Taylor bubbles

The hot-wire anemometer can be modified for hquid measurements, although difficulties are encountered because of bubbles and dirt adhering to the wire. See Stevens, Borden, and Strausser, David Taylor Model Basin Rep. 953, December 1956 Middlebrook and Piret, Ind. Eng. Chem., 42, 1511-1513 (1950) and Piret et al., Ind. Eng. Chem., 39, 1098-1103 (1947). 

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 ... 

Bubble-shaped limif flame propagating up moves wifh a velocify defermined by buoyancy forces, like an air bubble in a column of wafer (in bofh cases, fhe Davies and Taylor formula [10] can be applied). 

Davies R.M. and Taylor F.R.S., The mechanism of large bubbles rising through extended liquids and through liquids in tubes, Proc. R. Soc. A, 200 375-390,1950. 

In the design of optimal catalytic gas-Hquid reactors, hydrodynamics deserves special attention. Different flow regimes have been observed in co- and countercurrent operation. Segmented flow (often referred to as Taylor flow) with the gas bubbles having a diameter close to the tube diameter appeared to be the most advantageous as far as mass transfer and residence time distribution (RTD) is concerned. Many reviews on three-phase monolithic processes have been pubhshed [37-40]. 

Sauter mean, as in dSM, Sauter mean diameter subcooled condition superheated condition transition boiling, or Taylor bubble crossflow due to droplet deposition a group of thermodynamic similitude... 

Because the bubble population increases with heat flux, a point of peak flux may be reached in nucleate boiling where the outgoing bubbles jam the path of the incoming liquid. This phenomenon can be analyzed by the criterion of a Hemholtz instability (Zuber, 1958) and thus serves to predict the incipience of the boiling crisis (to be discussed in Sec. 2.4.4). Another hydrodynamic aspect of the boiling crisis, the incipience of stable film boiling, may be analyzed from the criterion for a Taylor instability (Zuber, 1961). 

Figure 3.10 Two types of Taylor bubbles. From Venkateswararao et al., 1982. Copyright 1982 by Elsevier Science Ltd., Kidlington, UK. Reprinted with permission.)...

The basic mechanism for transition from bubble to slug flow appears to be the same as in vertical pipe flow. That is, as the gas flow rate is increased for a given liquid flow rate, the bubble density increases, many collisions occur and cell-type Taylor bubbles are formed, and the transition to slug flow takes place. As shown in the case of vertical pipe upflow, Taitel et al. (1980) assumed that this transition takes place when ac = 0.25. This criterion is also applicable here. However, because of the preferable geometry in the rod bundle, where the bubbles are observed to exist, instead of in the space between any two rods, this void fraction of 0.25 applies to the local preferable area only, a.L. The local voids, aL, can be related to the average void by (Venkateswararao et al., 1982)... 

The liquid in the film alongside the Taylor bubble flows in the opposite direction, with negligible interfacial shear from the gas on the bubble. The average gradient due to friction and acceleration across a slug unit is... 

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. 

The mechanism of alkali-metal atom emission has been discussed by various authors since Taylor and Jarman proposed the model of emission in the gas phase inside bubbles. This mechanism is still under debate and will be discussed in the following section. 

Particles Penetrate Into Bubble Roof Due to Taylor Instability When Penetration Completely Pierces Bubble - Bubble Splits... 

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 ... 

Davies, R. M. and Taylor, G. I. Proc. Roy. Soc. A200 (1950) 375. The mechanics of large bubbles rising through extended liquids and liquids in tubes. 

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. 

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. 

A horizontal interface between two fluids such that the lower fluid is the less dense tends to deform by the process known as Rayleigh-Taylor instability (see Section UFA). Spikes of the denser fluid penetrate downwards, until the interface is broken up and one fluid is dispersed into the other. This is observed, for example, in formation of drops from a wet ceiling, and of bubbles in film boiling. For low-viscosity fluids, the equivalent diameter of the particle formed is of order Ja/gAp. 

When one fluid overlays a less dense fluid, perturbations at the interface tend to grow by Rayleigh-Taylor instability (LI, T4). Surface tension tends to stabilize the interface while viscous forces slow the rate of growth of unstable surface waves (B2). The leading surface of a drop or bubble may therefore become unstable if the wavelength of a disturbance at the surface exceeds a critical value... 

Breakup of water drops due to strong electrical forces has been studied in connection with rain phenomena [e.g. (A4, L8, L9, M4, M7)]. As a strong electrical field is imposed on a freely falling drop, marked elongation occurs in the direction of the field and can lead to stripping of charge-bearing liquid. A simple criterion derived by Taylor (T6) can be used to predict the critical condition for instability. It has also been shown (W6) that soap bubbles can be rendered unstable by electric fields. 

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