Bubble drift velocity

This condition was tested for water in columns with diameters up to 5.5 m and g varying between 0.1 ms-1 and lms 1. Further, is was found to be satisfactory for non-Newtonian slurries containing up to 10wt% of solids. The gas holdup may be affected by internals. For vertical heat exchange tubes present in the columns, Saxena et al. carried out an extensive research programme [39-43], The gas holdup increases if the internals in the column prevent bubble coalescence [43], Saxena et al. correlated their results in a relation based on the so-called drift velocity concept ... 

To complete the drift-flux model, the phenomenological theory of Lapidus and Elgin (9) is used, wherein it was suggested for dispersed flow systems that the slip velocity depends directly on terminal bubble rise velocity, U, so that... 

Height of the column, m Dimensionless height of bubble column Parameter of the stability criterion The drift velocity, m/s Separation constant in (166)... 

In [373], bubble thermocapillary drift was considered in the external temperature gradient at high Peclet numbers. The drift velocity was found to be... 

Fining can be achieved by increasing the temperature of the molten glass by about 150°C to reduce its viscosity. From Stokes law (or by comparing the rise of bubbles in Cola versus liquid soap) we know that the drift velocity... 

Glicksman and McAndrews (1985) determined the effect of bed width on the hydrodynamics of large particle bubbling beds. Sand particles with a mean diameter of 1 mm were fluidized by air at ambient conditions. A rectangular-cross-section bubbling bed was used. The bed width ranged from 7.6 to 122 cm, while the other cross-sectional dimension was held constant at 122 cm. Most experiments were carried out with an open bed. The bubble rise velocity increased with the bed width when the bubble velocity was represented as the drift flux plus the rise velocity of an isolated bubble,... 

The drag coefficient is now explicitly a function of the gas fraction. Moreover, the relative velocity between the bubbly phase and the hquid phase needs to be averaged. As it is a nonlinear combination, this will, as discussed above, result in an additional term that needs to be closed. Simonin [46] derived an expression for this and provided the required closure based on mathematical derivations and some phenomenological modeling. A so-called drift velocity is introduced, which takes the nonlinear averaging into account, and the drag force (per unit volume) is written as... 

Optical probes were used to measure the bubble size, frequency and velocity within the dense bed. The bubble velocity for an actively bubbling bed was found to closely agree with the drift flux form proposed by Davidson and Harrison (1963). In contrast, the volumetric flow rate of the bubbles was found to be far less than that predicted by the two-phase hypothesis (Fig. 40). 

Bhaga (B3) determined the fluid motion in wakes using hydrogen bubble tracers. Closed wakes were shown to contain a toroidal vortex with its core in the horizontal plane where the wake has its widest cross section. The core diameter is about 70% of the maximum wake diameter, similar to a Hill s spherical vortex. When the base of the fluid particle is indented, the toroidal motion extends into the indentation. Liquid within the closed wake moves considerably more slowly relative to the drop or bubble than the terminal velocity Uj, If a skirt forms, the basic toroidal motion in the wake is still present (see Fig. 8.5), but the strength of the vortex is reduced. Momentum considerations require that there be a velocity defect behind closed wakes and this accounts for the tail observed by some workers (S5). Crabtree and Bridgwater (C8) and Bhaga (B3) measured the velocity decay and drift in the far wake region. 

Flowmeters. Even after modification the pumps usually showed some long-time drift in the pumping velocity, mainly due to changes in valve operation caused by corrosion, dirt accumulation or trapped air bubbles. Thus all flowrates have to be measured at regular intervals and the pumps adjusted when needed. Various devices for flowrate measurements were tested and two were finally selected. 

Darton and Harrison (1975) derived a criterion for the point of transition to predict whether a solid-liquid fluidized bed will expand or contract when the gas is first introduced. The definition of Pa used by Darton and Harrison was the ratio of upper clear (particle-free) wake volume to the bubble volume. But since they did not consider the circulation of sohds associated with the lower nonclear portion of the wake, their Pa was effectively the same as that of Bhatia and Epstein (1974). The use of the Wallis drift flux approach by Darton and Harrison (1975) also represents no real difference from the relative velocity approach taken by Bhatia and Epstein (1974), since the two methods are rigorously interrelated. It is therefore not surprising that the final criteria of Bhatia and Epstein (1974) and Darton and Harrison (1975) are identical. 

Understanding of gas-liquid flow in electrochemical systems is very important for system optimization, enhance mass transport and thus gas release efficiency. There are relatively little theoretical studies available in the literature which considers process as a two-phase flow problem. Zeigler and Evans[2] applied the drift - flux model of Ishii[3] to electrochemical cell and obtained velocity field, bubble distribution, mass transfer rate. Instead of treating the bubbles as a second phase, they obtained bubble distribution from concentration equation. Dahikild [4] developed an extensive mathematical model for gas evolving electrochemical cells and performed a boundary layer analysis near a vertical electrode. 

Because of the film between the bubble and the wall, the bubble and liquid velocities are not the same. The bubble velocity, Ub, is given by the drift flux model ... 

In two-phase pipe flows, the slip velocity or, equivalently, the drift flux is related to the void fraction. This leads to the occurrence of kinematic waves which convey void fraction signals. Kinematic waves have been investigated experimentally in air-water two-phase flows by inducing small void fraction disturbances at the inlet of vertical ducts, the average void fraction varying from 0.01 (bubbly flows) to 0.41 (slug flows). The temporal fluctuations of the void fraction are detected in regularly spaced cross sections by non intrusive impedance probes. The statistical... 

This correlation reqnires information on u, which can be estimated using Equation 10.7. This latter equation requires data on as a function of superficial gas velocity to evaluate the terminal rise velocity of the bubble, These data can be obtained throngh simple gas holdup measurements. The drift flux model of Zuber and Findlay (1965) can be used to obtain as per Equation 10.10 ... 

Figure 13 The regime transition velocity (a) in a bubble column. Open symbols are obtained by standard deviation of pressure fluctuation and drift flux model closed symbols are calculated by the correlation of Wilkinson et al. (1992). (From Lin et al., 1999.) (b) In a three-phase fluidized bed. (From Luo et al., 1997a.)...

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