into account the Boltzmann distribution Onsager reciprocal relations can be derived. but also for other distributions (but not for all) the reciprocal relations follow. The sections on the Fokker-Planck equation, on microscopic reversibility, and on the regression axiom are written very clearly.

In the sixth chapter mass and heat transfer by multicomponent diffusion is treated in the Maxwell-Stefan description which is characterized by a special splitting of the entropy production density into fluxes and forces, independent of the choice of the reference velocity. ... It is shown that the Maxwell-Stefan description, although linear, is not restricted to dilute systems or to ideal gases.

In the seventh chapter the thermodynamic theory of relaxation is treated by the pre-supposition that there are internal variables of scalar, vector, and tensor character. After a heuristic characterization of the elastic, anelastic, viscous and plastic parts of deformation the Reiner rheological axioms from 1960 are mentioned, linear rheological bodies and various deformation tensors are defined. ... Thermostatic and dynamic equations of state, relaxation equations, velocity of sound, and the fundamental Iinear rheological bodies are discussed. General linear rheological equations of state for isotropic bodies, and bodies with continuous spectra are investigated.

...the book is a very valuable help for becoming acquainted with fundamentals, methods, formalisms, and shortcomings of TIP and its applications especially to linear rheology. Beyond that a lot of phenomena is treated which cannot be found together in literature. Students can use the book with advantage parallel to a more modern course on non-equilibrium thermodynamics which presents theoretical facts properly in more detail and TIP as a special case of continuum physics.

W. Muschik, J. Non-Equilib. Thermodyn., vol. 21, 1996, pp. 193-195; Zeitschrift fuer Physikalische Chemie, 1995, pp. 137-138.

The book is an excellent treatise of physics of natural irreversible processes, which unify the formulations of the continuum theory applied to all process that can be treated as linear in mechanics, fluid dynamics, mass transport, magnetohydrodynamics and thermodynamics, with a particular regard to the applications of irreversible thermodynamics to diffusion and viscoelasticity.

Reading of this book is recommended to any physicist involved in research topics ranging from polymer and material sciences to rheology. Seven chapters cover the subject matters ...

To conclude this review, a very valuable and accurate "Nomenclature" and "Subject Index" Sections will assist a lot in looking through the pages for rapid inspection of particular subjects of interest.

A. Longhetto, Il Nuovo Cimento, vol. 19, Italy, July-August 1996.

Corrections to the second printing with corrections, February 1995, of *Thermodynamics of Irreversible Processes* will become available as a downloadable PDF file.