Rising bubbles

Zinc ores are generally floated at the mine (18). In the case of simple zinc sulfide ores, flotation is carried out by treatment with copper sulfate to activate the sphalerite causing it to be wet by the organic collector (eg, xanthate). The now-hydrophobic zinc ore particles attach themselves to the rising bubbles. Oxidized ore particles present must be sulftdized with sodium sulfide to be floated (19). Flotation produces concentrates which are ca 50—60% zinc. In mixed ore, the lead and copper are usually floated after depressing the sphalerite with cyanide or zinc sulfate. The sphalerite is then activated and floated. 

Other scale-up factors are shear, mixing time, Reynolds number, momentum, and the mixing provided by rising bubbles. Shear is maximum at the tip of the impeller and may be estimated from Eq. (24-5), where the subscripts s and I stand for small and large and Di is impeller diameter [R. Steel and W. D. Maxon, Biotechnm. Bioengn, 4, 231 (1962)]. 

In studying gas absorption from single bubbles, Hammerton and Gamer (H7) clearly demonstrated that contamination of the surface of a rising bubble by surface-active material initially present in trace amount can convert a... 

For saturated pool boiling on vertical surfaces, the Weber number (a ratio of dynamic force to the stabilizing force) alone determines the stability of a rising bubble ... 

Solids Circulation Pattern. Yang et al. (1986) have shown that, based on the traversing force probe responses, three separate axial solids flow patterns can be identified. In the central core of the bed, the solid flow direction is all upward, induced primarily by the action of the jets and the rising bubbles. In the outer regions, close to the vessel walls, the solid flow is all downward. A transition zone, in which the solids move alternately upward and downward, depending on the approach and departure of the large bubbles, was detected in between these two regions. 

Internals. Commercial fluidized beds are often equipped with internals, eg., baffle plates and heat exchanger tubes. Due to their interaction with the rising bubbles they will certainly cause particle attrition. Unfortunately, no systematic investigations are available in the open literature which could serve as practical guidelines. 

In its passage through a water column, a bubble acts as an interface between the liquid and vapour phases, and as such collects surface-active dissolved materials as well as colloidal micelles on its surface. Thus in a well-aerated layer of water, the upper levels will become progressively enriched in-surface-active materials. In the open ocean, an equilibrium undoubtedly exists between the materials carried downward by bubble injection from breaking waves and those carried upward by rising bubbles. In the laboratory, however, this effect will enrich the surface layer with organic materials. 

Fig. 2. Simulated positions and shape variations of a rising bubble in a water column. Initial bubble diameter 0.8 cm and time increment 0.05 s.

An advantage of this approach to model large-scale fluidized bed reactors is that the behavior of bubbles in fluidized beds can be readily incorporated in the force balance of the bubbles. In this respect, one can think of the rise velocity, and the tendency of rising bubbles to be drawn towards the center of the bed, from the mutual interaction of bubbles and from wall effects (Kobayashi et al., 2000). In Fig. 34, two preliminary calculations are shown for an industrial-scale gas-phase polymerization reactor, using the discrete bubble model. The geometry of the fluidized bed was 1.0 x 3.0 x 1.0 m (w x h x d). The emulsion phase has a density of 400kg/m3, and the apparent viscosity was set to 1.0 Pa s. The density of the bubble phase was 25 g/m3. The bubbles were injected via 49 nozzles positioned equally distributed in a square in the middle of the column. 

For bubble columns of moderate height the static head is sufficiently low for the expansion of the rising bubbles to be negligible. Consequently, the gas density, the volumetric flow rate of the gas, and the void fraction are sensibly constant. In this case, equation 7.31 is readily integrated to give the pressure drop over a dispersion of height H ... 

In a further paper1571, it has been shown that a wake extends for about 1.1 bubble diameters behind each rising bubble. If a second bubble follows in this wake, its velocity is increased by an amount equal to the velocity of the leading bubble, and in this way coalescence takes place. 

The bubbles appear to be responsible for a large amount of mixing of the solids. A rising bubble draws up a spout of particles behind it and carries a wake of particles equal to about one-third of the volume of the bubble and wake together. This wake detaches itself at intervals. The pattern in a bed containing a large number of bubbles is, of course, very much more complex. 

It was soon recognized that this difficulty stemmed from lack of knowledge of the contacting and flow pattern in the bed in effect, the bypassing of much of the solids by the rising bubble gas. This led to the realization that adequate prediction of bed behavior had to await a reasonable flow model for the bed. 

Transfer of gas from a rising bubble into a liquid is becoming increasingly important bubble and foam columns are often more efficient than... 

The relative velocity between rising bubbles and liquid is also a matter of interest in transport processes. For bubbles in still liquid, this is given by Nicklin (N2) and by Wallis (Wl) as... 

In order to design an efficient reactor using a faUing film reactor, we would need to have many small tubes in parallel so that the interfacial area can be large. This is difficult to accomphsh with flow down tubes, but it is easy to accomplish with rising bubbles or faUing drops. The interfacial area is not now the area of the cyYilid T between gas... 

In order to avoid a surge of helium when the spray valve is opened (as this would contaminate the entire environment) it is advisable to install a choke valve to adjust the helium quantity, directly before or after the spray pistol (see Fig. 5.15). The correct quantity can be determined easiest by submerging the outlet opening in a container of v/ater and setting the valve on the basis of the rising bubbles. riable-area flowmeters are indeed available for the required small flow quantities but are actually too expensive. In addition, it is easy to use the water-filled container at any time to determine whether helium is still flowing. 

This section follows Zhang and Xu (2008). In most liquids, a bubble rises rapidly under buoyancy, which induces forced convection. For rising bubbles, two factors cause the bubble to become larger mass increase in the bubble and the pressure decrease as the bubble rises. The second factor is significant only when rising distance is large (e.g., >10 m). For clarity of discussion, CO2 bubble growth in water is considered. The mass in the bubble increases as... 

Figure 4-26 (a) The height and (b) radius of a rising bubble in a Budweiser beer as a function of time. Data points are from Shafer and Zare (1991). The viscosity of beer is measured to be 1.44 times that of pure water. The diffusivity and solubility of CO2 in beer are assumed to be the same as those in pure water. The temperature is assumed to be 9°C. The initial CO2 content is assumed to be 1.5 bar. From Zhang and Xu (2008). 

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