Characteristic bubble frequency

The comparison of the two figures shows that the characteristic bubble frequency for ground conditions is two times smaller than that for microgravity conditions. The most probable reason for the decrease of the characteristic bubble frequency under ground conditions is the bubble shape deformation due to gravity on which the characteristic frequency strongly depends. 

Sevik and Park (S9) suggested that resonance can cause bubble and drop breakup in turbulent flow fields when the characteristic turbulence frequency matches the lowest or natural frequency mode of an entrained fluid particle. Breakup in turbulent flow fields is discussed below. 

Bubble Frequency. In estimating the heat transfer characteristics in nucleate boiling, the frequency / at which bubbles of diameter dd depart from a given site is also an important parameter, / is given by... 

The experimental results suggest that empirical correlations of the bubble characteristics and the axial mean velocity and turbulence components of liquid flow, derived from cold model experiments, are applicable to actual reflning processes stirred by bottom gas injection when the radial distributions of gas holdup and bubble frequency follow Gaussian distributions. These distributions appear to be a result of the disintegration of rising bubbles due to highly turbulent liquid motion in the bath. 

The bubble characteristics represented by the bubble frequency, gas holdup, mean bubble rising velocity, and mean bubble chord length were measured at z = 0.050, 0.100, 0.150, and 0.190m with a two-needle electroresistivity probe [14-20]. The inner and outer diameters of the nozzle were 2.0 x 10 and 4.0 x 10 m, respectively, and the distance 7 was 2 x 10 m. The gas flow rate gg was 41.4 X 10 , lOOx 10 , or 293x 10 m /s. Although the measurements were carried out in the r, 9, and z directions, the results obtained on the r — z plane (9 = 0) will be primarily presented to discuss the Coanda effect on an air-water bubbling jet rising near the side wall of a cylindrical vessel. 

In order to compare the experimental results for dual nozzle gas injection system, the two nozzles are removed, and subsequently gas is injected through a single-hole nozzle of inner diameter of 2.0 x 10 m. The center of the nozzle exit is placed at the origin of the coordinate system. The air flow rate is set to 80 x 10 m /s, being equal to the sum of ggi and 0g2. The center of the nozzle is placed at the vertical axis of the vessel. Bubble characteristics represented by gas holdup a, bubble frequency /b, mean bubble rising velocity b, and mean bubble chord length Lb are measured by making use of a two-needle electroresistivity probe [23,37]. 

The bubble characteristics, represented by the bubble frequency /b, gas holdup a, mean bubble rising velocity b, and mean bubble chord length Lb, were measured mainly on the y—z plane with a two-needle electroresistivity probe. Water velocity was measured with a two-channel laser Doppler velocimeter [25], The locations at which measurements were made were chosen by reference to the results for the bubble characteristics. The characteristics of water flow were represented by the vertical mean velocity u, the root-mean-square value of the vertical turbulence component w rms, and the skewness and flatness factors of the vertical turbulence component, and F . Data aquisition time was 600 s for each position. 

Kovalchuk VI, Kragel J, Makievski AV, Ravera F, Liggieri L, Loglio G, Fainerman VB and Miller R (2004). Rheological surface properties of C12DMPO solution as obtained from amplitude- and phase-frequency characteristics of oscillating bubble system. J Colloid Interface Sci 280 498-505... 

Hence we can see from this example of a bubble with weak time-periodic oscillations of volume that the qualitative condition for stability Gk < 0 does not apply unless Gk is constant or only very slowly varying with time (and in the latter case, strictly only for an interval of time that is short compared with the characteristic time scale for variation of Gk ). If the coefficient Gk varies at a rate that is comparable with the natural frequency of shape oscillation for a bubble of constant volume, then the bubble may undergo a resonant oscillation of shape to very large amplitudes even though Gk < 0 for all times. 

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