Rectified diffusion

There are two mechanisms in growth of a bubble in acoustic cavitation [14], One is coalescence of bubbles. The other is the gas diffusion into a bubble due to the area and shell effects described before. This is called rectified diffusion. 

Relative importance of coalescence and rectified diffusion in the bubble growth is still under debate. After acoustic cavitation is fully started, coalescence of bubbles may be the main mechanism of the bubble growth [16, 34], On the other hand, at the initial development of acoustic cavitation, rectified diffusion may be the main mechanism as the rate of coalescence is proportional to the square of the number density of bubbles which should be small at the initial stage of acoustic cavitation. Further studies are required on this subject. 

Lee J, Kentish S, Ashokkumar M (2005) Effect of surfactants on the rate of growth of an air bubble by rectified diffusion. J Phys Chem B 109 14595-14598... 

Louisnard O, Gomez F (2003) Growth by rectified diffusion of strongly acoustically forced gas bubbles in nearly saturated liquids. Phys Rev E 67 036610... 

The bubble formed in stable cavitation contains gas (and very small amount of vapor) at ultrasonic intensity in the range of 1-3 W/cm2. Stable cavitation involves formation of smaller bubbles with non linear oscillations over many acoustic cycles. The typical bubble dynamics profile for the case of stable cavitation has been shown in Fig. 2.3. The phenomenon of growth of bubbles in stable cavitation is due to rectified diffusion [4] where, influx of gas during the rarefaction is higher than the flux of gas going out during compression. The temperature and pressure generated in this type of cavitation is lower as compared to transient cavitation and can be estimated as ... 

Fig. 3. Thresholds of cavitation. Region A Bubble growth through rectified diffusion only. Region B Bubble growth through transient cavitation. RD, Threshold for rectified diffusion Rlt threshold for predomination of inertial effects RB, Blake threshold for transient cavitation. [After R. E. Apfel (S).]...

The qualitative understanding of the process of rectified diffusion may be obtained from consideration of three effects of cavity pulsation ... 

The character of cavitation bubbles pulsation as well as the conditions of rectified diffusion of hydrogen inside a cavity allow us to confirm the supposition that the cavitation threshold for liquid aluminum and magnesium is 0.65 to 1.0 MPa at a frequency of 18 kHz. 

At low ultrasound intensities, bubble growth primarily occurs via rectified diffusion, which is the unequal mass transfer of species into the bubble during rarefaction and compression cycles. This phenomenon was first recognized by Harvey et al. during their experiments on animals, and Leighton has recently expounded on a well established theory that describes rectified diffusion in terms of an area effect and a shell effect. These two effects derive directly from basic mass transfer principles, which demonstrate that the rate of mass transfer is directly related to the surface area across which transfer can occur and the concentration (or more exactly, chemical potential) driving force. 

Fig. 3 Concentration profiles for species in the gas and liquid phases of a microbubble undergoing rectified diffusion the shell effect.

Various mathematical models have been put forth to describe the rate of bubble growth and the threshold pressure for rectified diffusion.f ° The most widely used model quantifies the extent of rectified diffusion (i.e., the convection effect and bubble wall motion) by separately solving the equation of motion, the equation of state for the gas, and the diffusion equation. To further simplify the derivation, Crum and others made two assumptions 1) the amplitude of the pressure oscillation is small, i.e., the solution is restricted to small sinusoidal oscillations, and 2) the gas in the bubble remains isothermal throughout the oscillations.Given these assumptions, the wall motion of a bubble in an ultrasonic field with an angular frequency of co = 2nf can be described by the Rayleigh-Plesset equation ... 

Eller, A. Flynn, H.G. Rectified diffusion during nonlinear pulsations of cavitation bubbles. J. Acoust. Soc. Am. 1965, 37 (3), 493-503. 

A more illustrative description of the bubble motion in an acoustic field can be introduced by the concept of cavitation thresholds for different types of bubble behavior. Depending on the nature of the motion four basic types of cavitating voids are distinguished stable cavitation, rectified diffusion, dissolving bubbles, and transient cavitation. 

The upper size limit is made up by the transient cavitation threshold. Smaller bubbles may exist as stable oscillating bubbles that eventually grow in size by rectified diffusion or their path into regions with higher sound pressures. Bigger bubbles than this will collapse and create smaller daughter bubbles. The bubble size Rq is rather small and is of the order of several micrometers. 

Rectified diffusion due to alternating compression and rarefaction (Muralidhara and Ensminger, 1986 Muralidhara et al., 1986). 

The situation for the gas content is different. Observation shows that a bubble pulsating under the stable cavitation regime grows progressively. This phenomenon, rectified diffusion, requires two contributions the area and the shell effects. The area effect takes into consideration the fact that during the contraction phase, the gas inside is at a pressure higher than the equilibrium value and consequently diffuses from the bubble. During expansion, the pressure within the cavity is less than the equilibrium value, so that some gas diffuses into... 

Figure 11 - The shell ejfect of rectified diffusion (a) bubble at equilibrium surrounded by a liquid shell (b) expanding bubble (c) shrinking bubble...

Rectified diffusion was first recognized by Harvey et al The basic idea behind the theoretical treatment consists in coupling Tick s law of mass transfer and the equation of motion. After the preliminary attempt by Blake, who only considered the area effect, the shell effect was included, nd then different improvements were effected. Crum gave a comprehensive paper on the topic, and experimental studies were reported by Strasberg, and Gould. A summarized theoretical description was reported by Atchley and Crum. ... 

However, a bubble cannot grow indefinitely. Several developments are possible, the first of which consists of the rise of the bubble to the surface because of the buoyancy force (degassing process). The second is the development of non-radial oscillations in the bubble as soon as its radius approaches or reaches the resonance value. This leads to microstreaming which, in turn, influences rectified diffusion and favors the transfer of the liquid in the vicinity of the bubble. This type of behavior is given in Fig. 13. A third possibility is associated... 

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