Yakov B. Zeldovich

Presently there is a third, posthumous edition of the remarkable monograph "Diffusion and Heat Transfer" in preparation.

Published in the USSR in 1947 and a second edition in 1967, the book was translated in the FRG in 1959 and in the USA in 1969.

The monograph played an enormous role in the development of post-war science and technology, and in the education of more than one generation of chemists, engineers and chemical physicists.

To this day precisely this monograph has remained the best known and most cited in papers relating to the foundations of chemical machine design and to the theory of combustion.

The book has become a bibliographic rarity and in this connection, of course, the question arose of a new edition. To our great regret, the third edition will be posthumous. David Albertovich Frank-Kamenetskii prematurely died on June 2, 1970, before he reached 60.

In planning a new edition without the participation of its author, it seems necessary to speak in detail in the foreword both about the book and about its author. One must explain the reason for the unique longevity and importance of the book. Its distinctive feature is the abundance of results of the author himself - one of those who constructed the foundations of a new branch of science.

In the foreword to the first edition, Academician N. N. Semenov writes: “The author also managed to work out new, fruitful methods, to single our important limiting areas, to introduce a number of new physical concepts and to obtain valuable physical results. One may say that this work heralds the beginning of the transformation of macroscopic kinetics into an independent branch of science. The author has succeeded in showing that the problems at hand have not only particular and practical value, but also general scientific value and are of general theoretical interest.”

The development of science over the last 35-40 years has completely confirmed this evaluation by N. N. Semenov: Macroscopic kinetics, under the new names "synergetics," "theory of dissipative structures" and "catastrophe theory," is rapidly developing. In this, naturally, new problems and new results arise. However, for a deep understanding of the new branches of science with their historical roots it is necessary to turn to the foundations, to the pioneering works in the area of macroscopic kinetics - and here the book by Frank-Kamenetskii is the best resource.

But there is still another task related to the passing of the book's author. Fewer and fewer people remain who knew him personally. Not all readers of the book are aware of the creative path and personality of the author, not all know of the breadth of David Albertovich's scientific interests and, in particular, of his results in other areas of science - in plasma physics, astrophysics and cosmology. The present sketch makes the attempt to fill this gap. I think that such a story will also help to evaluate the present monograph “Diffusion and Heat Transfer in Chemical Kinetics.”

David Albertovich began his scientific career under somewhat unusual circumstances. He spent his childhood and youth in Siberia; there too he received his engineering-metallurgy degree (he graduated from the Tomsk Technological Institute) and began to work at an ore-enrichment factory. In early 1935 David Albertovich wrote a letter to N. N. Semenov in which he discussed problems of chemical thermodynamics. The author's talent was so obvious that he was invited to the Institute of Chemical Physics. At that time, at the Leningrad Physico-Technical Institute and associated institutes, in particular the Institute of Chemical Physics, there was broad, conscious and successful effort made to find and attract capable young people.

As part of a large collective David Albertovich took part in work on the problem of oxidation and fixation of atmospheric nitrogen in combustion and explosions. Mentions of this problem, for example by Cavendish, appeared immediately after the discovery of nitrogen and after the composition of air was established. This problem was addressed by such outstanding chemists as F. Gaber, V. Nernst (Germany) and R. Bone (England). In connection with the development of the theory of chain reactions there arose the problem of the possibility of direct use of combustion energy to transform nitrogen into nitrogen oxide. Research carried with David Albertovich's participation showed that the process was related to the mechanism of chain reaction with the participation of N and O atoms, but that the yield of nitrogen oxides was limited by conditions of thermodynamic equilibrium. The directions of David Albertovich were outlined quite naturally: on the one hand - the theory of combustion and explosion, and on the other - the general foundations of chemical engineering. David Albertovich was close to these questions through his engineering education and experience as well.

In a fundamental paper in 1939, David Albertovich posed the problem of thermal explosion taking into account the spatial temperature distribution in a medium in which a chemical reaction is occurring. The solution of this problem concluded almost a century's research. The possibility appeared of exactly precalculating the conditions of explosion. Numerous experiments fully confirmed D. A. Frank-Kamenetskii's theory. Thanks to this theory important results were obtained in chemical kinetics.

Hidden in this work, however, was a deeper content, one which went beyond the bounds of the problem of explosion. Only after many years was the fruitfulness of the way the problem of critical conditions was posed as the limit of existence of a solution understood. Using the example of thermal explosion David Albertovich developed a similarity theory of processes of energy release and removal. He proposed an asymptotic expression, k₁ exp(a(T –T₁)), replacing the exponential dependence k₂ exp(-A/RT), in which the solution relating to some temperature is obtained by a similarity transformation of the solution relating to some other temperature. In modern terminology, David Albertovich used group properties of the equations and consciously chose the approximation needed for the appearance of a group which is additive in temperature and multiplicative in coordinates.

