Critical bubble size

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. 

Fig. 16. Thermal boundary-layer development and critical bubble size for Freon-22 T, = 60°C. [After Henry and Fauske (1975).]...

The dynamic and steady-state characteristics of a shallow fluidized bed combustor have been simulated by using a dynamic model in which the lateral solids and gas dispersion are taken into account. The model is based on the two phase theory of fluidization and takes into consideration the effects of the coal particle size distribution, resistance due to diffusion, and reaction. The results of the simulation indicate that concentration gradients exist in the bed on the other hand, the temperature in the bed is quite uniform at any instant in all the cases studied. The results of the simulation also indicate that there exist a critical bubble size and carbon feed rate above which "concentration runaway" occurs, and the bed can never reach the steady state. 

Figure 4 shows the effect of bubble size on the transient, average carbon concentration. Note that a critical bubble size exists, above which a concentration runaway occurs, i.e., the bed cannot reach a steady state. This is the result of an insufficient rate of oxygen transfer from the bubble phase to the emulsion phase. It can also be seen in the figure that the steady-state average carbon concentration is strongly influenced by the bubble size it increases sharply when the bubble size exceeds a certain value, e.g., 5 cm in this case. 

In Figure 7 the effects of carbon feed rate and bubble size on the steady-state average carbon concentration are shown. The existence of critical bubble size for a fixed carbon feed rate can clearly be observed in this figure. It can also be observed that a critical carbon feed rate exists above which concentration runaway occurs, and a stable or steady-state condition can not be reached for a given bubble size. The value of the critical feed rate increases with a decrease in the bubble size. Under the critical condition, the maximum attainable rate of oxygen transfer from the bubble phase to the emulsion phase is reached, and it becomes the rate determining step for combustion as explained previously. To increase the carbon feed rate to a fluidized bed combustor, either the oxygen concentration in the air (gas) stream or the rate of mass transfer between the bubble and emulsion phase needs to be increased. ... 

The effects of bubble size and specific areas of heat exchangers on the transient average carbon concentration and bed temperature are presented in Figure 9. It can be seen that the critical bubble size is about 5 cm, which is much smaller than that for the type A combustor. This is because of the relatively small excess air rate used and the large carbon concentration gradient... 

Soluble substances exist which can immobilise the surface even of large bubbles present in water at extremely low concentrations. The problem of the effect of residual mobility of a bubble surface loses its meaning if these impurities are contained in water. However, their influence on surface mobility can be hampered at retarded adsorption kinetics. At a given surface tension decrease due to impurities a critical bubble dimension exists. For bubbles exceeding the critical size a residual surface mobility is present. Eq. (10.40) interrelates the critical bubble size with the surface tension drop. On the basis of Eq. (10.45) it was shown that residual mobility is important even for highly contaminated river water at high Reynolds numbers (cf. Section 10.2.7). 

FIG. 3 In this diagram, the Y axis represents AGtotai, and the X axis is the radius of the bubble, in units of r, the critical bubble size. The height of the curve at the point where x = 1, or r = r is the height of the kinetic barrier the system must overcome to undergo the phase change, AG. The curve crosses the X axis at the point r = 1.5r, and this is where the surface term exactly equals the volume term, and AG,otai = 0. 

It is, thus, possible to estimate the critical bubble size marking the transition from a no-slip to a mobile surface using the criterion of Bond and Newton (1928), although the reasons for its success are still somewhat elusive. The abruptness and the magnitude of the jump itself appear to remain unresolved. That is to say, until recently, it was not very clear whether this discontinuity effect was real or an artifact associated with the very sensitive nature of the experimental work, to say contamination for example. 

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