Bubble, physico-chemical hydrodynamics

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... 

In connection with the development of the theory of convective diffusion in liquids the foundation of the theory of diffusion boundary layers and dynamic adsorption layers are given by Levich (1962) in his works on physico-chemical hydrodynamics. A variety of problems of convective diffusion in liquids was solved which are of essential interest for the description of different heterogeneous processes in liquids the rate of which is limited by diffusion kinetics. In connection with the objectives of the present chapter, only a general approach to problems of diffusion boundary layers and their concrete results (Levich 1962) are reported. These are of direct interest for the theory of dynamic adsorption layers of bubble. 

Main Stages IN the Development of Physico-Chemical Hydrodynamics of Bubble... 

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). 

Summarising the work done in Russia, we can conclude that physico-chemical hydrodynamics of bubbles at Re 1 was developed for low and high surfactant concentration where the entire bubble surface in the former case is slightly and in the latter case strongly retarded. 

The coupling of the transport of momentum with the mass transport practically excludes any analytical solution in the field of physico-chemical hydrodynamics of bubbles and drops. However, a large number of effective approximate analytical methods have been developed which make solutions possible. Most important is the fact, that the calculus of these methods allows to characterise different states of dynamic adsorption layers quantitatively weak retardation of the motion of bubble surfaces, almost complete retardation of bubble surface motion, transient state at a bubble surface between an almost completely retarded and an almost completely free bubble area. 

Above ambient temperatures are generally required to speed up the physico-chemical processes involved, e.g., for enzymatic assays. Temperatures should not be too high however, in order to prevent the formation of gas bubbles in the analytical path, which would affect sample dispersion and impair detection. This drawback can be minimised by increasing the hydrodynamic pressure, e.g., by adding a back-pressure coil, which is usually a large thin coil placed after the detection unit (see also 4.3). 

Indeed, as for hydrodynamics, mass transfer depends strongly on the physico-chemical properties of the gas-liquid system and many correlations have been proposed to predict the interfacial areas a and liquid mass transfer coefficient kLa, reported to the unit volume of dispersion. They have been recently reviewed by Botton et al. (97) and Hikita et al. (111). It seems that for the scale-up prevision in bubble flow regime (u <0.3 m/s), small scale experiments with the system of interest will allow scale-up on the basis of equal superficial velocity of the gas. So the data in Fig. 17, or those found in the many literature references, or of specific experiments can be used noting that a, k a, k a and a vary approximatively as For other flow regimes and for... 

---