Slip velocity, bubble

For various flow regimes, they used the terminal bubble rise velocity as the local bubble slip velocity. 

In conclusion, for a homogeneously bubbling bed, the velocity of bubble rise Mb relative to the bed wall is equal to or lower than the bubble slip velocity relative to the continuous phase. 

For single bubbles u is the bubble velocity, for bubble swarms u is the bubble/(slip velocity), v is the kinematic viscosity (length) / , and D the molecular diffusivity (length) /1. 

As remarked earlier, because in-line static mixers are plug flow devices, the gas fraction is comparatively easy to determine from the ratio of mean gas flow rate to total flow rate, with adjustment for bubble slip if the flow orientation is nonhorizontal. Often, vertical downflow is preferred, since the gas-buoyancy leads to the bubble velocity being less than the liquid velocity, so the gas fraction (and hence the gas-liquid interface area) is greater than for other configurations. While there is much literature on bubble slip velocities, the predictions are said to be unreliable (Zuber and Findlay, 1965) and it is usually preferred to use empirical correlations of the gas fraction based on measurements [such as those in Middleton (1978)], although so far these all seem to be for air-water systems with negligible depletion of bubble size, so may need adjustment for other systems. 

Ghatage SV, Sathe MJ, Doroodchi E, Joshi JB, Evans GM Effect of turbulence on particle and bubble slip velocity, Chem Eng Sd 100 120-136, 2013. http //dx.doi.0rg/lO.lOl6/j. ces.2013.03.031. 

In the riser, baffles are placed at intervals to break up bubbles by increasing turbulence and shear. At the top erf the riser the expanded section decreases the upward flow rate of the medium and this, together with the lack of baffles, decreases turbulence and shear, which in turn promotes coalescence of bubbles. Larger bubbles form which have increased slip velocity, so they more easily disengage from the medium. 

Thus, if the gas is injected in the form of small dispersed bubbles in order to reduce the slip velocity, coalescence rapidly occurs to give large bubbles and slugs. 

Fig. 3a indicates that the bubble-rise velocity measured based on the displacement of the top surface of the bubble ( C/bt) quickly increases and approaches the terminal bubble rise velocity in 0.02 s. The small fluctuation of Ubt is caused by numerical instability. The bubble-rise velocity measured based on the displacement of the bottom surface of the bubble (Ubb) fluctuates significantly with time initially and converges to Ubt after 0.25 s. The overshooting of Ubb can reach 45-50 cm/s in Fig. 3a. The fluctuation of Ubb reflects the unsteady oscillation of the bubble due to the wake flow and shedding at the base of the bubble. Although the relative deviation between the simulation results of the 40 X 40 x 80 mesh and 100 x 100 x 200 mesh is notable, the deviation is insignificant between the results of the 80 x 80 x 160 mesh and those of the 100 X 100 x 200 mesh. The agreement with experiments at all resolutions is generally reasonable, although the simulated terminal bubble rise velocities ( 20 cm/s) are slightly lower than the experimental results (21 25 cm/s). A lower bubble-rise velocity obtained from the simulation is expected due to the no-slip condition imposed at the gas-liquid interface, and the finite thickness for the gas-liquid interface employed in the computational scheme.

Bakker increased the local values of e as obtained with FLUENT by a contribution related to the slip velocity of the bubbles. Working with a single... 

For many dispersed systems (gas bubbles in liquids, liquid droplets in another liquid, solid particles in a liquid), it has been found that the slip velocity is related to the terminal velocity u, of a single bubble, droplet or particle by the equation... 

Further, one can define a slip-velocity ratio, to show the difference between the mean true bubble velocity and the mean true liquid velocity ... 

Since the velocity of a given phase in the bubble column usually differs from the other phases, the volumetric flow rate fraction of that phase is not equal to its corresponding holdup, and hence the slip velocity is introduced to account for this difference ... 

Vasconcelos variant of the slip velocity model based on bubble contamination kinetics, Eqs. (4)-(8), was used by Alves et al. [9] to interpret kl data in a double Rush-ton turbine-stirred tank. The application of Vasconcelos model to the interpretation of unreliable mass transfer co-... 

Chen8,9 studied the gas holdup of a 7-cm i.d. 244-cm long column randomly packed with open-end screen cylinders of various sizes (1.27 cm x 1.27 cm and 1.9 cm x 1.9 cm) and screen meshes (8-14 mesh). The results with an air-water system were obtained in the bubble-flow regime. The screen cylinders were found to reduce the gas holdup. The results showed that for t/0g < 4 cm s, the gas holdup was a linear function of gas velocity, a result similar to the one obtained in an unpacked bubble-column bul not in a column packed with Raschig rings or other conventional packings. He also showed that for low gas velocity, l/0G < 3.64 cm s 1 the parameter (hG - 1ig)//ig was a unique linear function of liquid velocity (independent of gas velocity). Here, /iG is the gas holdup at zero liquid velocity. He also obtained a relationship between the gas holdup and the slip velocity between gas and liquid. All the data were graphically illustrated, however, no analytical correlation was presented. 

Imafuku et al.46 measured the gas holdup in a batch (i.e., no liquid flow) three-phase fluidized-bed column. They found that the presence of solids caused significant coalescence of bubbles. They correlated the gas holdup with the slip velocity between the gas and liquid. They found that the gas holdup does not depend upon the type of gas distributor or the shape of the bottom of the column when solid particles are completely suspended. Kato et al.53 found that the gas holdup in an air-water-glass sphere system was somewhat less than that of the air-water system and that the larger solid particles showed a somewhat smaller... 

Yashitome et al.148 studied the mass transfer from single samples of benzoic acid suspended in an air-water bubble-column. Spherical, cylindrical, and diskshaped samples were used. The diameters of the particles (ranging from 25 through 75 mm) were considerably larger than the catalyst sizes normally used in gas-liquid-solid catalytic slurry operation. The data were correlated using the slip velocity theory. 

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... 

In the presence of a surfactant (Terpineol), Rice et al. (2) obtained a very good fit between theory and experiment using ( )( ) = (l- ) which is the Wallis model with n = 2. In the work cited, average bubble size was around 1 mm diameter. This particular structure shows, according to equation (3), that the slip velocity approaches terminal rise velocity as voidage becomes small, as one expects. 

Various model parameters involved in the derivation of the stability criterion need to be specified in order to use the stability criterion for quantitative predictions. Model parameters essential for this purpose include the slip velocity, the virtual mass coefficient, and the dispersion coefficient. The procedure for estimation of these parameters is given for gas-solid (and solid-liquid) fluidized beds and bubble columns. 

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