Velocity of single bubbles

For a better understanding of the interactions between parameters, it is often helpful to calculate the effective bubble rise velocity from measurea valves of for example, the data of Mersmann (loc. cit.) indicated = 0.6 for = 0.05 iti/s, giving U, = 0.083 m/s, which agrees with the data reported in Fig. 14-43 for the rise velocity of bubble clouds. The rise velocity of single bubbles, for d - 2 mm, is about 0.3 m/s, for liquids with viscosities not too different from water. Using this value in Eq. (14-220) and comparing with Fig. 14-104, one finds that at low values of the rise velocity of the bubbles... 

The large bubble rise velocities calculated from equation 19 are shown in Table II and they are significantly higher than the rise velocities of single bubbles of the same diameter. 

Figure 9-2 Rising velocity of single bubbles in beds of 500-/im sand particles [after Darntn and flarri.stw20).

Mean slip velocity of bubble Free-rising velocity of single bubble... 

Even though (10.7) is strictly valid in liquids, the formula is widely used for calculations of the ideal rise velocity of single bubbles in fluidized beds, when the ratio of bubble to bed diameters is dt,/dt < 0.125 [29, 82] ... 

This is of course valid only for isolated bubbles moving in clean water, and corrections (i.e. reductions) of the terminal velocity are applied to account for the presence of the other bubbles or partial contamination. Alternatively the terminal velocity can be determined experimentally or by resorting to detailed simulations. Simulations for the determination of the terminal velocity of single bubbles or groups (swarms) of bubbles can be based on the volume-of-fluid (VOF) method or similar methods (Bertola et al, 2004 Petitti et at, 2007). 

Tomiyama, A., Celata, G. R, Hosokawa, S. Yoshida, S. 2002a Terminal velocity of single bubbles in surface tension force dominant regime. International Journal of Multiphase Flow 28, 1497-1519. 

Figure 6 Effect of pressure on rise velocity of single bubbles at different temperatures (a) 27°C and (b) 78°C. (From Lin et al., 1998.)...

Studies concerning bubbles characteristics in three-phase fluidized beds can be grouped into three categories. The first category includes the analysis of the relationship between bubble size and the velocity of single bubbles. The second group considers the characteristics of bubbles in freely bubbling beds. 

Rising Velocity (Terminal Velocity) of Single Bubbles [83]... 

Bakker increased the local values of e as obtained with FLUENT by a contribution related to the slip velocity of the bubbles. Working with a single... 

An accepted empirical correlation for the terminal rise velocity of single isolated bubbles is that of Peebles and Garber (1953), who identified four regions as shown in Table 7.1. 

Grace, J.R., Wairegi, T. and Nguyen, T.H., Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, Transactions of the Institution of Chemical Engineers, 54, pp. 167-73 (1976). 

FIG. 14-93 Velocity of rising bubbles, singly and in clouds. To convert feet per second to meters per second, multiply by 0.305. [From Chem. Eng. Sci., 7, 48 1957).]... 

The number of bubbles formed is equal to the volume of air in the vessel divided by the average volume of a single bubble. The volume of air in the vessel is equal to the rate of inflow of air ga times its detention time t . The detention time, in turn, is equal to the depth of submergence h (see Figure 6.7g) divided by the average total rise velocity of the bubbles. If Vj is the average rise velocity of the bubbles... 

If the bubbles in case a of Fig. 42 do not interfere with each other (D3), then the velocity of the bubbles should equal the free-fise velocity so of a single bubble in a cross-sectional area of liquid large enough for the liquid phase to have no net vertical velocity. This has been indicated by TUrner (T28) in regard to the fluidized bed, for which he modified Eq. (5-1) to the form... 

Krishna, R., van Eaten, J.M. and Urseanu, M.I. and Ellenberger, J. (2000b), Rise velocity of single circular-cap single bubbles in two-dimensional beds of powders and liquids, Chem. Eng. Proc., 39, 433-440. 

As discussed in Chap. 7, bubbles change in shape from spherical to ellipsoidal to lens-shaped as their diameter increases. Larger bubbles often rise in spiral paths, at terminal velocities that are almost constant and independent of their size (see Fig. 7.8). In clouds or swarms of bubbles there may be considerable coalescence the rate of rise of clouds of small bubbles is considerably less than that of single bubbles if the bubbles are distributed uniformly over the cross section of the vessel. A cloud of bubbles rising at one location creates an upflow of liquid, and this chimney effect may greatly increase the bubble velocity. 

The variation of the bed voidage in a gas fluidized bed was used by Colver (1981, 1996) and Donahoe and Colver 1984 to track single injected air bubbles, fast moving waves, a rising plastic float, and falling objects for both ac and dc electric fields. The rise velocity of the bubble slows from about 25 cm/s to 10.5 cm/sec near a the surface of the bed. A fast compression wave moving at about 270 cm/s was detected just ahead of the bubble. 

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