Introduction to Critical Phenomena in Fluids PDF

My interest in writing this book grew out of research in the supercritical fluids area that I have been pursuing for some time. The term supercritical fluid is used quite loosely in the literature, often simply to describe a high-pressure fluid above its critical temperature. However, many of the most interesting phenomena in these systems arise only with close proximity to the critical point itself. As a consequence, my own knowledge of the subject, such as it is, has required me to steadily familiarize myself with concepts from much farther afield than is traditionally considered in engineering books dealing with molecular thermodynamics. This text describes some of what I have learned during this process. My objective has been to describe the critical behavior of supercritical fluid systems within a statistical mechanical framework.

The treatment is introductory and meant to provide the relatively uninitiated reader with as transparent an analysis as I could possibly come up with of some of the major fundamental ideas underpinning the physics of critical phenomena. The systems of interest fall within the Ising universality class, which covers, as far as we understand, the simple fluids that are usually of interest in supercritical fluid chemical process technology. The focus on basic ideas has been motivated by my own belief that the better one's mastery of fundamentals, the more likely one is to both enjoy reading the wider literature on the subject and engage in creative teaching and research. A good example of what I mean by this is provided by the Boltzmann energy distribution in systems exhibiting fluctuations. This important result, though often described in the first few pages of texts that deal with statistical mechanics, to a large extent also provides the intellectual foundations for many newer areas of scientific investigation. A good example of this is the growing importance of a field like molecular simulation, where Monte Carlo methods, which rely heavily on Boltzmann sampling ideas, are now used in myriad different ways.

This text is divided into two main sections. Chapters 1-6 deal mainly with a macroscopic description of thermodynamic stability theory, and its consequences for describing phase transitions and critical behaviors in fluid systems. Chapter 1 is an attempt to express thermodynamic stability theory using a few fundamental theorems taken from linear algebra. The purpose is to provide a formulation of the topic with expanded "reach," which will hopefully then allow many of the more unfamiliar results in stability theory to be relatively easily derived. For this part of the book, in particular, I am indebted to the late Francisco Munoz, whose untimely passing was a severe personal and professional loss. Chapter 3 introduces many of the fundamental concepts concerned with critical scaling behavior in pure systems, with the extension of these ideas to multicomponent mixtures described in chapter 4. Chapters 5 and 6 are concerned with practical topics relevant to engineering applications that use supercritical fluid solvents. Chapter 5 deals with solvation behaviors and describes some unique solution behaviors in the critical region. These include retrograde phenomena, and the ancillary crossover effect, which is potentially useful in designing chemical separation processes.

Chapters 7-12 deal with more theoretical topics developed in the context of fluid systems falling within the Ising universality class. Chapter 7 deals with mean-field theory, while chapter 8 discusses the important role of fluctuations in the critical region. Chapter 9 introduces the reader to finite-size effects in critical systems and focuses upon the important role that finite-size scaling theories have come to play in computer simulations in the critical region. Chapter 10 is an introduction to the renormalizationgroup method, which is not only intellectually exciting, even in its simplest formulations, but also now an integral part of modern theoretical physics. My own forays into this area have relied upon several prior texts and, when these treatments have proven particularly illuminating, I have tried to weave some of this into the narrative given here. Chapter 11 deals with the role of pore-confinement on the critical behavior of fluids. Much of the analysis in this chapter has come from our own group's research over the past few years, especially the developments leading to the pore-confined fluid equation of state given in the chapter. Chapter 12 deals with transport phenomena in the critical region. It introduces the reader to the interesting phenomenon of critical slowing down and a significant part of this chapter again describes recent work from our research group. In particular, we describe a relaxation-dynamics simulation method that enables the efficient, accurate simulation of both dynamical and static proprieties in the critical regions of fluids. Exercises are interspersed throughout the chapters, with additional ones provided at the end of each one. The bibliographies provided are not meant to be exhaustive, but rather represent work that I thought could most closely be tied to the flow of ideas presented here.

In carrying out this project I am deeply indebted to many people with whom I have been fortunate to interact over the years. From an educational perspective, my graduate students have been extraordinary partners who have helped to sharpen ideas and maintain the forward momentum of our group's research efforts. These former students include Ken Pennisi, Doug Kelley, Ta Wei Li, Francisco Munoz, George Afrane, Frank van Puyvelde, Carlos Tapia, Vikram Kumaran, Subhranil De, and An Chen, who have, at one time or another, each made significant contributions to material described in this text. These efforts have largely been supported by the U.S. National Science Foundation, for which I am grateful. I also want to acknowledge support from faculty colleagues and administrative staff in the chemical engineering department at the University of Rochester; in particular, Jacob Jome and Yonathan Shapir for their indispensable humor and counsel. I fondly remember the late Professor Leroy Stutzman, teacher and a founder of the Control Data Corporation, who epitomized the generosity of this country to a new graduate student, and Mr. Wyngaard and Stanley Schur, who demonstrated to me, as a young man, the twin virtues of analysis and persistence. The editorial staff at Oxford University Press and Keyword Publishing Services have also provided invaluable input while helping to steer this project to a successful conclusion. This group has, at various times, included Bob Rogers, Peter Gordon, Cliff Mills, Lisa Stallings, Sue Nicholls, and the copyeditor, John Bentin. Without their encouragement all of this would have been far less fun.

Finally, this work has been accomplished within a much larger context and, for their support and encouragement, I am indebted to my wife Maria, sons Andre and Michael, and, of course, Shadow. As a small measure of my thanks I dedicate this book to them.