BIBLIOGRAPHY

V. G. Levich, Physicochemical Hydrodynamics, Publishing House of the Academy of Sciences of the USSR, 1952, 538 pp., 82 figs., price 23 rubles 60 kopecks; responsible editor Acad. A. N. Frumkin.

As the title of the monograph under review indicates, it is devoted to hydrodynamic problems in which the specific physical and physicochemical properties of the liquid play an essential role. This monograph, being the first generalizing work of its kind, is of undoubted interest, and its appearance is very timely.

The contents of the book may be divided basically into two parts. The first of these includes various questions connected with the transport of particles (dissolved molecules or ions) by a liquid flow. The phenomenon of substance transport by a moving liquid (convective diffusion) plays an essential role in various physicochemical and physical processes. Examples include the dissolution or deposition of precipitates from solutions, physical and chemical processes occurring at phase boundaries: adsorption, heterogeneous chemical reactions, the process of electrolysis, etc.

The second group of questions is connected with the influence of the physicochemical properties of liquids on their motion. This may include the influence on the process of liquid motion of surface tension, surface-active substances or charges on the surface of the liquid, and other factors.

The book under review is a theoretical survey of this range of phenomena, summing up the results of many years of work by its author in a field lying on the boundary between physics and physical chemistry. The fairly considerable experimental material presented and analyzed in it serves only as an illustration of theoretical propositions.

The book is intended for physical chemists, physicists, and chemists interested in the indicated problems, which find wide application both in laboratory and in industrial practice. The book will also be of benefit to specialists in the field of the study of colloids, since its content borders on problems of the rheology of colloid-disperse systems. It is of interest to theoretical physicists and specialists in hydrodynamics, since it makes extensive use of and develops the computational methods of modern hydrodynamics.

The book consists of ten chapters.

The first chapter is of a reference character. It presents the necessary information and relations from the field of modern hydrodynamics, chiefly the theory of the boundary layer and the theory of turbulence. The presence of this chapter in the book is fully justified, since these questions of hydrodynamics are almost not covered in ordinary physical and physicochemical manuals. However, from the point of view of the experimental reader, a more extensive exposition in this chapter would have been desirable.

BIBLIOGRAPHY

The second and third chapters of the book are devoted to consideration of the phenomenon of convective diffusion. As is known, the rate of transformations occurring at the boundary separating a solid and a liquid (dissolution, precipitation, adsorption, catalytic and heterogeneous reactions in solutions) depends substantially on the rate of delivery to them and removal from them of the initial or final products of the transformation, for example, the removal of dissolving molecules from the surface of a dissolving specimen.

In the case when the transformation process at the surface (for example, the transition of molecules from a crystal into solution, a chemical reaction at the surface) proceeds sufficiently rapidly, the overall rate of the process is determined by transport phenomena. Therefore in practice one always resorts to stirring the solution, which ensures convective transport of the substance superimposed on molecular diffusion.

In the second chapter the methods of calculating the process of convective diffusion in liquids under laminar flow are set forth. Various exact and approximate methods for calculating convective diffusion are considered; exact solutions are given for problems under simple geometrical conditions; the case is considered when the rate of transformation at the surface is comparable with the rate of transport of the substance; questions of modeling heterogeneous transformations are analyzed, and a comparison with the theory of heat transfer is given.

The third chapter is devoted to the theory of transfer of matter in turbulent motion of a liquid. The analysis shows that the diffusion process depends substantially on the structure of the turbulent flow, in particular on the presence of turbulent motion in the viscous sublayer directly adjoining the solid surface. Theoretical formulas for diffusion flux, derived by the author on the basis of the assumption of the existence of decaying turbulence in the viscous sublayer, are in agreement with experimental data. On the contrary, the assumption of the complete absence of turbulence in the viscous sublayer leads to disagreement with experiment. Thus, the question of the existence of turbulence in the viscous sublayer proves to be resolved in the affirmative sense.

Chapter four is devoted to the theory of the electrolyte. Questions of the passage of current in electrolyte solutions in recent decades have almost completely ceased to be discussed in the physical literature. Even in the most serious manuals on the theory of electricity this question is treated very briefly, and from out-of-date positions. Therefore it appears very valuable that the author of the reviewed monograph has sought to illuminate the present state of the question as fully as possible. Without dwelling on questions of the theory of electrical conductivity, he sets forth in detail the theory of convective transport of ions and the methods of quantitative calculation of the electrolysis process.

In the same chapter the author compares the theory of convective diffusion in laminar and turbulent flow with considerable experimental material, and also touches upon a number of practical applications of the theory to the calculation of electrolyzers, dissolution and corrosion of metals, etc.

