Bubble detachment frequency

Decreasing rate of bubble release The mean bubble detachment frequency Af6-1 directly controls the onset of the gas film. For large enough bubbles, such as the infinite cluster, the bubble detachment time Atb becomes so large that the gas film can be formed. Atb is affected by other parameters such as the wetting of the electrode, viscosity and density of the electrolyte, or the local hydrodynamical fluxes. 

As shown in Section 2.2.5.1, a value of C d of 1.5 X 10-4 is recommended for sodium and a value of 4.65 X 10-4 for potassium (because of their respective modified Jakob numbers). Suffice it to say that the relationship between bubble size and detachment frequency in nucleate boiling of liquid metals is not yet well established, even though it is fundamental to a good understanding of such boiling process. 

Malenkov, I. G., 1971, Detachment Frequency as a Function of Size of Vapor Bubbles (transl.), Inzh. 

In the bubble formation from a horizontal surface, the bubble development and the bubble detachment are coupled. When the buoyancy of a developing bubble overcomes the bubble attachment force due to the interfacial tension, the bubble detaches from the surface and completes the process of the bubble formation. A higher flow rate of air in the low flow rate regime (e.g., 0.2-30 seem) simply increases the frequency of the bubble formation but does not change the volume of bubble [1]. 

In the bubble formation from an inclined surface, however, the bubble development and the bubble detachment processes are decoupled because a developing bubble could drift out of the orifice due to the component of the buoyancy parallel to the inclined surface. Once a sessile bubble drift out of the orifice, the bubble development ceases because no air is fed into a sliding bubble. Since the bubble development and detachment are decoupled, the flow rate of air becomes an important factor, which controls the frequency of sliding bubble... 

The diagram of the liquid-vapor phase equilibrium is eharacterized by a decrease in the derivative dp/dT with the polymer concentration (dp/dT —> 0 at k 0). This leads to increase in bofli die nucleation energy and the detachment size of a bubble (equation [7.2.59]) and, consequently, to reduction of the bubbles generation frequency. Note that in reality the critical work, W , for a polymeric liquid may exceed the value predicted by the formula [7.2.59] because of manifestation of the elasticity of macromolecules. 

Equation (46) and the experimental bubble frequency, n= Ijt, were used to predict the expected bubble diameter. The predicted bubble diameters are very close to those actually observed. Theoretically, Eqs. (46) and (48) can be solved to obtain both the bubble frequency and the bubble diameter if the total gas leakage at the moment of bubble detachment, F, is known. The bubble growth equations can be similarly derived for a circular jet in a three-dimensional bed. The same experimental observation and conclusions described above for a semicircular bed are expected to hold as well. Bubble frequency from the jet was also studied using a force probe in the same bed. The results were published in Ettehadieh et al. (1988). 

Janssen and Hoogland (J3, J4a) made an extensive study of mass transfer during gas evolution at vertical and horizontal electrodes. Hydrogen, oxygen, and chlorine evolution were visually recorded and mass-transfer rates measured. The mass-transfer rate and its dependence on the current density, that is, the gas evolution rate, were found to depend strongly on the nature of the gas evolved and the pH of the electrolytic solution, and only slightly on the position of the electrode. It was concluded that the rate of flow of solution in a thin layer near the electrode, much smaller than the bubble diameter, determines the mass-transfer rate. This flow is affected in turn by the incidence and frequency of bubble formation and detachment. However, in this study the mass-transfer rates could not be correlated with the square root of the free-bubble diameter as in the surface renewal theory proposed by Ibl (18). 

While the interfacial tension and the buoyancy of the bubble determine the sliding speed of an attached bubble, the flow rate of air determines the frequency of creating a sliding bubble. Figures 27.12 and 27.14 show the influence of the flow rate of air on the detachment of sliding bubbles on the surface. In the case shown in... 

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