Bubbles shape

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Fig. 1. Photograph illustrating the microstmcture of the foam which stiU persists two hours after shaking an aqueous solution containing 5% sodium dodecylsulfate. The bubble shapes ate more polyhedral near the top, where the foam is dry, and more spherical near the bottom, where the foam is wet.

Studies of individual bubbles rising in a two-dimensional gas—Hquid—soHd reactor provide detailed representations of bubble-wake interactions and projections of their impact on performance (Fig. 9). The details of flow, in this case bubble shapes, associated wake stmctures, and resultant bubble rise velocities and wake dynamics are important in characteri2ing reactor performance (26). 

The bubbles shapes in gas purging vary from small spherical bubbles, of radius less than one centimen e, to larger spherical-cap bubbles. The mass transfer coefficient to these larger bubbles may be calculated according to the equation... 

Observations of bubbles emerging through the bed surface show that bubble shape is markedly dependent on liquid velocity. This indicates the existence of a relationship between bed viscosity and liquid velocity. A bed near incipient fluidization is characterized by a high viscosity, and an emerging bubble is of nearly spherical shape, whereas a fluidized bed of high porosity is characterized by a viscosity not very much higher than that of water, so that an emerging bubble is of spherical cap shape. 

Bubble-shaped limif flame propagating up moves wifh a velocify defermined by buoyancy forces, like an air bubble in a column of wafer (in bofh cases, fhe Davies and Taylor formula [10] can be applied). 

The structure of a bubble-shaped lean limit propane flame (Le > 1) is different. At the flame front inflow, the streamlines are much less divergent and soon converge again. 

It is also interesting to examine the global gas dynamic structure of upward propagating flames. Figure 3.1.6 gives an example of the global velocity field for the lean limit methane flame in the flame coordinates. The velocity distributions for all near limit flames studied share certain features. The central part of the bubble-shaped flame is... 

Hsu and Graham (1961) took into consideration the bubble shape and incorporated the thermal boundary-layer thickness, 8, into their equation, thus making the bubble growth rate a function of 8. Han and Griffith (1965b) took an approach similar to that of Hsu and Graham with more elaboration, and dealt with the constant-wall-temperature case. Their equation is... 

Note that the average void fraction of a slug unit depends only on the liquid and gas flow rates, the dispersed velocity ub, the translational velocity w, and the void fraction within the liquid slug, a, and it is independent of the bubble shape or bubble length, the liquid slug length, as well as the film thickness in the film zone (Barnea, 1990). 

These different approaches are complementary to each other in basic concept. However, these analyses have not provided clear insight information of the bubble layer at the CHF about the bubble shape (spherical or flat elliptical), bubble population and its effect on turbulent mixing, and bubble behavior. The bubble behavior in a bubble layer could involve bubble rotation caused by flow shear, normal bubble velocity fluctuation, and bubble condensation in the bubble layer caused by the subcooled water coming from the core. Further visual study and measurements in this area may be desired. 

Barnea, D., 1990, Effect of Bubble Shape on Pressure-Drop Calculations in Vertical Slug Flow, Int. J. Multiphase Flow, 16 79-89. (3)... 

Newtonian liquid viscosity, U is the bubble velocity, and aQ is the equilibrium surface tension), where surface tension and viscous forces dominate the bubble shape (15). Using a lubrication analysis, Bretherton established that the bubble slides over a stationary, constant-thickness film whose thickness divided by the radius of the tube, h R., varies as the... 

Here we also consider sorption kinetics as the mass-transfer barrier to surfactant migration to and from the interface, and we follow the Levich framework. However, our analysis does not confine all surface-tension gradients to the constant thickness film. Rather, we treat the bubble shape and the surfactant distribution along the interface in a consistent fashion. 

The shape of the front and rear menisci change as a result of the resistance to bubble flow. Calculation of this deviation in bubble shape establishes the dynamic pressure drop across the bubble. 

In region III near the tube center, viscous stresses scale by the tube radius and for small capillary numbers do not significantly distort the bubble shape from a spherical segment. Thus, even though surfactant collects near the front stagnation point (and depletes near the rear stagnation point), the bubble ends are treated as spherical caps at the equilibrium tension, aQ. Region... 

II provides a transition between the two asymptotic limits. Viscous stresses now scale by the local thickness of the film, h, and the bubble shape varies from the constant thickness film to the spherical segment. Here the surfactant distribution along the interface may be important. Fortunately, for small capillary numbers, dh/dx < 1 and the lubrication approximation may be used throughout. Region II is quantified below. 

Figure 6. The bubble shape at the front for the elasticity number equal to 0 and 1.

The third mechanism for nucleation is the fragmentation of active cavitation bubbles [16]. A shape unstable bubble is fragmented into several daughter bubbles which are new nuclei for cavitation bubbles. Shape instability of a bubble is mostly induced by an asymmetric acoustic environment such as the presence of a neighboring bubble, solid object, liquid surface, or a traveling ultrasound, or an asymmetric liquid container etc. [25-27] Under some condition, a bubble jets many tiny bubbles which are new nuclei [6, 28]. This mechanism is important after acoustic cavitation is fully started. 

The simulation results on bubble velocities, bubble shapes, and their fluctuation shown in Fig. 3 are consistent with the existing correlations (Fan and Tsuchiya, 1990) and experimental results obtained in this study. Bubble rise experiments were conducted in a 4 cm x 4 cm Plexiglas bubble column under the same operating conditions as those of the simulations. Air and tap water were used as the gas and liquid phases, respectively. Gas is introduced through a 6 mm nozzle. Note that water contamination would alter the bubble-rise properties in the surface tension dominated regime. In ambient conditions, this regime covers the equivalent bubble diameters from 0.8 to 4mm (Fan and Tsuchiya, 1990). All the air-water experiments and simulations of this study are carried out under the condition where most equivalent bubble diameters exceed... 

The thickness of the gas-liquid interface is set as 3A based on the parameters used in the case of Sussman (1998), with the same density-ratio on the interface and similar Reynolds number. An interface thickness of 5A is also examined in the simulation and no significant improvement is observed. The accurate prediction of the bubble shape (shown in Figs. 3 and 4) can be attributed, in part, to the manner in which the surface-tension force is treated as a body force in the computation scheme. Specifically, since the surface-tension force acting on a solid particle is considered only when a solid particle crosses the gas-liquid interface and the solid particle is considered as a point, the accuracy of the calculation of this force can be expected if the surface tension is interpreted as a body force acting on each grid node near the interface. 

Bubble point calculation, 24 680, 685 Bubble process, 23 408 Bubble shapes, 11 776-777 in foams, 12 7—11... 

FIGURE 6.4 Schematic representation of capillaries with (A) bubble shape, (B) Z-shape, and (C) multire-flective absorption detection zone configuration. The arrow indicates how the light beam travels through the capillary at the detection zone. 

Fig. 9.11 Slug flow bubble shapes (a) Eo > 10, M < 10 (low viscosity liquid) (b) viscous liquid (c) inclined tube.

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