In the fifth chapter the author dwells on the special features of liquids with a free surface and on the influence of surface tension on the motion of a liquid. A system of boundary conditions at a free surface is formulated in the presence of surface-active substances and variable surface tension.

The sixth chapter is devoted to the hydrodynamics of drops and bubbles. The motion of liquid drops in a liquid medium is considered with allowance for the influence of surface-active substances dissolved in the liquid. The author dwells in detail on the hypothesis of surface viscosity, according to which, near the phase-boundary surface, a liquid has an anomalously high viscosity, substantially exceeding the viscosity in the bulk of the liquid. The hypothesis of surface viscosity was put forward in connection with the fact that the velocities

Bibliography

The velocities of motion of liquid drops and bubbles in liquid media, as experience shows, do not differ from the velocities of solid particles. The author’s opinion, however, that the apparent “solidification” of drops and bubbles is connected not with the existence of an anomalous surface viscosity, but with the influence of surface-active substances present in the liquid medium, still seems open to discussion.

Here, too, questions of the dissolution of substances from drops and bubbles are considered. The author examines the theory of gas dissolution from a single bubble, having various sizes and moving under various conditions. This process forms the basis of the widely used method of absorption of gases and vapors, the so-called bubbling.

The seventh and eighth chapters of the book are devoted to the theory of motion of particles carrying an electric charge (more precisely, an electric double layer) on their surface in electrolyte solutions. This includes the theory of electrophoresis—the motion of solid particles, as well as the theory of the motion of mercury drops. On the surface of particles in an electrolyte solution a double layer is formed, the inner plate of which is associated with the particle, while the outer one is associated with the ionic cloud in the solution. In an external electric field a force acts on the double layer, setting the liquid in motion. The difference in the physical conditions on the surfaces of a solid and a liquid particle leads to a difference in mobilities of approximately \(10^6\) times.

In the eighth chapter the theory of the motion of mercury particles is applied to polarographic analysis of solutions, which has become very widely used in analytical laboratories and in industry. The polarographic method of analysis is based, as is well known, on measurement of the current flowing through a mercury drop issuing from a capillary and serving as the electrode. Different regimes of drop outflow correspond to different mixing of the solution and, accordingly, to different values of the current flowing to the dropping electrode. The eighth chapter of the book is devoted to a detailed analysis of the theory of the action of the dropping electrode under various outflow regimes, in the presence of surface-active substances, etc.

In the ninth chapter of the book the theory of capillary waves is considered; in particular, it analyzes the theory of the process of damping of waves by surface-active substances, based on ideas about the elastic properties of the film of a surface-active substance.

The last, tenth chapter of the book contains the theory of the flow of liquid in thin films. The flow of thin liquid layers is often encountered in laboratory practice and in various fields of technology (viscometry, etc.). The author consistently considers the various regimes of flow of a liquid film, as well as the theory of gas dissolution in a moving film. The latter phenomenon forms the basis of the widely used technique of gas dissolution (the so-called scrubbing process). In this chapter, in particular, important works by B. V. Deryagin and M. M. Kusakov on the study of the rheological properties of thin films on the surface of solids by the blowing method, which have become widely known, are presented. Interesting works by P. L. Kapitsa on the wave flow of thin liquid layers are also described.

One may reproach the author for a certain incompleteness in the coverage of the material. For example, the book lacks such sections as diffusion kinetics in the gas phase, heat transfer during boiling, and the theory of capillary oscillations in jets and drops. All these questions of physicochemical hydrodynamics are closely connected with a number of sections of the reviewed book. The book also lacks the rheology of non-Newtonian liquids, although it should be noted that this extensive area of rheology probably requires an independent monograph. In chapter ten, where the motion of liquid in thin films is considered, it would have been necessary to indicate the most important

the practical significance of this section for the theory of lubrication and to refer to the works of N. P. Petrov, who, in particular, pointed out the possibility of anomalous hydrodynamic phenomena in lubricating oils near the surface of a solid wall. A gap is also the absence of a reference to the work of I. S. Gromeka devoted to the motion of drops, where assumptions were made about the existence of surface viscosity.

To confirm the validity of the theoretical conclusions, one could have cited, by way of illustration, somewhat more experimental data for a number of sections. The works of A. A. Leont’eva on the motion of liquid drops in a liquid medium could have been presented more fully. The works of D. M. Tolstoy on wall slip are not mentioned at all.

The book is well published, and the number of misprints in it is small.

In summary, it should once again be noted that this monograph by V. G. Levich is of substantial interest and fills a definite gap that existed in the literature in this field. It is also necessary to emphasize that physicists have so far paid too little attention to the questions set forth in this book. The appearance of the book under review should draw the attention of physicists to the problems of physicochemical hydrodynamics.

M. P. Volarovich