Experimental Study of Bubble Pairs (a) Bubbles in Vertical Alignment

Harrison and Leung (1962), the earliest systematic researchers o f bubble coalescence, employed a cine camera for studying coalescence o f vertical bubble pairs in 2D and 3D beds. The experiments were carried out to measure the rate o f bubble coalescence as well as the volumes and the rise velocities o f bubbles which formed successively from a single nozzle. They decreased the time interval between bubble

Table 2-1. Models for coalescence o f a pair o f bubbles

Authors Case

Bubble

alignment Theory background Bubble shape

Emulsion phase Pressure constant points * Note Toei and Matsuno (1967) 2D Vertical

Oblique Jackson’s theory o f single bubble

Circular Ideal fluid P3, P4 • Difficult to calculate the unsteady state solution for bubbles in oblique alignment Toei et al. (1968) 3D Vertical Clift and Grace (1970) 2D Vertical Ui = Ua i + i

(see Eq. (2-1)) Non-circular Ideal fluid P 1,P 2

• Each bubble represented by a single doublet Clift and Grace (1971) 2D 3D Oblique Vertical Clift and Grace (1974) 3D Oblique

Lin(1970) 2D Vertical M urray’s theory (1965a, b)

Circular (equal-sized)

Ideal fluid P 1 ,P 2 • That interaction reduced bubble velocity was predicted

Miwa et al. (1972)

2D 3D

Oblique Davidson and

Schuler’s theory (1960)

Circular (equal-sized)

Ideal fluid P5 • Each bubble represented by a single doublet • Extend to a swarm o f bubbles

Gera and Gautam (1995)

2D Vertical Oblique

Clift and Grace’s model

(1970,1971) Non-circular Ideal fluid P 1 ,P 2

• Each bubble represented by a single doublet • Voidage is a dependent variable

• Throughflow velocity is determined

0 IT Q}

CD

1

Chapter Two ■ 3 3

injections until a single bubble broke the surface o f the bed at incipient fluidization. The results showed that the velocity o f the leading bubble is unaffected by the following bubble and agreed with Cliff and Grace’s model (1970) which predicted a maximum increment o f 14 % in the velocity o f the leading bubble. Moreover, it was observed that the following bubble accelerates when it moves closely towards the wake o f the leading bubble and at this point the velocity o f the following bubble approximately equals that o f the leading bubble and coalescence takes place. During the coalescence process, because the front o f the following bubble moves more rapidly than the rear, the bubble is elongated.

Furthermore, when two bubbles approached, an increase in velocity o f the following bubble was ascribed to the effect o f the leading bubble was defined as the wake velocity o f the leading bubble. In this case, the wake velocity was not equal to the rise velocity o f the leading bubble. From an analysis o f the results in a 3D bed, it can be shown that the wake velocity is very near to the rise velocity o f the leading bubble when the bubble is up to a certain size. Consequently, possibly due to the wall effect, the wake velocity is markedly less than the rise velocity o f the leading bubble if the bubble diameter exceeds half o f the bed diameter. The experimental results suggest that the active wake extends in excess o f about 1.1 bubble diameters behind a leading bubble.

In addition to developing the coalescence models, Toei and his co-workers (Toei and Matsuno, 1967; Toei et al., 1968), and Clift and Grace (Clift and Grace, 1970, 1971; Grace and Clift, 1974) have shown some experimental results on bubble coalescence including vertically and obliquely ahgned bubbles in 2D and 3D beds. The process o f bubble coalescence in a 2D bed explained initially by Toei and Matsuno (1967) has already been described in Section 2.1. For the coalescence o f two bubbles in spite o f their size in a vertical direction, the critical distance defined by Toei and Matsuno (1967) at which the following bubble is affected by the leading bubble is approximately the distance between the centres o f two bubbles, i.e. the sum o f the two bubble diameters. A relation o f coalescence between the bubble position and time is shown as Fig. 2-4. When the distance between two successive bubbles is less than

Chapter Two ■ 3 4 Two b u b b le s S in g le bubble I C o a l e s c e n c e - ^ ! r y 2 » / L y / p ] i / /

I

Q

O Û

O

( T f

[1]

[2]

P]

Figure 2-4 Relation o f bubble coalescence betw een the bubble position and time (reploted from Toei and M atsuno, 1967).

Chapter Two ■ 3 5

the critical distance, bubble coalescence occurs. This distance is greater than that observed by Harrison and Leung (1962). In addition, the velocity o f the leading bubble is greater by up to 10 % than the velocity o f a bubble in isolation. Compared with their model, the experimental results o f the relation between the velocity o f the following bubble, and the distance between the tops o f the two bubbles are higher than the numerical estimate. The deviation was attributed to the elongation o f the following bubble. As for two different sized bubbles, when the initial distance between the bubbles is large, the time required for bubble coalescence increases with decreasing diameter ratio o f the following to the leading bubble. In addition, Toei et al. (1968) found that the following bubble decelerates when it reaches the wake o f the leading bubble. This results was in disagreement with other researchers (e.g. Clift and Grace, 1970).