These general physical and mathematical ideas were used widely in works on the theory of combustion, both those carried out with the direct participation of D. A. Frank-Kamenetskii and as continuations of his research.

David Albertovich's research on the foundations of chemical engineering are summarized in his remarkable monograph.

Heat transfer, diffusion and hydrodynamics are all branches of classical physics. The monograph wonderfully combines analytic solutions, similarity theory and a semi-empirical approach to phenomena and processes of varying degrees of complexity. The broad scientific program of a physico-mathematical approach to technology presently being carried out uses in many ways the deep ideas and methods presented in this work.

The scientific interests of David Albertovich soon after the war and after writing the book shifted to the area of astrophysics. Problems of the calm evolution of stars are masterfully presented in the monograph “Physical Processes in Stars.” D. A. Frank-Kamenetskii also solved the problem of how a shock wave intensifies in the outer layers in the explosion of a star. This phenomenon is significantly related to laws of variation of luminosity of supernova stars and also, perhaps, with the process of the initial acceleration of cosmic rays. David Albertovich was among the first to understand, as evidenced by works on “epiplasm,” the role in astrophysics and in particular in cosmology played by the process of generation of particle-antiparticle pairs in extreme conditions. In 1956, on an invitation by I. V. Kurchatov, D. A. Frank-Kamenetskii moved to the Institute of Atomic Energy where he led a new direction - research on the interaction of waves with plasma. Here he was the first to clearly formulate the problem of plasma heating due to dissipation of waves excited within it by an external source of oscillations.

David Albertovich theoretically predicted the important phenomenon of magneto-sonic resonance which was later found experimentally with his direct participation. Subsequently he and his students studied this phenomenon in detail both theoretically and experimentally. The dispersional properties of a wide class of oscillations were studied: normal and oblique magneto-sonic waves. The appearance of resonant oscillation of electromagnetic fields in plasma with magneto-sonic resonance (the effect of “spatial amplification of a magnetic field”). Finally, an anomalous dissipation of magneto-sonic oscillations was found and, as a result, the possibility of heating plasma to high temperatures by magneto-sonic resonance was demonstrated experimentally. In particular, using this method heating of dense hydrogen and helium plasma to a temperature of 5 · (10⁶ - 10⁷) K was accomplished.

In recent years together with this study David Albertovich undertook an investigation of the instability of plasma in electron cyclotron heating, and also began work on plasma phenomena in a solid body.

I should note the immense influence of David Albertovich on creative young people. As early as 1956-1957 he called for studies of collective processes in plasma and the phenomena in which they should appear: nonlinear and shock waves without collisions, pinch, etc. His ideas without doubt played a fundamental role in the development of plasma physics.

The breadth of erudition, encyclopedic knowledge, unusual literary talent and the ability to speak simply and clearly about the most complex things made him one of the greatest populizers in the natural sciences. He is the author of a series of popular books on various areas of physics: Energy in Nature and Technology, The Formation of Chemical Elements in the Depths of Stars, Nuclear Astrophysics. The most popular and well-known book was that written on the suggestion of I. V. Kurchatov, Plasma-The Fourth State of Matter, which has been reprinted many times and translated into Bulgarian, Polish, Czech, German and Japanese.

David Albertovich was one of the most competent specialists on a huge spectrum of questions in physics, chemistry, astrophysics and biophysics. His honest and completely selfless desire to help everyone who came to him for advice, his colossal erudition, and constant readiness to enthusiastically delve into the solution of scientific problems, even those lying outside his current interests, made David Albertovich an irreplaceable creative consultant. A vivid picture of the unique breadth of his scientific interests, and also of his lively style of presentation and sense of humor, is given in reviews printed over many years in the bulletin "New Books Abroad," and by articles and notes on the latest accomplishments of Soviet and world science and on a number of fundamental philosophical problems in the journal “Nature.” D. A. Frank-Kamenetskii edited many Russian editions of scientific and popular science books by famous foreign scientists. His public lectures on the most important problems of modern natural science and his brilliant appearances on radio and television have become well-known.

D. A. Frank-Kamenetskii's teaching activity, begun as early as the early thirties in the Chitin Mining-Metallurgy Technical School and at Irkutsk University, continued almost without interruption all of his life. In his last years he headed the department of plasma physics, organized by him, at the Moscow Physico-Technical Institute. David Albertovich is the author of the textbook Lectures on Plasma Physics.

The Soviet government held the work of D. A. Frank-Kamenetskii in high regard: he was awarded the Lenin Prize and the Red Banner of Labor, and three times received the State Prize of the USSR.

A simple enumeration of David Albertovich's scientific works does not give a full idea of the authority and scientific influence of D. A. Frank-Kamenetskii; these in many ways depended on his personal qualities and the generosity with which he related his ideas not only to his own students and colleagues, but to anyone who turned to him for advice.

