Rise velocity

If the bed is slugging, bubble motion is retarded by the bed wall, and the bed or tube diameter, Z9, rather than the actual bubble diameter, determines the bubble rise velocity, ie... 

The velocity of a bubble ia a bubbling bed has been observed to be higher than equation 14 predicts, and it has been suggested that the actual bubble rise velocity in a bubbling bed (15) is... 

This empirical equation attempts to account for complex bubble coalescence, spHtting, irregular shapes, etc. Apparent bubble rise velocity in vigorously bubbling beds of Group A particles is lower than equation 16 predicts. 

Studies of individual bubbles rising in a two-dimensional gas—Hquid—soHd reactor provide detailed representations of bubble-wake interactions and projections of their impact on performance (Fig. 9). The details of flow, in this case bubble shapes, associated wake stmctures, and resultant bubble rise velocities and wake dynamics are important in characteri2ing reactor performance (26). 

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. 

The difference between the curves for pure water and seawater again illustrates the significance of small concentrations of solute with respecl to bubble behavior. In commercial bubble columns and agitated vessels coalescence and breakup are so rapid and violent that the rise velocity of a single bubble is meaningless. The average rise velocity can, however, be readily calculated from holdup correlations that will be given later. 

It is often helpful to use the relationship between and superficial gas velocity (t/sg) and the rise velocity of a gas bubble relative to the liquid velocity (U + Ui, with L/l defined as positive upward) ... 

Rise velocities of bubbles through liquids have been discussed previously. 

For a better understanding of the interactions between parameters, it is often helpful to calculate the effective bubble rise velocity from measurea valves of for example, the data of Mersmann (loc. cit.) indicated = 0.6 for = 0.05 iti/s, giving U, = 0.083 m/s, which agrees with the data reported in Fig. 14-43 for the rise velocity of bubble clouds. The rise velocity of single bubbles, for d - 2 mm, is about 0.3 m/s, for liquids with viscosities not too different from water. Using this value in Eq. (14-220) and comparing with Fig. 14-104, one finds that at low values of the rise velocity of the bubbles... 

In design of separating chambers, static vessels or continuous-flow tanks may be used. Care must be taken to protect the flow from turbulence, which coiild cause back mixing of partially separated fluids or which could cany unseparated hquids rapidly to the separated-hquid outlet. Vertical baffles to protect rising biibbles from flow currents are sometimes employed. Unseparated fluids should be distributed to the separating region as uniformly and with as little velocity as possible. When the bubble rise velocity is quite low, shallow tanks or flow channels should be used to minimize the residence time required. 

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 ... 

When the bubble diameter approaches the diameter of the containing vessel, slug flow is said to exist. In such cases, the bubble rise velocity is given by... 

Knowing the bubble rise velocity, the bed expansion can be predicted from a material balance on the bubble phase gas. Thus, total gas flow through the bubble phase equals absolute bubble velocity times the volume fraction E of bubbles in the bed. 

The bubble size at formation varied with particle characteristics. It was further observed that the bubble size decreased with increasing fluidization intensity (i.e., with increasing liquid velocity). The rate of coalescence likewise decreased with increasing fluidization intensity the net rate of coalescence had a positive value at distances from 1 to 2 ft above the orifice, whereas at larger distances from the orifice the rate approached zero. The bubble rise-velocity increased steadily with bubble size in a manner similar to that observed for viscous fluids, but different to that observed for water. An attempt was made to explain the dependence of the rate of coalescence on fluidization intensity in terms of a relatively high viscosity of the liquid fluidized bed. 

Anderson (A2) has derived a formula relating the bubble-radius probability density function (B3) to the contact-time density function on the assumption that the bubble-rise velocity is independent of position. Bankoff (B3) has developed bubble-radius distribution functions that relate the contacttime density function to the radial and axial positions of bubbles as obtained from resistivity-probe measurements. Soo (S10) has recently considered a particle-size distribution function for solid particles in a free stream ... 

In a drop extractor, liquid droplets of approximate uniform size and spherical shape are formed at a series of nozzles and rise eountercurrently through the continuous phase which is flowing downwards at a velocity equal to one half of the terminal rising velocity of the droplets. The flowrates of both phases are then increased by 25 per cent. Because of the greater shear rate at the nozzles, the mean diameter of the droplets is however only 90 per cent of the original value. By what factor will the overall mass transfer rate change ... 

Unlike at adiabatic conditions, the height of the liquid level in a heated capillary tube depends not only on cr, r, pl and 6, but also on the viscosities and thermal conductivities of the two phases, the wall heat flux and the heat loss at the inlet. The latter affects the rate of liquid evaporation and hydraulic resistance of the capillary tube. The process becomes much more complicated when the flow undergoes small perturbations triggering unsteady flow of both phases. The rising velocity, pressure and temperature fluctuations are the cause for oscillations of the position of the meniscus, its shape and, accordingly, the fluctuations of the capillary pressure. Under constant wall temperature, the velocity and temperature fluctuations promote oscillations of the wall heat flux. 

Gas holdup and liquid circulation velocity are the most important parameters to determinate the conversion and selectivity of airlift reactors. Most of the reported works are focused on the global hydrodynamic behavior, while studies on the measurements of local parameters are much more limited [20]. In recent years, studies on the hydrodynamic behavior in ALRs have focused on local behaviors [20-23], such as the gas holdup, bubble size and bubble rise velocity. These studies give us a much better understanding on ALRs. 

Bubble size in the circulating beds increases with Ug, but decreases with Ul or solid circulation rate (Gs) bubble rising velocity increases with Ug or Ul but decreases with Gs the ffequeney of bubbles increases with Ug, Ul or Gs. The axial or radial dispersion coefficient of liquid phase (Dz or Dr) has been determined by using steady or unsteady state dispersion model. The values of Dz and D, increase with increasing Ug or Gs, but decrease (slightly) with increasing Ul- The values of Dz and Dr can be predicted by Eqs.(9) and (10) with a correlation coefficient of 0.93 and 0.95, respectively[10]. 

Silicones exhibit an apparently low solubility in different oils. In fact, there is actually a slow rate of dissolution that depends on the viscosity of the oil and the concentration of the dispersed drops. The mechanisms of the critical bubble size and the reason a significantly faster coalescence occurs at a lower concentration of silicone can be explained in terms of the higher interfacial mobility, as can be measured by the bubble rise velocities. 

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). 

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