Around the bubble

A variation of the preceding process is used to produce oriented vinyUdene chloride copolymer films. The plastic is extmded into tube form and then is supercooled and subsequently biaxiaHy oriented in a continuous bubble process. The supercooled tube is flattened and passed through two sets of pinch roUs, which are arranged so that the second set of roUs travels faster than the first set. Between the two sets, air is injected into the tube to create a bubble that is entrapped by the pinch roUs. The entrapped air bubble remains stationary while the extmded tube is oriented as it passes around the bubble. Orientation is produced in the transverse and the longitudinal directions, creating excellent tensile strength, elongation, and flexibiUty in the film. The commercial procedure has been described (157). 

The absorption is assumed to occur into elements of liquid moving around the bubble from front to rear in accordance with the penetration theory (H13). These elements maintain their identity for a distance into the fluid greater than the effective penetration of dissolving gas during the time required for this journey. The differential equation and initial and boundary conditions for the rate of absorption are then... 

Bubble size at departure. At departure from a heated surface, the bubble size may theoretically be obtained from a dynamic force balance on the bubble. This should include allowance for surface forces, buoyancy, liquid inertia due to bubble growth, viscous forces, and forces due to the liquid convection around the bubble. For a horizontally heated surface, the maximum static bubble size can be determined analytically as a function of contact angle, surface tension, and... 

Brown (1967) noted that a vapor bubble in a temperature gradient is subjected to a variation of surface tension which tends to move the interfacial liquid film. This motion, in turn, drags with it adjacent warm liquid so as to produce a net flow around the bubble from the hot to the cold region, which is released as a jet in the wake of the bubble (Fig. 4.10). Brown suggested that this mechanism, called thermocapillarity, can transfer a considerable fraction of the heat flux, and it appears to explain a number of observations about the bubble boundary layer, including the fact that the mean temperature in the boundary layer is lower than saturation (Jiji and Clark, 1964). 

The expected surfactant distribution is also portrayed qualitatively in Figure 2. At low Ca, recirculation eddies in the liquid phase lead to two stagnation rings around the bubble, as shown by the two pairs of heavy black dots on the interface (18>19). Near the bubble front, surfactant molecules are swept along the interface and away from the stagnation perimeter. They are not instantaneously replenished from the bulk solution. Accordingly, a surface stress, rg, develops along the interface... 

Gas within a bubble essentially remains in the bubble, but recirculates internally, and penetrates slightly into the emulsion to form a transitional cloud region around the bubble all parameters involved are functions of the size of bubble (Davidson and Harrison, 1963). 

That boiling produces bubbles of vapor creates an additional problem for performing the experiment. If a bubble of gas forms at the bottom of a capillary tube, its expansion and rise to the top of the capillary will expel the rest of the liquid. This is due to the fact that the surface tension of most liquids combined with the narrow bore of the capillary will not allow fluid to drain around the bubble as it rises. The solution is that a larger sample tube and sample is required for the experiment. One advantage of the boiling point experiment is that the thermal conductivity of a liquid is higher than its solid because of the mobility of the molecules. 

The most common cause of it is the neglect of 3-dimensional effects as compared with those in two dimensions. Thus, all stresses in a loaded wire or ribbon are disregarded in the shrinkage method, Section III. 1. The work of deformation leading to rupture is a bulk effect which does not receive its due consideration in the calculation of fracture energy, Section III.3. Bulk deformations associated with thermal etching, Section III.4, demand more attention than was alloted to them by many scientists. The method of bubbles, Section III.5, is invalid both because of the above neglect (that is, that of the volume stresses around the bubble) and because of another popular error, namely an erroneous treatment of capillary pressure Pc. 

Since mass transfer in the liquid around the bubbles limits the rate, the ItiasS-balance equation on in the liquid phase becomes... 

In the previous problem the hydrogen bubbles are initially 0.1 cm in diameter, and they contain pure H2 gas at a concentration of 0.05 moles/cm (which does not change as the bubbles rise). Hydrogen is transferred from the bubbles to the liquid with a rate limited by mass transfer (k, = Dyi lR) in the liquid around the bubble with Dq, = 1 x 10 cm /sec. There is no reaction in the bubbles. 

Normally, even when the bubble phase is a gas mixture, the major mass transfer resistance for slightly soluble gases is in the gas-liquid interface. Thus, the mass transfer coefficient in the liquid film around the bubble is the important one in gas bubble-to-liquid mass transfer (Smith, 1981 Treybal, 1980). 

Two-Phase theory of Davidson According to the two-phase theory, two phases exist in the bubbling fluidized bed (a) the bubbling phase consisting of gas bubbles, and (b) the particulate phase, namely the solids around the bubbles. The particulate phase is alternatively called the emulsion phase. Bubbles stay in the bubble phase and penetrate only a small distance into the emulsion phase. This zone of penetration is called cloud since it envelops the rising bubble. 

Aeration. This interphasic property of protein products, also called foaming or whipping, depends on the ability of the protein to form protective films around gas bubbles. Coalescence, and subsequent break-up of the membrane-like system around the bubbles by the proteins is thereby prevented (55-60). 

II Figure 1). Adsorption continually occurs around the bubbles to replace protein in areas of the interface where coagulation or stretching of the film is occurring. The actual bubble size in the foam depends upon the rate of protein adsorption as well as upon the ease of film rupture. The protein films on adjacent bubbles come in contact and trap the liquid, preventing it from flowing freely. This restriction is governed by the viscosity of the colloidal solution. The polypeptides of denatured proteins situate to positions where their hydrophobic side chains are directed outward toward each other. Because liquid... 

Spreading of bitumen around the bubble to complete attachment... 

To describe the particle and gas flows around the bubble in fluidized beds, the pioneering model of Davidson and Harrison (1963) is particularly noteworthy because of its fundamental importance and relative simplicity. On the basis of some salient features of this model, a number of other models were developed [e.g., Collins, 1965 Stewart, 1968 Jackson, 1971]. The material introduced later follows Davidson and Harrison s approach. 

Figure 9.11 shows a comparison between the measured dynamic pressure and the calculated results based on Eq. (9.24). The profile indicates that there is a local high-pressure region near the bubble nose and a local low-pressure region around the bubble base, i.e., the wake region. The low pressure in the wake region promotes pressure-induced bubble coalescence in the bed. 

Figure 20 An example of the approximated 3D bubble shape and corresponding flow structure estimated from the measurement using PIV/LIF combining with double-SIT system (a) characteristic vorticity structure around the bubble (bubble moves in the y-z plane) (b) reconstructed 3D bubble shape (c) relation between bubble location and measured plane for PIV and (d) 3D bubble trajectory (Fujiwara et al., 2004a) (see Plate 7 in Color Plate Section at the end of this book).

Unlike formation in a liquid the boundary of a fluidised bed bubble can only expand by gas flowing across it to produce the drag force that will cause the particles to move appropriately. During the time that a bubble grows to the size shown in Figure 9 the gas that produced it has advanced to fill the volume indicated by the outer broken line. The annular region above and around the bubble now contains an excess of gas and so the powder void-age must increase. This is unstable and as the bubble detaches and rises through the expanded dense phase the powder relaxes and and returns the excess gas to the bubble. This appears to be completed by the time it has risen about one diameter (of order 1/10 second) and thereafter is of constant volume until it coalesces. 

Unless restrained by selectivity requirements, catalyst developers may search for more active catalysts until mass transfer around the particles is rate controlling. Reactor engineers then will load the slurry with catalysts until mass transfer around the bubbles becomes rate limiting, for example... 

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