Liquids, terminal bubble velocity

The mass transfer coefficient is expected to relate gas power per unit volume and gas terminal velocity. Measurement of gas bubble velocity is troublesome in the experimental stage of aeration. Extensive research has been conducted for an explanation of the above correlation. Gas-liquid mass transfer in low viscosity fluids in agitated vessels has been reviewed and summarised as stated in (3.5.1.7)—(3.6.2) 3... 

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.

In these equations, a is the specific interfacial area for a significant degree of surface aeration (m2/m3), I is the agitator power per unit volume of vessel (W/m3), pL is the liquid density, o is the surface tension (N/m), us is the superficial gas velocity (m/s), u0 is the terminal bubble-rise velocity (m/s), N is the impeller speed (Hz), d, is the impeller diameter (m), dt is the tank diameter (m), pi is the liquid viscosity (Ns/m2) and d0 is the Sauter mean bubble diameter defined in Chapter 1, Section 1.2.4. 

Figure 4.10 displays a typical vertical vessel program run printout. The program calculation output gives a minimum required diameter. This diameter is based on the terminal velocity of liquid drop fall velocity, gas bubble in oil rise velocity, or the water drop fall velocity. The smaller this terminal velocity, the greater the vessel cross-section area required and thus the greater the vessel diameter required. In this example, the oil-phase gas bubble rise terminal velocity is controlling. If you reduce the oil flow to, say, 10,000 lb/h, then the gas-phase liquid... 

In bubble columns, the estimation of parameters is more difficult than in the case of either gas-solid or solid-liquid fluidized beds. Major uncertainties in the case of bubble columns are due to the essential differences between solid particles and gas bubbles. The solid particles are rigid, and hence the solid-hquid (or gas-solid) interface is nondeformable, whereas the bubbles cannot be considered as rigid and the gas-liquid interface is deformable. Further, the effect of surface active agents is much more pronounced in the case of gas-liquid interfaces. This leads to uncertainties in the prediction of all the major parameters such as terminal bubble rise velocity, the relation between bubble diameter and terminal bubble rise velocity, and the relation between hindered rise velocity and terminal rise velocity. The estimation procedure for these parameters is reviewed next. 

In the first alternative, if the terminal rise velocity of gas bubbles is known (or can be estimated with confidence), the top surface of the dispersion may be defined as an inlet . Normal liquid velocity may be set to zero while normal gas velocity may be set to terminal rise velocity. The implicit assumption here is that gas bubbles escape the dispersion with terminal rise velocity. It should be noted that even after defining the top surface as an inlet, gas volume fraction at the top surface is a free variable. There is no implicit forcing of gas volume fraction distribution. Alternatively, the top surface of the dispersion can be modeled as a no shear wall. This will automatically set normal liquid velocity to zero. It will also set normal gas velocity to zero. In order to represent escaping gas bubbles, an appropriate sink may be defined for all the computational cells attached to the top surface (Figure 11.7) ... 

As discussed in Chap. 7, bubbles change in shape from spherical to ellipsoidal to lens-shaped as their diameter increases. Larger bubbles often rise in spiral paths, at terminal velocities that are almost constant and independent of their size (see Fig. 7.8). In clouds or swarms of bubbles there may be considerable coalescence the rate of rise of clouds of small bubbles is considerably less than that of single bubbles if the bubbles are distributed uniformly over the cross section of the vessel. A cloud of bubbles rising at one location creates an upflow of liquid, and this chimney effect may greatly increase the bubble velocity. 

High viscosity of a sonicated liquid lowers the cavitation threshold markedly. Viscous liquids generate bubbles only at high sound pressures. Bubble motion is damped by the dissipative effect of the viscosity and the smaller maximum bubble radii, and the lower inward wall velocities terminate most sonochemical effects. 

Re Reynolds number (pU Djr ) Velocity of the liquid phase, m/s Bubble terminal rise velocity Relative velocity of bubbles to the surrounding liquid, m/s V Bubble volume, m ... 

Determination of gas hold-up from Equation 26 requires a knowledge of the superficial liquid circulation rate, given by Equation 9 and the single bubble terminal rise velocity Most researchers have used = 0.25 msThe gas holdup and liquid circulation data in 250 L pilot-scale internal-loop airlift bioreactor for Saccharopolyspora erythmea (n = 0.55) were satisfactorily correlated by this model. 

GAS ABSORPTION AND GAS-LIQUID SYSTEM DESIGN TABLE 14-22 Terminal Velocity of Standard Air Bubbles Rising in Water at 20 C ... 

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