Bubble radius

The final result is very well known in experimental studies and is usually used to evaluate a32 from known and s values. Other studies in this field include the work by Shinnar and Church (S7) who used the Kolmogoroff theory of local isotropy to predict particle size in agitated dispersions, and an analysis by Levich (L3) on the breakup of bubbles. Levich derived an expression for the critical bubble radius (the radius at which breakup begins) ... 

Anderson (A2) has derived a formula relating the bubble-radius probability density function (B3) to the contact-time density function on the assumption that the bubble-rise velocity is independent of position. Bankoff (B3) has developed bubble-radius distribution functions that relate the contacttime density function to the radial and axial positions of bubbles as obtained from resistivity-probe measurements. Soo (S10) has recently considered a particle-size distribution function for solid particles in a free stream ... 

X = 10 4 r0 = initial bubble radius tcou = collapse time scale, for an inviscid fluid, collapse occurs at t = 0.915 xco ... 

These studies consider the dynamics of a single bubble that grows in infinity space, which is filled by superheated liquid. Under these conditions the bubble expansion depends on inertia forces or on intensity of heat transfer. In the case when inertia forces are dominant the bubble radius grows linearly in time (Carey 1992) ... 

When the heat transfer is dominant, bubble radius is directly proportional to the square root of time... 

According to Eq. (6.44) such a behavior may be analyzed using parameter Hi. In the range of Hi = 0.00791—0.0260 linear behavior of the bubble radius was observed, when Hi > 0.0260 exponential bubble growth took place (Fig. 6.24). 

Fig. 6.24 Behavior of bubble radius with time. The values of Hi were calculated from experimental results presented by Lee et al. (2004)...

Dimensional analysis shows that the behavior of the bubble radius with time depends on the parameter TI = qf (plUCpLATs). In the range of 17 = 0.0079-0.026, linear behavior was observed, and when 17 > 0.026 exponential bubble growth took place. 

Fig. 31. Maximum pressures produced throughout the bursting process plotted against bubble radius [118]...

Fig. 32. Maximum energy dissipation rates produced throughout the bursting process, plotted against bubble radius. The logarithmic scale indicates an exponential dependence of maximum stress on bubble radius for large bubbles. The slight drop in the data point for the smallest bubble as compared to the next smallest may be because of the difficulty in locating the exact place and time of the peak, due to large spatial and temporal gradients beneath the forming jet [113]...

Figure 9. Bubble radius and pressure transients of the water vapor inside the bubbles. The first maximum in pressure at 650 ps marks the collapse of the bubbles. The following modulations are only expected for oscillatory bubble motion.

The maximum bubble radius occurs when dRIdt = 0 at time t = tm, where... 

Bubble growth occurs rapidly and is followed by a period when the bubbles radius remains relatively constant. Bubbles do not grow and collapse on the wall, but start to slide away from their nucleation sites almost immediately after nucleation. 

Figure 3. Schematic of matching to the spherical cap at the bubble front. The radius of the flow-altered sphere is For a static bubble, the bubble radius is R. ...

In Fig. 1.1, the parameter space for transient and stable cavitation bubbles is shown in R0 (ambient bubble radius) - pa (acoustic amplitude) plane [15]. The ambient bubble radius is defined as the bubble radius when an acoustic wave (ultrasound) is absent. The acoustic amplitude is defined as the pressure amplitude of an acoustic wave (ultrasound). Here, transient and stable cavitation bubbles are defined by their shape stability. This is the result of numerical simulations of bubble pulsations. Above the thickest line, bubbles are those of transient cavitation. Below the thickest line, bubbles are those of stable cavitation. Near the left upper side, there is a region for bubbles of high-energy stable cavitation designated by Stable (strong nf0) . In the brackets, the type of acoustic cavitation noise is indicated. The acoustic cavitation noise is defined as acoustic emissions from... 

Fig. 1.1 The regions for transient cavitation bubbles and stable cavitation bubbles when they are defined by the shape stability of bubbles in the parameter space of ambient bubble radius (R0) and the acoustic amplitude (p ). The ultrasonic frequency is 515 kHz. The thickest line is the border between the region for stable cavitation bubbles and that for transient ones. The type of bubble pulsation has been indicated by the frequency spectrum of acoustic cavitation noise such as nf0 (periodic pulsation with the acoustic period), nfo/2 (doubled acoustic period), nf0/4 (quadrupled acoustic period), and chaotic (non-periodic pulsation). Any transient cavitation bubbles result in the broad-band noise due to the temporal fluctuation in the number of bubbles. Reprinted from Ultrasonics Sonochemistry, vol. 17, K.Yasui, T.Tuziuti, J. Lee, T.Kozuka, A.Towata, and Y. Iida, Numerical simulations of acoustic cavitation noise with the temporal fluctuation in the number of bubbles, pp. 460-472, Copyright (2010), with permission from Elsevier...

Fig. 1.4 The calculated results for one acoustic cycle when a bubble in water at 3 °C is irradiated by an ultrasonic wave of 52 kHz and 1.52 bar in frequency and pressure amplitude, respectively. The ambient bubble radius is 3.6 pm. (a) The bubble radius, (b) The dissolution rate of OH radicals into the liquid from the interior of the bubble (solid line) and its time integral (dotted line). Reprinted with permission from Yasui K, Tuziuti T, Sivaknmar M, Iida Y (2005) Theoretical study of single-bubble sonochemistry. J Chem Phys 122 224706. Copyright 2005, American Institute of Physics...

The amplitude of oscillation of cavity/bubble radius, which is reflected in the magnitude of the resultant pressure pulses of the cavity collapse... 

Whereas the amount of gas in the system influences the extent of bubble-bubble coalescence and, in turn, the bubble radius, the composition of the gas atmosphere within the bubble plays a crucial role in determining the conditions of collapse. 

Fig. 14.8 Bubble radius as a function of the dissolved gas concentration for a solution of argon-saturated NaCl under sonication at 515 kHz (data adapted from reference [41])...

The dynamic process of bubble collapse has been observed by Lauter-born and others by ultrahigh speed photography (105 frames/second) of laser generated cavitation (41). As seen in Fig. 4, the comparison between theory and experiment is remarkably good. These results were obtained in silicone oil, whose high viscosity is responsible for the spherical rebound of the collapsed cavities. The agreement between theoretical predictions and the experimental observations of bubble radius as a function of time are particularly striking. 

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