Bubbles ellipsoidal bubble

Moreover, ellipsoidal bubbles and drops commonly undergo periodic dilations or random wobbling motions which make characterization of shape particularly difficult. Chapter 7 is devoted to this regime. 

Few observations have been reported on wakes of ellipsoidal bubbles and drops at Re > 1000. Yeheskel and Kehat (Y4) characterized shedding in this case as random. However, Lindt (L7, L8) studied air bubbles in water and distinguished a regular periodic component of drag associated with an open helical vortex wake structure. Strouhal numbers (defined as 2af/Uj, where / is the frequency and 2a is the maximum horizontal dimension) increase with Re, to level off at about 0.3 as bubbles approach the transition between the ellipsoidal and spherical-cap regimes. 

Surface-active contaminants play an important role in damping out internal circulation in deformed bubbles and drops, as in spherical fluid particles (see Chapters 3 and 5). No systematic visualization of internal motion in ellipsoidal bubbles and drops has been reported. However, there are indications that deformations tend to decrease internal circulation velocities significantly (MI2), while shape oscillations tend to disrupt the internal circulation pattern of droplets and promote rapid mixing (R3). No secondary vortex of opposite sense to the prime internal vortex has been observed, even when the external boundary layer was found to separate (Sll). 

There is considerable evidence (D3, G7, PI, P4, SI) that bubbles in liquid metals show the behavior expected from studies in more conventional liquids. Because of the large surface tension forces for liquid metals, Morton numbers tend to be low (typically of order 10 ) and these systems are prone to contamination by surface-active impurities. Figure 8.10a shows a two-dimensional nitrogen bubble in liquid mercury. For experimental convenience, the bubbles studied have generally been rather large, so that there are few data available for spherical or slightly deformed ellipsoidal bubbles in liquid metals. Data... 

Most bubbles in gas-solid fluidized beds are of spherical cap or ellipsoidal cap shape. Configurations of two basic types of bubbles, fast bubble (clouded bubble) and slow bubble (cloudless bubble), are schematically depicted in Fig. 9.7. The cloud is the region established... 

Fig. 2.25 illustrates a device for the study of the deformation of a spherical foam film in an electric field, proposed in [130]. The surfactant solution is fed into the glass cell through the tube 2, so that its level reaches the porous plate 4. When air is blown through the tube 3, a foam bubble forms at the capillary orifice. An electric field is created between electrode 1 and 6, which deforms the foam film (bubble). The bubble transforms from spherical to ellipsoidal shape. The value of the deformation A/ depends on the surface tension of the film... 

Up — Uc represents the resultant slip velocity between the particulate and continuous phase. Some other commonly used drag coefficient correlations are listed in Appendix 4.2. For fluid particles such as gas bubbles or liquid drops, the drag coefficient may be different than that predicted by the standard drag curve, due to internal circulation and deformation. For example, Johansen and Boysen (1988) proposed the following equation to calculate Cd, which is valid for ellipsoidal bubbles in the range 500 < Re < 5000 ... 

Jakobsen [12] used a drag coefficient formulation for the bubbles formulated by Johansen and Boysan [13] based on the terminal velocities for ellipsoidal bubbles given by Clift et al [7]. 

Rise of an Ellipsoidal Bubble at High Reynolds Numbers... 

The rise velocity f/j of an ellipsoidal bubble and the ratio °f its axes were obtained in [337,495] as functions of the equivalent radius ae = (ab2) /3. In the general case, the expression for the rise velocity of a bubble has the form... 

If the bubble size continues to grow, ae > 3.7 ao, then, by virtue of the increase in x, the viscous drag grows faster than the buoyancy force, and the bubble velocity decreases. For ae/ao > 8, the ellipsoidal bubble model cannot be applied any longer. 

The dimensionless total diffusion flux corresponding to a potential flow past an ellipsoidal bubble (Re = oo) is calculated at high Peclet numbers by the formula [174]... 

The mean Sherwood number for an ellipsoidal bubble is calculated with the help of (4.10.13) by the formula Sh = I/S, where the dimensionless surface area 5 is obtained from the first expression in (4.10.5). 

Petrov, A. G., Curvilinear motion of an ellipsoidal bubble, J. Appl. Mech. Techn. Phys., No. 3, 1972. 

Figure 16. Ellipsoidal bubble. (Top row) The contour plots of the constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side).

The virtual volume coefficient Cy for potential flow around a sphere is 0.5. For ellipsoidal bubbles with a ratio of semiaxes 1 2, Cy is 1.12. For ellipsoidal bubbles with random wobbling motions, Fopez de Bertodano [26] calculated to be about 2.0. In addition, Cy is a function of the specific gas holdup [27-29] ... 

Stewart, C. W., Coalescence of Ellipsoidal Bubbles Rising Freely in Low-Viscosity Liquids, Ph.D. Dissertation, Washington State University, Pullman, Washington (1993). 

L = circumference of the ellipsoidal bubble length of the heat transfer probe... 

Growing gas content makes bubbles merge until ultimately they occupy the central part of the pipe section, reaching 1 metre and more in length these long bubbles are separated from the pipe wall by a thin layer of water. They have the shape of an ellipsoid at the front, and are cut off at the back, not unlike artillery shells. Hence the term, shell mode. 

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