Taylor bubble velocity

The acceleration loss, Apa, results from the force needed to accelerate the liquid in the film around the Taylor bubble from its velocity, ULTB, to that of the liquid slug, ULLS. 

In the narrow tubes used by Beek and van Heuven, the bubbles assumed the shape of Dumitrescu (or Taylor) bubbles. Using the hydrodynamics of bubble rise and the penetration theory of absorption, an expression was developed for the total absorption rate from one bubble. The liquid surface velocity was assumed to be that of free fall, and the bubble surface area was approximated by a spherical section and a hyperbola of revolution. Values calculated from this model were 30% above the measured absorption rates. Further experiments indicated that velocities are reduced at the rear of the bubble, and are certainly much less than free fall velocities. A reduction in surface tension was also indicated by extreme curvature at the rear of the bubble. 

The excess velocity of the Taylor bubbles can thus be calculated if the thickness of the liquid film is known from measurement or predictions, which are discussed in the next paragraph. If the liquid film is very thin compared to the tube diameter (as is usually true), the excess velocity will be small, too. 

The capillary pressure will have an effect only at high capillary numbers when the curvatures of the front and rear ends of the Taylor bubble are not symmetrical. At low velocity and in narrow channels, the frictional pressure drop is viscosity-dominant and can be calculated using the Hagen-Poisseuille equation... 

Figure 2 presents three typical flow patterns were observed at narrow annulus, which are the flow with small bubbles whose size is less than a channel width (see Fig. 2a), the flow with large Taylor bubbles (see Fig. 2b) and the flow with the cell structure of liquid plugs, (see Fig. 2c). The flow pattern map is presented on Fig. 3. The first type of the flow is observed at the superficial liquid velocities greater than 2 m/s when the flow becomes turbulent (point 1 and line A in Fig. 3). At such velocities the flow is turbulent and small bubbles...

Data have been presented allowing identification of different flow patterns in a narrow annular channel with a gap less than capillary constant. For large superficial velocities the flow with Taylor bubbles and cell flow regime with liquid plugs are typical. 

The measured bubble velocity is much greater than predicted from equations derived by Davidson and Harrison (D3) and Taylor (T8), respectively ... 

In Table 2.3, empirical correlations for the prediction of the bubble velocity during gas-liquid Taylor flow, as well as the analytical solution of Bretherton (1961) are summarised. 

Qualitative sketches of the flow streamlines in the hquid slug ahead of the bubble have been presented by Taylor [3] (see Fig. 2). These were related to the capillary number, Ca (Ca = where p is the liquid viscosity and U, is the bubble velocity), and to the dimensionless number m, that gives the relative velocity between the bubble and the liquid ... 

Extensive numerical simulations on the formation and channel flow of Taylor bubbles have also been conducted by Qian and Lawal [12] for gas and liquid superficial velocities from 0.01 to 0.25 m/s in a 1 mm capiUaty, for 0.09 < Eg... 

One of the first applications of Taylor bubbles was in flow measurements where the bubbles acted as tracers to determine the velocity of the liquid in the capillaries. Later, however, it was recognized that the presence of the film between the bubble and the wall makes the bubble velocity different from the liquid one. 

The movement of a Taylor bubble through a tubular membrane and the wall shear stress under different conditions Movement of bubbles and shear-stress distributions near the membrane surface at different air velocities of a side-stream MBR... 

David W. Taylor Model Basin, Washington, September 1953 Jackson, loc. cit. Valentin, op. cit.. Chap. 2 Soo, op. cit.. Chap. 3 Calderbank, loc. cit., p. CE220 and Levich, op. cit.. Chap. 8). A comprehensive and apparently accurate predictive method has been publisned [Jami-alahamadi et al., Trans ICE, 72, part A, 119-122 (1994)]. Small bubbles (below 0.2 mm in diameter) are essentially rigid spheres and rise at terminal velocities that place them clearly in the laminar-flow region hence their rising velocity may be calculated from Stokes law. As bubble size increases to about 2 mm, the spherical shape is retained, and the Reynolds number is still sufficiently small (<10) that Stokes law should be nearly obeyed. 

Single gas bubbles in an inviscid liquid have hemispherical leading surfaces and somewhat flattened wakes. Their rise velocity is governed by Bernoulli s theory for potential flow of fluid around the nose of the bubble. This was first solved by G. I. Taylor to give a rise velocity Ug of ... 

The formation of bubbles at orifices in a fluidised bed, including measurement of their size, the conditions under which they will coalesce with one another, and their rate of rise in the bed has been investigated. Davidson el alP4) injected air from an orifice into a fluidised bed composed of particles of sand (0.3-0.5 mm) and glass ballotini (0.15 mm) fluidised by air at a velocity just above the minimum required for fluidisation. By varying the depth of the injection point from the free surface, it was shown that the injected bubble rises through the bed with a constant velocity, which is dependent only on the volume of the bubble. In addition, this velocity of rise corresponds with that of a spherical cap bubble in an inviscid liquid of zero surface tension, as determined from the equation of Davies and Taylor ... 

For large bubbles where inertia effects are dominant, enclosed vertical tubes lead to bubble elongation and increased terminal velocities (G7). The bubble shape tends towards that of a prolate spheroid and the terminal velocity may be predicted using the Davies and Taylor assumptions discussed in Chapter 8, but with the shape at the nose ellipsoidal rather than spherical. The maximum increase in terminal velocity is about 16% for the case where 2 is small (G6) and 25% for a bubble confined between parallel plates (G6, G7) and occurs for the enclosed tube relatively close to the bubble axis. 

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