Bubble formation frequency

A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. 

The design of a maximum bubble pressure method for high bubble formation frequencies must address three main problems the measurement of bubble pressure, the measurement of bubble formation frequency, and the estimation of surface lifetime and effective surface age. 

The first problem can be solved easily if the system volume, which is connected with the bubble, is big enough in comparison with the volume of the bubble separating from the capillary. In this case the system pressure is equal to the maximum bubble pressure. On the contrary, the use of an electric pressure transducer for measuring the bubble formation frequency presumes that pressure oscillations in the measuring system are distinct enough. This condition is fulfilled in systems with comparatively small volumes only. As shown by Mysels... 

Relatively new are the developments of microfluidic surface or interfacial tension methods. Such methods offer the potential for rapid, online measurements on small volume samples. Typically, use is made of a property change (such as droplet deformation or pressure drop) associated with fluid flow through some kind of constriction in a microchannel. The fundamental principles are usually the same as in the examples just given above, such as shape or pressure changes. If the device is used to generate bubbles, then the bubble formation frequency can be used as the basis for surface tension calculation. In a multiple-channel device, multiple bubbles or droplets are usually sensed simultaneously. These kinds of approaches have been applied to the determination of both surface and interfacial tensions [20-22]. 

The asterisks refer to the corresponding parameters in the critical point. Therefore, the dead time in the critical point L (shown by an arrow in Fig. 16) for the capillary employed is 11.0 and 11.5 ms for water and the C12DMPO solution, respectively. The lines calculated from Eq. (49) agree quite well with the measured values. At the same time, the results indicate that the minimum dead time determined from gas flow oscillations is about 1 ms lower than the calculated value. This difference results from the hydrodynamic effects which occur at high bubble formation frequencies and are considered so far only in the software of the BPA. At a fixed bubble volume, any increase of the capillary radius results in a decrease of the dead time, and vice versa. 

The bubble formation frequency is equal to the number of unit cells passing a certain location in the channel per unit of... 

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). 

Bubble Dynamics. To adequately describe the jet, the bubble size generated by the jet needs to be studied. A substantial amount of gas leaks from the bubble, to the emulsion phase during bubble formation stage, particularly when the bed is less than minimally fluidized. A model developed on the basis of this mechanism predicted the experimental bubble diameter well when the experimental bubble frequency was used as an input. The experimentally observed bubble frequency is smaller by a factor of 3 to 5 than that calculated from the Davidson and Harrison model (1963), which assumed no net gas interchange between the bubble and the emulsion phase. This discrepancy is due primarily to the extensive bubble coalescence above the jet nozzle and the assumption that no gas leaks from the bubble phase. 

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. 

First, they cannot be used for the evaluation of volumes of individual bubbles. Only an average bubble volume is obtained. Bubble formation is generally a cyclic phenomenon, and for a definite flow rate in a particular system, the frequency and the bubble volume are time-independent. However, there are situations where each bubble is followed by smaller secondary bubbles. In such cases, the above methods cannot yield reliable values and photographic methods have to be resorted to. 

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. 

The simplest instrument that finds extensive use is the strobotac which illuminates the object at varying frequencies. When the frequency of the strobotac flash coincides with that of bubble formation, the image of the bubble appears to be stationary. This method is evidently useful only when the system is transparent. 

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. 

Krishnamurthi, Kumar, and Datta (K7) employed a circular orifice of arbitrarily chosen dimensions as the standard, and constructed two sets of noncircular orifices having either the perimeter or the area equal to that of the standard orifice. The configurations chosen were an equilateral triangle, a square, and a rectangle. The system used by these authors was air-water, and their studies were confined to extremely small flow rates (<0.5 cm3/sec). Their results indicate that noncircular orifices do not utilize their entire perimeter for bubble formation, and, for equi-sided orifices at low frequencies of formation, the bubble is formed as if from a circle inscribed in the noncircular orifice. In this range, the perimeter and the area are important in determining the final bubble size. 

Availability change to form embryo Initial bubble diameter Frequency factor in nucleation Enthalpy of vaporization Rate of formation of critical-sized embryos per unit volume Jacob numter [Eq. (17)] Boltzmann s constant or thermal conductivity... 

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