Clift and Grace (1970) gave a theoretical treatment o f vertical interaction o f 2D and 3D bubbles as well as an experimental study o f bubble coalescence in a 2D bed, and compared it with Toei and M atsuno’s model (1967) using Harrison and Leung’s data (1962) for a 3D fluidized bed. The predictions agree very approximately with the measurements on 2D bubble coalescence except that the separation distance between two bubble noses is less than that from the nose o f the leading bubble to the lower suffice o f the layer o f particles distinguishing the original bubbles, but the model is not expected to account for the motion o f this layer. Alternatively, disagreement with the existence o f the critical distance (Toei and Matsuno, 1967), Clift and Grace (1970) suggested that if the bed is sufficiently deep, the bubbles in vertical alignment will constantly coalesce. For bubble coalescence in a 3D bed, the acceleration o f the leading bubble is much less than in a 2D bed.

For studying the effect o f bubble coalescence on interface mass transfer in 2D beds. Sit and Grace (1981) applied a UV light system to photo the features o f bubble coalescence. During coalescence bubble volumes were found to increase. When two bubbles approach, the leading bubble increased in volume 2.5 times as much as an isolated bubble, and the following bubble increased 3.5 times. As a result, the following bubble grows more than the leading one, so the following bubble becomes

Chapter Two ■ 3 6

larger than the leading one when coalescence occurs. In addition, most o f the mass transfer occurs during pre-coalescence periods, especially for large particles. It was suggested that the throughflow transfer increases.

A capacitance system used for image analysis was developed to investigate the voidage distribution during coalescence in a cylindrical fluidized bed by Halow and Nicoletti (1992). From the image data, the bubble velocities and sizes were also measured. The results showed the relative velocity could be high when two bubbles approached by less than two bubble diameters. During coalescence, the velocity o f following bubble was more than twice the velocity o f leading bubble. This effect occurred where the following bubble was behind the leading bubble around 5 bubble diameters. In other words, the area between two approaching bubbles could be represented as an extensive solid wake, in which voidage was higher than in the emulsion phase at minimum fluidization. From the image data, they found the area between tw o approaching bubbles was like a ‘chaimeF, which connected the two bubbles, and offered a lower resistance path for gas flowing through the bubble. Therefore the following bubble rose along the ‘channel’ and was easily able to overtake the leading bubble. In addition, some types o f coalescence were noticed in their observations which have been described in the previous Section 2.1.

Recently, Yates et al. (1994) employed X-ray attenuation equipment to examine the coalescence o f successive bubbles issuing from a single nozzle in a 3D bed. The results showed that the volume o f the coalesced bubble was some 28% greater than the sum o f the volumes o f the original bubble pair due to the incorporation o f gas from the ‘shell’ which is a zone surrounding a bubble with an intermediate voidage between those o f the bubble void and the emulsion phase. This volume is higher than that found in earlier observations. Grace and Venta (1973) studied the volume changes accompanying bubble splitting in 2D fluidized beds and found that the increased volume o f coalesced bubble was 10-20 % for coalescence o f bubbles in oblique alignment, and was 2-14 % for that in vertical alignment.

Chapter Two ■ 3 7

Some o f the experimental works for bubble coalescence in a pair o f bubbles are summarised in Table 2-2.

(b) Bubbles in Oblique Alignment

In Toei and M atsuno’s (1967) observation, if two equal-size bubbles are arranged in a horizontal level, they rarely coalesce. When one bubble is obliquely below another one, coalescence takes place.

Clift and Grace (1971) found that when bubble coalescence is caused by oblique alignment, the following bubble moves across behind the leading bubble and accelerates in order to coalesce. During the coalescence process, the leading bubble practically rises in a vertical path with a slight horizontal motion because o f the fluctuations o f velocity, therefore the following bubble overtakes the leading one almost in the vertical direction (see Fig. 2-5). When the oblique angle between two bubbles is small, the velocity o f the leading bubble is greater than that o f the following one, and the separation distance between two bubble centres becomes large (Toei and Matsun, 1967). As the oblique angle increases, the velocity o f the following bubble also increases, then the bubble moves towards the leading bubble to coalesce. They also showed that the time required for bubble coalescence in oblique alignment is longer than that in vertical alignment.

Sit and Grace (1981) found the bubble area increases linearly when bubble coalescence in vertical alignment, but in the case o f oblique alignment, the increases o f the bubble area are much scattered.