Terminal rise velocity, bubbles estimation

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 same Fig. 5, two more curves based on experimental data of Gaudin (1977) are given for air-water systems. From this figure, one of the key problems in estimation of terminal bubble rise velocity becomes apparent. For a widely used system such as air-water, if a bubble diameter of 2 mm is taken, the rise velocity can have any value between 150 mm/s and 300 mm/s. Conversely, if we take the terminal rise velocity of bubbles to be 200 mm/s, bubble diameter can be anywhere between 1 and 10 mm, depending upon the degree of contamination, which is difficult to quantify and can change over a period of time. In the present work, we have used correlations of Clift et aL (1978) for the predictions. We also have used the... 

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) ... 

This correlation reqnires information on u, which can be estimated using Equation 10.7. This latter equation requires data on as a function of superficial gas velocity to evaluate the terminal rise velocity of the bubble, These data can be obtained throngh simple gas holdup measurements. The drift flux model of Zuber and Findlay (1965) can be used to obtain as per Equation 10.10 ... 

The method of dynamic gas disengagement (Sriram and Mann, 1977 Patel et al., 1989) to obtain an estimate of bubble size distribution is worthy of mention since it is convenient to use, sometimes even in real systems, especially for lower gas fractions. The impeller is stopped and the trend in the level measured against time. This trend indicates the bubble size distribution if terminal rise velocities are known and if coalescence is negligible. 

Gravity separation occurs try merely reducing die velocity of a stream an that terminal particle settling or rise velocities due to gravity exceed die velocity of the bulk Row. The terminal particle or bubble velocities can be estimated try die methods described in Section 3.1. 

When combined with boundary layer analysis, potential flow theory provides estimates for the velocity of a rising bubble. The lowest-order result for the terminal velocity of a freely rising bubble is... 

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