Motion of bubbles

A theory of two-phase bubble flow has been developed by Nicklin (N1), who shows that the motion of bubbles arises partly from buoyancy and partly from the nominal velocity caused by the entry of the two phases into the tube. Theoretical and semiempirical studies of bubble flow have also been presented by Azbel (A2) and by Azizyan and Smirnov (A3), and further experimental data on holdup have been recently reported by Yoshida and Akita (Yl), by Braulick et al. (B9) and by Towell et al. (T3). 

A hydrodynamic model of fluidization attempts to account for several essential features of fluidization mixing and distribution of solids and fluid in a so-called emulsion region, the formation and motion of bubbles through the bed (the bubble region ), the nature of the bubbles (including their size) and how they affect particle motion/distribution, and the exchange of material between the bubbles (with little solid content) and the predominantly solid emulsion. Models fall into one of three classes (Yates, 1983, pp. 74-78) ... 

There has been relatively little work on the motion of bubbles and drops in well-characterized turbulent flow fields. There is some evidence (B3, K7) that mean drag coefficients are not greatly altered by turbulence, although marked fluctuations in velocity (B3) and shape (K7) can occur relative to flows which are free of turbulence. The effect of turbulence on splitting of bubbles and drops is discussed in Chapter 12. 

As for steady motion, shape changes and oscillations may complicate the accelerated motion of bubbles and drops. Here we consider only acceleration of drops and bubbles which have already been formed formation processes are considered in Chapter 12. As for solid spheres, initial motion of fluid spheres is controlled by added mass, and the initial acceleration under gravity is g y - l)/ y + ) (El, H15, W2). Quantitative measurements beyond the initial stages are scant, and limited to falling drops with intermediate Re, and rising... 

Fligh-speed photography and strobe lighting were used to monitor the motion of bubbles (Liger-Belair, 2002). It was foimd that the bubble radius R of bubbles increases at a constant rate k = d R /d t, as they rise toward the liquid surface. Thus,... 

Motion resulting in liquid due to motion of bubble surface... 

A second problem, closely related to Stokes problem, is the steady, buoyancy-driven motion of a bubble or drop through a quiescent fluid. There are many circumstances in which the buoyancy-driven motions of bubbles or drops are of special concern to chemical engineers. Of course, bubble and drop motions may occur over a broad spectrum of Reynolds numbers, not only the creeping-flow limit that is the focus of this chapter. Nevertheless, many problems involving small bubbles or drops in viscous fluids do fall into this class.23... 

This is in qualitative accord with the experimental observation that the bubble reverts to noslip behavior for small radii below some critical threshold value. This effect of nonuniform surfactant concentrations is one of the most easily observed manifestations of Marangoni effects in the motion of bubbles or drops. 

An excellent review of work through 1972 is J. F. Harper, The motion of bubbles and drops through liquids, Adv. Appl. Mech. 12, 59-129 (1972). 

V G. Levich, Motion of gas bubbles with high Reynolds numbers, Zh. Eksp. Teor. Fiz. 19, J8-24 (1949). An excellent summary of theoretical and experimental work (up to 1972) on the motion of bubbles and drops is, J. F. Elarper, The motion of bubbles and drops through liquids, Adv. Appl. Mech. 12, 59-129 (1972). 

Liquid-liquid reactors are similar to gas-liquid reactors. In the former case, the dispersed phase is in the form of droplets as against bubbles in the latter. The motion of bubbles and drops can be described using a unified approach. A spray column (or a drop column) is the equivalent of a bubble column but with one difference. The dispersed gas phase is always lighter than the continuous liquid phase (p < Pl)- However, the dispersed liquid phase in spray columns may be lighter or heavier than the continuous immiscible liquid phase. Nevertheless, spray columns can be easily described similar to bubble columns. Furthermore, packed bubble columns and sectionalized bubble columns can be considered equivalent to packed extraction columns and plate extraction columns. External-loop and internal-loop reactors are also possible (for equivalent gas-liquid reactors, refer to Section 11.4.2.1.4). 

Subramanian, R. S., The motion of bubbles and drop in reduced gravity. In Transport Processes in Bubbles, Drop and Particle, pp. 1-42, Hemisphere, New York, 1992. 

In practical systems, the motion of bubbles or droplets in surfactant solutions is strongly retarded by gradients of the surface tension. The schematic in Fig. 3.11. clearly demonstrates the retardation effect on rising bubbles or sinking drops. In surfactant solutions gravitation and the Marangoni effect move in the opposite direction. 

The motion of bubbles in a surfactant solution depends on the bubble size and the properties of the solution/bubble interface (Malysa 1992). Adsorbed surfactants control the bubble motion in a way not fully understood. With increasing surfactant concentration the floating speed increases, passes a maximum and then decreases again (Loglio et al. 1989). The maximum of the speed of floating is passed at very low surfactant concentration so that the phenomenon can even be used as a measure for the contamination of water by surface active compounds. 

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. 

HERBOLZHEIMER, E. 1988. The effect of surfactant on the motion of bubbles in a capillary. Exxon Research and Engg. Co., Annandale, N.J. To be published. HIEMENZ, P.C. 1986. Principles of Colloid and Surface Chemistry, 2nd edn. New York Marcel Dekker. 

Because of his relatively larger differences in drop diameter, Garwin s results cannot be properly considered here. They conform with the concept that internal natural convection currents enhance the mobility of the interface which nevertheless fail in the light of Johnson s as well as Woodward s experimental results. The question is obviously open, and the need for controlled experiments under identical temperature and flow conditions is indicated. The theoretical study of Young et al. (Yl) on the motion of bubbles... 

In the present section, the main attention will be given to the motion of the bubble s surface caused by the change of its volume, rather than the motion of bubbles relative to the liquid. This volume can change as a result of evaporation of the liquid phase or condensation of the gaseous phase. If both the liquid and the bubble are multi-component mixtures, then chemical reactions are possible at the bubble surface, which too can result in a change of the bubble s size. 

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