Frequency of bubble formation

To illustrate, consider the hmiting case in which the feed stream and the two liquid takeoff streams of Fig. 22-45 are each zero, thus resulting in batch operation. At steady state the rate of adsorbed carty-up will equal the rate of downward dispersion, or afV = DAdC/dh. Here a is the surface area of a bubble,/is the frequency of bubble formation. D is the dispersion (effective diffusion) coefficient based on the column cross-sectional area A, and C is the concentration at height h within the column. 

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). 

A common dimensionless number used to characterize the bubble formation from orifices through a gas chamber is the capacitance number defined as Nc — 4VcgpilnDoPs. For the bubble-formation system with inlet gas provided by nozzle tubes connected to an air compressor, the volume of the gas chamber is negligible, and thus, the dimensionless capacitance number is close to zero. The gas-flow rate through the nozzle would be near constant. For bubble formation under the constant flow rate condition, an increasing flow rate significantly increases the frequency of bubble formation. The initial bubble size also increases with an increase in the flow rate. Experimental results are shown in Fig. 6. Three different nozzle-inlet velocities are used in the air-water experiments. It is clearly seen that at all velocities used for nozzle air injection, bubbles rise in a zigzag path and a spiral motion of the bubbles prevails in air-water experiments. The simulation results on bubble formation and rise behavior conducted in this study closely resemble the experimental results. 

In these methods the volumetric flow corrected to the nozzle tip, Q, and the frequency of bubble formation, /, are directly measured. The bubble volume is then calculated. These methods have a number of limitations. 

Reservoir method This method makes use of the displacement principle. Brine or any other saturated solution in which a gas has low solubility is used as the liquid. Gas from the column is collected in a burette from which the displaced liquid flows to a reservoir. As the gas collection proceeds, the gas is collected under increasing pressure conditions, thereby changing the flow rate as well as the frequency of bubble formation. In order to collect gas under atmospheric conditions, the levels of the liquid in the burette and the reservoir must always be kept equal. This requires manual adjustments. 

When the frequency of bubble formation is very low (<200 bubbles per minute), the bubbles can be visually counted without the aid of any instrument. When the frequency is higher than this, other methods have to be employed. 

Calderbank (Cl) employed a crystal microphone located in the gas supply line near the nozzle tip, which was connected to an oscilloscope through a preamplifier. The photographic comparison of this signal with a constant-frequency (60 cps in this case) test signal, yielded the frequency of bubble formation. 

The signal, amplified to a good sound level at the loudspeaker, is fed to the vertical input of the oscilloscope. A stationary trace is obtained on the oscilloscope. The frequency of the sine wave of the oscilloscope is varied until a single trace is obtained. This frequency is then equal to the frequency of bubble formation. 

Deviations from the theories tend to occur at large Q where the frequency of bubble formation becomes essentially independent of Q, whereas theory predicts / oc For example, the frequency in air-water systems levels out... 

Very little is iaiown about the effects of wettability of a plate on bubble and molten metal flow characteristics except for the frequency of bubble formation, /b [20-22], These studies have shown that the frequency of bubble formation from a single-hole nozzle or a porous nozzle that is not wetted by the liquid is significantly different from that from a single-hole nozzle of good wettability. This result suggests that the bubble and liquid flow characteristics near a vertical flat plate would... 

Iguchi M, Chihara T (1998) Water model study of the frequency of bubble formation under reduced and elevated pressures, Metall Mater Trans B 298 755-761... 

---