The importance of two-phase flows.
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Air bubble
Two phase flows occurs in many industrial process as chemical, petroleum, nuclear, refrigeration, space, geothermal, etc. In addition they are essential in biochemical processes as glucose-gluconic acid biotransformation, fermentation in bioreactors, biological wastewater, etc.
In spite of the simple design of industrial equipment, the behavoir of gas bubbles is complicated and difficult to predict. Is know that the understanding the behaviour of a single bubble can support a better knowledge of the overall behavior and has been the subject of many studies.
In these studies the bubble diameter and its motion affect the design of mass transfer equipment and the gas injector design is meaningful in the determination of bubbling regimes and their evolution, and bubble diameter and motion can be studied experimentally with high quality results there is only one bubble.
In reality, however the bubbles are generated by porous ceramic stones and pipes or plates with multiples orifices (spargers), flexible membranes, agited tanks or capillary tubes, and of course, complex bubbly flows can result with multiple scales of motion and bubble size.
The need to understand complex bubbly flows is the great importance and has inspired the developed of numerous techniques over last decade that can specify the shape and volume of bubbles.
In many experimental studies the flow regimes are classified with respect to bubble production frequency or air flow rate(Q).
Sato et al. (1979) described three regimes of bubbling: periodic bubbling, dispersed bubble production, and sparking-larger bubble production for those bubbles generated with an electrical field. Similarly, Shin et al. (1997) outlined three bubbling modes—dripping, an erratic mixed mode,and a spray mode. To characterize these bubbling regimes several techniques are used, such as high speed video (Teresaka et al., 2000; Lee et al., 2003; Oliveira and Ni, 2004), impedance tomography (George et al., 2000; Wang et al., 2002; Zenit et al., 2003), pressure transducers (Johnsson et al., 2000; Ruzicka et al., 2000; Barghi et al., 2004; Chilekar et al., 2005), acoustic hydrophone probes (Zukowski 2001; Manasseh et al., 2001, 2004; Vazquez et al., 2005; Al-Masry et al., 2005, 2007), and X-ray emissions (Xie and Tan, 2003; Hulmea and Kantzasa, 2004; Hubersa et al., 2005). However, pressure and acoustic transducers are widely used because of their low price, high resistance to corrosive liquids and their ability to operate at elevated operational temperatures and pressures.
Recently proposed approach for laboratory, field and industrial measurements is passive acoustics which uses the sound produced by the bubble formation to derive the bubble size. This sound is a pulse that originates when bubble inflation leads to appearance of a neck (that connects the bubble’s body to the orifice) that then collapses. Collapse of the air neck drives a bubble breathing mode which causes bubble volume oscillations within a narrow-frequency range band and an exponentially lightly-damped sinusoidal signal. The formation of this sound is characterized by the Minnaert frequency. The Minnaert resonance is the acoustic resonance frequency of a single bubble in an infinite domain of water (neglecting the effects of surface tension and viscous attenuation). The resonant frequency is given by
where f is the frequency (Hz), a is the equivalent bubble radius (the radius assuming the bubble is a spherical volume), PA is the absolute liquid pressure (1X105 Pa), ρ is the liquid density (Kg/m3), γ is the ratio of specific heats for the gas assuming adiabatic compression and expansion, and this relation is valid for millimeter-scale bubbles. The previous relation was created by Marcel Minnaert (below) in 1933 because he was interested in bubbles and musical nature of the sounds made by running water. Marcel Gilles Jozef Minnaert (12 February 1893 – 26 October 1970) was a Dutch astronomer of Belgian origin but he was born in Bruges and died in Utrecht.