Intermediate size bubbles

The flow and shape transitions for small and intermediate size bubbles and drops are summarized in Fig. 7.13. In pure systems, bubbles and drops circulate freely, with internal velocity decreasing with increasing k. With increasing size they deform to ellipsoids, finally oscillating in shape when Re exceeds a value of order 10. In contaminated systems spherical and nonoscillating ellipsoidal... 

Group B intermediate size, bubbles at incipient fluidization (umb/umf = 1), detectable to short-range fast regime ... 

The bubble coalescence becomes very intensive in non-Newtonian liquids. The coalescence of bubbles near the sparger and the rupture of large bubbles at the top surface generate very tiny bubbles. During the motion of intermediate size bubbles... 

Similarly, small (0.2—0.6 mm) air bubbles are introduced into a 2.6-m Deister Flotaire column at an intermediate level allowing rapid flotation of readily floatable material in the upper recovery zone. The bottom air permits longer retention time of the harder-to-float particles in the presence of micrometer-sized bubbles at a reduced downward velocity. The first commercial unit went on stream in 1986. It was used to improve the recovery of <0.6 mm (—28 mesh) coal in the plant s tailings. An average of 5.5% increase in coal recovery resulted from its use (14). The second commercial use processed <0.15 mm (—100 mesh) coal feed. 

When intermediate-sized particles are used, the behavior of bubbles within the fluidized... 

Figure 23.9 Schematic representation of regions of bubbling-bed model for intermediate-sized particles...

The conditions under which fluid particles adopt an ellipsoidal shape are outlined in Chapter 2 (see Fig. 2.5). In most systems, bubbles and drops in the intermediate size range d typically between 1 and 15 mm) lie in this regime. However, bubbles and drops in systems of high Morton number are never ellipsoidal. Ellipsoidal fluid particles can often be approximated as oblate spheroids with vertical axes of symmetry, but this approximation is not always reliable. Bubbles and drops in this regime often lack fore-and-aft symmetry, and show shape oscillations. 

Motion of Intermediate Size Air Bubbles Through Water at 28.5 C... 

Bubbles and drops of intermediate size show two types of secondary motion ... 

Previous correlations of the influence of z on terminal velocities (El, H4, Ml, SI, S6, T3, Ul) are limited to specific systems, fail to recognize the different regimes of fluid particles (see Chapter 2), or are difficult to apply. In the present section we consider both bubbles and drops, but confine our attention to those of intermediate size (see Chapter 7) where Eo < 40 and Re > 1. Only the data of Uno and Kintner (Ul), Strom and Kintner (S6) and Salami et ai (SI) are used since other workers either failed to use a range of column sizes for the same fluid-fluid systems, or it was impossible to obtain accurate values of the original data. This effectively limits the Reynolds number range to Re > 10 for the low M systems studied. 

Fig. 9.8 Retarding effect of column walls on the terminal velocity of drops and bubbles of intermediate size.

B 100-800 intermediate size e.g., sand bubble at incipient fluidization viz., umb/umf = 1 collapse immediately upon shutoff of gas flow bubbles have clouds fast bubbles ... 

The liquid flow envelops the bubble surface, and the particles are entrained to a greater or a lesser extent by the liquid. The smaller the particles and the less different their density relative to that of the medium, the weaker are the inertia forces acting upon them and the more closely the particle trajectory coincides with the liquid streamlines. Thus, at the same target distance fairly large particles move almost linearly (Fig. 10.1, line 1), while fairly small particles move essentially along the corresponding liquid flow line (line 2). The trajectories of particles of intermediate size are distributed within lines 1 and 2 as the size of particles decreases, the trajectories shift from line 1 to line 2 and the probability of collision decreases. 

As shown in Section 10.12, effective microflotation is possible as a two-stage process. At the first stage the problem of residual mobility does not arise because bubbles of decimicron dimension are used. At the second stage the use of bubbles of millimetre size is technologically effective if their surface is not completely retarded. Methods to obtain intermediate-size... 

Modeling of the bubbling bed region is based on several special char-acteristics/assumptions/definitions. These are outlined below along with the governing equations in each case. The equations will depend on the nature of particles used fine, intermediate size, or large. We restrict our treatment to small particles. 

For aromatic molecules of intermediate size these hydrophobic interactions seem to be more important than electrostatic charge effects, as has been concluded from work on soluble polymers [33]. However, it is also possible for hydrophobic interactions to become so strong that substrate and product molecules block the polymeric catalyst, and some observations of decreasing activity of catalyst with progressing reaction have been ascribed to this cause [1]. It has been noted that a similar effect may be caused by degradation (desulphonation) of the polysulphonic acid [1] or, as in Noller and Gruber s study of the decomposition of ethyl diazoacetate [19], by the accumulation of bubbles of a gaseous reaction product in the pores of the resin. 

The bed depth has no influence on the size of the bubble produced. This indicates that the bubbles are foxmed under either constant flow or constant pressure conditions. In the intermediate region, Padmavathy, Kumar, and Kuloor (PI) have shown that the bubble volume in an air-water system is highly sensitive to the variation in the depth of the liquid column above the bubble forming nozzle. As the bed has no surface tension, no variation of flow is expected during bubble formation, and the conditions of constant flow are approximated. This explanation is due to present authors. 

Figure 20.12 Different bubble sizes give different bed sizes for maximum production of intermediate.

G. Gerber I do not think this bubble picture applies to the fragmentation of particular Na clusters. We observed that the intermediate resonance strongly influences the time and the predominant decay channel. We did not study yet cluster sizes beyond n = 41. It appears that, for larger cluster sizes, no predominant picosecond decay channel exists. 

The frequency of the ultrasound determines the critical size of the cavitation bubbles. The reaction rate dependence on the ultrasonic frequency has been observed in many cases [12-14]. Usually, an optimum intermediate value of frequency exists, lying in the range of hundreds of kilohertz. For volatile solutes reacting inside the cavity, this effect can be understood as a balance between increasing numbers of excited bubbles... 

Group B powders are of intermediate particle size, such as sand. They do not fluidize so smoothly as Group A, for bubbles form as soon as the incipient fluidization velocity is reached. It is thus evident that the ratio umJum is equal to unity. When the fluidizing gas is turned off suddenly, Group B powders would collapse immediately. In the fluidized state, the rising bubbles travel upward faster than the interstitial gas flow rate, and are therefore designated as fast bubbles. ... 

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