Frumkin-Levich theory

The Frumkin-Levich theory was of great methodological importance and was the basis for more rigorous considerations at Pe l by Derjaguin Dukhin (1959 - 1961). These results are discussed in the next sections. It turns out that uniform retardation and relatively small variation of adsorption exist along with other conditions which radically differ from predictions of the Frumkin-Levich theory. 

Thus, both a physically reasonable result which corresponds to condition (9.10), and complete quantitative agreement with Frumkin Levich theory is obtained using exactly the same equation (see Levich (1962), Eq. 74.3). Thus, Eq. (9.15) can be considered as a generalization of Frumkin Levich s equation which is independent of restriction (9.9). If condition (9.9) is not fulfilled, a substantial deviation of T(0) fi-om equilibrium appears and, in the general case, the angular dependence proves to be very complex. It is shown by Dukhin (1965) that the angular dependence F(0) becomes simpler at greater adsorption times ... 

This dynamic character of the adsorption equilibrium has contributed significantly to developments in non-equilibrium thermodynamics. The balance of adsorption and desorption fluxes as the first step in the description of the dynamics of adsorption is a key point in this book. The second step is the introduction of a sublayer concentration and the diffusion layer to describe the non-equilibrium state in the bulk phase. While the system surface-bulk is in nonequilibrium the presence of local equilibrium is assumed between the adsorption layer and the sublayer as the third important step. This allows us to generalise Eq. (2.36) to Eqs (2.36a) and (2.36b). The first examples of dynamic adsorption layers of rising bubbles were given already by Frumkin Levich (1947) and Levich s book (1962) on "Physico-Chemical Hydrodynamics" (cf. Chapter 8) offered the first theories. Simultaneously, Frumkin Levich... 

Special attention to limiting cases is generally characteristic in the theory of transport phenomena, but here it is caused by extreme difficulties in constructing a general theory without any simplifications. A substantial difference to the work of Frumkin Levich (1947) and Levich (1962) is the elimination of the three simplifying conditions mentioned above. Thus... 

Condition (8.18) can or caimot be fulfilled at Pe l and the angular distribution dependence of adsorption and surfactant concentration is more complex than the functions given in Eq. (8.19). The concentration distribution must obey the convective diffusion equation. In spite of this, Frumkin Levich (1947) have proposed an approximate theory of the diffusion boundary... 

At strong retardation the velocity distribution is approximately proportional to sin0 since the ratio F(0) / sin0 is nearly constant. This assumption was used by Frumkin Levich (1947) as the basis of the theory for a retardation coefficient concept and leads to the velocity distribution Eq. (8.14) and the retardation coefficient Eq. (8.35). 

Papers by Frumkin Levich (1947) and by Derjaguin Dukhin (1961) are apparently only of methodical nature, since they do not take into account the bubble surface effect which causes retardation at a < 0.03 cm. Indeed if at a < 0.03 cm a strong but not complete retardation of the bubble surface takes place, the discussed theories cannot be applied directly, but can be transformed to the hypothesis of incomplete retardation. 

V. G. Levich spent a major part of his career in the world s largest institute of physical electrochemistry, The Frumkin Institute in Moscow. He was a man who had the good fortune to create a subfield in science and to dominate it during his lifetime. The field concerned is hydrodynamics applied to the relative movement of the solution near an electrode. His early work is encapsulated in a famous book Physicochemical Hydrodynamics, which was finally published in English only in 1962. The most useful equation in this book is one used in this section [Eq. (7.112)]. Later, he was persuaded by Frumkin to apply his talents to the quantum theory of charge transfer, where he led a research group of some twenty-five members. 

Physico-chemical hydrodynamics of bubble and drops attract the attention of many investigators in different countries over the last fifty years. Despite the obvious difficulties in contact between groups in East and West, the main results of investigations published in Russian and English agree well and complement each other. A prerequisite for this agreement is the fact that all the theories were developed on the same basis given by the works of Frumkin and Levich (Sections 8.1.2 and 8.1.3). 

In 1958, Frumkin put forward the idea of a new experimental method—the method of the rotating ring-disk electrode, which allowed the direct observation of intermediates of electrode processes. The apparatus was buUt by L. N. Nekrasov, and the theory was elaborated by V. G. Levich and Yu. B. Ivanov [30]. Since then, the method of the rotating ring-disk electrode has become one of the standard techniques of electrochemical science. For example, it has played an important role in the study of oxygen electroreduction, with applications in fuel cells (Photos 4.15 and 4.16). 

Theoretically, Frumkin strongly supported quantum theoretical studies of the elementary act of electron transfer. In the Theoretical Division, led by V. G. Levich, several epochal studies were carried out by R. R. Dogonadze, Yu. A. Chizmadzhev, and A. M. Kuznetsov. In 1967-1968, Dogonadze, Kuznetsov, and Levich put forward the first quantum-mechanical theory of proton transfer later, A. M. Kuznetsov, J. Ulstrup, Ya. I. Kharkats, and M. A.Vorotyntsev systematically... 

---