Enormous optimism and good-will, nobility and attentiveness - these qualities of David Albertovich are well known not only to his colleagues and students, but also to a wide circle of physicists and chemists. He was distinguished by a complete lack of jealousy or envy toward others' results. The natural active desire of a scientist to open up his abilities and to obtain an important result was harmoniously combined in David Albertovich with an interest in the essence of the matter, an interest in nature.

David Albertovich lived a vital and happy life. His memory will remain forever in our hearts.

Time has confirmed the evaluations given above.

Problems of diffusion and heat transfer in chemical kinetics are, as before, at the center of attention of chemical engineering and the theory of combustion. In the last chapter of the book Diffusion and Heat Transfer in Chemical Kinetics David Albertovich devotes much attention to periodic chemical reactions. Today in our country a large cycle of studies has been performed on the periodic reaction of Belousov-Zhabotinskii.

At a recent international conference, “Synergetics 1983” (August 1983) at the Biological Center of the USSR Academy of Sciences in Pushchino, near Moscow, it became especially clear that research on periodic reactions and related spatial pictures are growing into an independent branch of science - synergetics. The theory of thermal explosion was the first proverbial swallow of the modern theory of catastrophe. Due to the development of catastrophe theory the results of David Albertovich and his co-workers are being generalized to a multitude of areas, areas which seem at first glance, externally, to be far from combustion and explosion - from polymer mechanics to biological phenomena. David Albertovich's work on the theory of plasma is of great value. His popular book, The Fourth State of Matter, remains even today the best introduction for young people to plasma physics. His deep penetration into the physics of dissipative processes allowed him to make a significant contribution to the theory of diffusion and heat transfer of plasma.

He has written a number of methodological manuals on the problems of transport and waves in plasma. He is the author of one of the methods of plasma heating using sonic resonance.

The book Physical Foundations of the Theory of Stars (1960) has no equals in clarity and penetration into the essence of problems, and in the rational application of similarity theory. In addition, the investigation of hydrogen stars has proved to be more important than it seemed 20 years ago. Today it is established that heavy elements did not form in the cosmological nucleosynthesis. Consequently, first-generation stars consisted of a hydrogen-helium combination without heavier ions.

David Albertovich developed the ideas on epiplasma, and he is also responsible for the very name plasma, consisting of particles and antiparticles. Today it is established without doubt that this was indeed the state of matter in the early stage of evolution of the Universe.

David Albertovich was the embodiment of broadness of knowledge and of striving toward synthesis of our knowledge.

There are sometimes complaints about the ever growing complexity and differentiation of individual branches of the natural sciences. The life and creative work of David Albertovich are a convincing rebuttal of these complaints. David Albertovich's talent and erudition made it possible for him to overcome barriers dividing different areas and to remain a universal scientist on a high professional level in our difficult second half of the twentieth century.

It' is becoming obvious today that in a whole series of questions David Albertovich's ideas were ahead of their time and, perhaps, have for that reason not gotten enough response.

All of us (and the author of this forewarn above all) are belatedly realizing that in the sixties we had insufficient contact with David Albertovich, did not listen enough to his ideas and advice. Maybe these lines will serve as an impetus to intensified contacts and discussions among Soviet physicists, chemists, biologists.

Although it is not customary to write of this, we recall that David Albertovich was not chosen either as an Academician or as a Member-Correspondent of the Academy of Sciences. I am convinced that David Albertovich was completely worthy of these titles. He did not receive them largely because the range of his work was wider than the subjects of the sections (general chemistry, physics and astronomy) into which the Academy is presently divided.

His personal modesty also played a role ... Yet, still, there remains a feeling of injustice and insufficient persistence by David Albertovich's colleagues and friends, including the author. It must be said here that David Albertovich himself was absolutely indifferent to careerist considerations.

He was a person with an exceptionally bright attitude; he loved nature and art. His work, his students and, finally (last but not least), his family provided him unsurpassed joy.

I wish to share one deeply personal reminiscence that is very dear to me. In March 1970 under the influence of some internal impulse, without concrete reason or invitation, my wife and I went to visit David Albertovich. After a discussion of science (mainly about astronomy), we went to the kitchen for dinner. We were joined by David Albertovich's wife, Elena Efimovna, his children, and his children's friends. The topic of poetry came up, and Albert Davidovich inspiredly read the poem “Ravenna” by Blok, beginning with the words, “All that is transient and fleeting was buried by you in the ages . . .”

I will remember always the delight of the young people.

David Albertovich was already very ill, but in my memory of this meeting his image remains as it was all his life - talented, inspired, happy.

This obituary was written as a preface for the posthumous edition of “Diffusion and Heat Transfer”, which was published in Russian in 1987. However, it had also been published in the selected works of Zeldovich (Russian edition, 1985). The English translation was taken from the “Selected Works of Yakov Borisovich Zeldovich” (J.P. Ostriker, Ed.), Vol. II, Princeton University Press, 1993.