Free rising velocity

The fractional dispersed phase holdup, h, is normally correlated on the basis of a characteristic velocity equation, which is based on the concept of a slip velocity for the drops, VgUp, which then can be related to the free rise velocity of single drops, using some correctional functional dependence on holdup, f(h). 

To avoid any wall effect or perturbation effect that may occur with these methods, a sampling apparatus for the photographic technique has been proposed by Kawecki et al. (K5). Bubbles are extracted from the tank containing the dispersion by means of a tube connected to a small square-section column through which a continuous flow of liquid and bubbles rises. The flow rate is chosen high enough so that differences in the free-rise velocity of the bubbles do not affect the mean residence time of the bubbles in the column. The bubbles in the column are then photographed. 

Experimental Mj values determined as the difference between the local mean velocities of bubbles and liquid are also shown in Fig, 34 as open keys. For these bubbles, the volume-surface mean diameters J32 have been measured experimentally. The free-rise velocity of the bubbles (Tl, V6) is... 

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

Now we derive an expression for the bubble rise velocity. This velocity consists of two contributions (1) the free rise velocity M, r which is determined only by the properties of the bed and the gas and is independent of gas velocity and (2) the bulk flow of the bubble phase as a whole which is dependent on gas velocity and is given by (mq - Mmf)- Thus... 

The free rise velocity Mbr ay be assumed equal to the velocity of a bubble released from a singe nozzle into an inviscid fluid, that is, the rise velocity when the bed is at M, f and is given by... 

A striking feature is the way the so-called diseontinuity in the free rise velocity of a bubble varies with its size. Indeed, Astarita and Appuzzo [1965] noted a six to ten fold increase in the rise veloeity at a eritieal bubble size, as seen in Figure 5.6 for air bubbles in two polymer solutions. Subsequently, similar, though less dramatic results, summarised in a reeent review [DeKee et al., 1996], have been reported. The critical bubble radius appears to hover around 2.6 mm, irrespective of the type or the degree of non-Newtonian properties of the continuous phase, and this value is well predieted by the following... 

Figure 5.6 Free rise velocity bubble volume data showing an abrupt increase in velocity...

All the above discussions are for particles with density larger than the surrounding fluid. For particles with density smaller than the surrounding fluid, it has long been assumed that the free rising velocity is governed by the same equations, the only difference being that of particle movement direction. However,... 

The shape of a bubble not only influences its free-rise velocity but also plays an important role in determining the rates of heat and mass transfer and coalescence. The shape of a bubble in free-rise motion is governed by the relative magnitudes of viscous, surface tension, inertial, and elastic forces. Additional complications arise when the bubble is rising in narrow tubes (Coutanceau and Hajjam, 1982). 

Very recently, Rodrigue (1995) performed an extensive experimental study in order to evaluate the effect of contamination on the free-rise velocity of air bubbles. Velocity-volume measurements involving Newtonian and non-Newtonian ffuids as well as surface active agents were performed. No discontinuity was observed in the case of Newtonian fluids for the concentration range of surfactant [0-80,000 wppm of sodium dodecyl sulfate (SDS)]. 

Turning our attention now to the behavior at high Reynolds number (Re - oo), bubbles tend to be of the cap type. Davies and Taylor (1950) showed that the free-rise velocity is given by... 

As mentioned earlier, one is usually interested in calculating the free-rise velocity of swarms of bubbles rather than the drag force. The drag results presented in Table 5 can be conveniently rearranged in terms of a velocity ratio as... 

V Free-rise velocity not corrected for wall effects... 

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