Bubble discrete

The raw ROM (run of mine) ore is reduced in size from boulders of up to 100 cm in diameter to about 0.5 cm using jaw cmshers as weU as cone, gyratory, or roU-type equipment. The cmshed product is further pulverized using rod mills and ball mills, bringing particle sizes to finer than about 65 mesh (230 p.m). These size reduction (qv) procedures are collectively known as comminution processes. Their primary objective is to generate mineral grains that are discrete and Hberated from one another (11). Liberation is essential for the exploitation of individual mineral properties in the separation process. At the same time, particles at such fine sizes can be more readily buoyed to the top of the flotation ceU by air bubbles that adhere to them. 

Bubbly Vessel Model The bubbly vessel model assumes uniform vapor generation throughout the hquid with hmited disengagement in the vessel. In this model, the liquid phase is continuous with discrete bubbles. 

Dispersed bubble (DB) - The gas phase is distributed as discrete bubbles within a continuous liquid phase. At the transition boundary most bubbles are located near the top. As the liquid rate increases, the bubbles are more uniformly dispersed. 

Bubble flow - The gas is roughly uniformly distributed in the form of small discrete bubbles in a continuous liquid phase. The flow pattern is designated as bubble flow (B) at low liquid flowrates, and as dispersed bubble (DB) at high liquid flow rates in which case the bubbles are finely dispersed in the liquid. 

These concepts were implemented according to the following scheme the liquid element surrounding the bubble and the bulk are considered as two separate dynamic reactors that operate independent of each other and interact at discrete time intervals. In the beginning of the contact time, the interface is being detached from the bulk. When overcome by the bubble, it returns to the bulk and is mixed with it. Hostomsky and Jones (1995) first used such a framework for crystal precipitation in a flat interface stirred cell. To formulate it for a... 

Minimum Bubbling Velocity (Umb). The velocity at which discrete bubbles begin to form. Typical minimum bubbling velocity for an FCC catalyst is... 

In bubble-flow operation, the gaseous phase moves upwards as discrete bubbles. The liquid phase may be in either co- or countercurrent flow. The liquid holdup is relatively high. 

Bubbly flow. Here the bubbles were shorter than the tube diameter and the vapor phase was distributed as discrete bubbles in a continuous liquid phase (Fig. 2.30a). 

Dispersed bubbly flow (DB) is usually characterized by the presence of discrete gas bubbles in the continuous liquid phase. As indicated in Fig. 5.2, for the channel of db = 2.886 mm, dispersed bubbles appeared at a low gas superficial velocity but a very high liquid superficial velocity. It is known that for large circular mbes dispersed bubbles usually take a sphere-like shape. For the triangular channel of dh = 2.886 mm, however, it is observed from Fig. 5.2 that the discrete bubbles in the liquid phase were of irregular shapes. The deformation of the gas bubbles was caused by rather high liquid velocities in the channel. 

Figure 5.9 shows various interesting aspects of two-phase flow patterns obtained in this observation. It should be noticed from these pictures that a variety of two-phase flow patterns were encountered in a clean micro-channel. The authors noticed that in a very clean tube, many small individual bubbles flow in a discrete way in the tube without coalescence in bubbly flow. The most interesting thing is the special flow pattern given in Fig. 5.9d, where several bubbles with various shapes are connected in a series by the gas stems located at the tube center line. The liquid ring flow is also clearly seen in Fig. 5.9e. 

Figure 2.22 Sketches of imagined profile views of three types of discrete growing bubbles. (From Kirby and Westwater, 1965. Copyright 1965 by American Institute of Chemical Engineers, New York. Reprinted with permission.)...

Gaertner (1965) studied nucleate pool boiling on a horizontal surface in a water pool under atmospheric pressure. He increased the surface heat flux gradually. The vapor structures on the surface progressed from discrete bubbles to vapor columns and vapor mushrooms, and finally to vapor patches (dryout). The observed pictures of vapor mushroom and vapor patch are also sketched in Figure 5.3. 

It is assumed that the discrete phase exists as drops (or bubbles) that can be characterized by an average velocity, an average size, and an average enthalpy at each axial position. A steady-state balance on the number of drops (or bubbles) present at each axial position is given by... 

Regime-IV flow patterns are of pragmatic interest when interphase heat and mass transfer are of key importance because the existence of the discrete phase generates a large interfacial area per unit tube volume. Evaluation of the interfacial area is made difficult because the bubbles or drops of the discrete phase are usually not of uniform size or shape. By assuming a characteristic size and shape for the drops or bubbles, the interfacial area and the other parameters can be estimated with reasonable accuracy for many situations. 

Foamed polystyrene - which is also known as expanded polystyrene - is used extensively in a variety of applications, ranging from packaging peanuts to insulation board and single-use cups and plates. We produce it by two processes foam extrusion and bead expansion. Both types of expanded polystyrene consist of closed cells, i.e., bubbles with continuous walls. We can visually distinguish the two types of foam by the fact that products made by the expanded bead process consist of discrete beads that are welded together... 

Acoustic cavitation can be considered to involve at least three discrete stages nucleation, bubble growth, and, under proper conditions, implosive collapse. The dynamics of cavity growth and collapse are strikingly dependent on local environment we therefore will consider separately cavitation in a homogeneous liquid and cavitation near a liquid-solid interface. 

The differences in behavior between small laboratory beds and larger demonstration units can, in part, be attributed to a switch from porous plate distributors in the small bed to discrete hole or bubble caps in... 

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 the discrete bubble model described in Section V.C, future work will be focused on implementation of closure equations in the force balance, like empirical relations for bubble-rise velocities and the interaction between bubbles. Clearly, a more refined model for the bubble-bubble interaction, including coalescence and breakup, is required along with a more realistic description of the rheology of fluidized suspensions. Finally, the adapted model should be augmented with a thermal energy balance, and associated closures for the thermophysical properties, to study heat transport in large-scale fluidized beds, such as FCC-regenerators and PE and PP gas-phase polymerization reactors. 

Bokkers, G. A., Van Sint Annaland, M., and Kuipers, J. A. M., Comparison of continuum models using kinetic theory of granular flow with discrete particle models and experiments extent of particle mixing induced by bubbles. Proceedings of Fluidization XI, May 9-14, 2004, 187-194, Naples, Italy (2004). 

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