Cavitation Diffusion

This type of damage is dealt with comprehensively in Section 8.8. It can be particularly severe in seawater giving rise to cavitation corrosion or cavitation erosion mechanisms, and hence can be a considerable problem in marine and offshore engineering. Components that may suffer in this way include the suction faces of propellers, the suction areas of pump impellers and casings, diffusers, shaft brackets, rudders and diesel-engine cylinder liners. There is also evidence that cavitation conditions can develop in seawater, drilling mud and produced oil/gas waterlines with turbulent high rates of flow. 

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. 

Acoustic cavitation increases a rate of mass transfer toward or from a solid surface. When a solute gradually diffuses onto a solid surface as in the case of electrolysis, a diffusion layer is formed near the solid surface in which the concentration of a solute changes from the saturated one at the solid surface to nearly the ambient one at the edge of the layer. A similar diffusion layer is formed when the solid material gradually dissolves into the liquid. Acoustic cavitation makes a diffusion layer... 

Transient cavitation is generally due to gaseous or vapor filled cavities, which are believed to be produced at ultrasonic intensity greater than 10 W/cm2. Transient cavitation involves larger variation in the bubble sizes (maximum size reached by the cavity is few hundred times the initial size) over a time scale of few acoustic cycles. The life time of transient bubble is too small for any mass to flow by diffusion of the gas into or out of the bubble however evaporation and condensation of liquid within the cavity can take place freely. Hence, as there is no gas to act as cushion, the collapse is violent. Bubble dynamics analysis can be easily used to understand whether transient cavitation can occur for a particular set of operating conditions. A typical bubble dynamics profile for the case of transient cavitation has been given in Fig. 2.2. By assuming adiabatic collapse of bubble, the maximum temperature and pressure reached after the collapse can be estimated as follows [2]. 

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).]...

Transient cavitation bubbles are voids, or vapour filled bubbles, believed to be produced using sound intensities in excess of 10 W cm. They exist for one, or at most a few acoustic cycles, expanding to a radius of at least twice their initial size, (Figs. 2.16 and 2.20), before collapsing violently on compression often disintegrating into smaller bubbles. (These smaller bubbles may act as nuclei for further bubbles, or if of sufficiently small radius (R) they can simply dissolve into the bulk of the solution under the action of the very large forces due to surface tension, 2a/R. During the lifetime of the transient bubble it is assumed that there is no time for any mass flow, by diffusion of gas, into or out of the bubble, whereas evaporation and condensation of liquid is assumed to take place freely. If there is no gas to cushion the implosion... 

Clarkson et al. (1986) conclude that proteolytic enzymes contribute to root lesion formation. Accordingly, Katz et al. (1987) found root cavitation with loss of matrix to occur in mild acidic solutions only in the presence of proteases. It is conceivable that the degradation of the matrix promotes the formation of a root lesion in two ways. First, the matrix forms a barrier to ionic diffusion, which is removed by degradation. Second, the degradation of the matrix yields nutrients, which may sustain the growth of cariogenic bacteria (Hojo et al., 1991). 

Fig. 8.1. Toughening mechanisms in rubber-modified polymers (1) shear band formation near rubber particles (2) fracture of rubber particles after cavitation (3) stretching, (4) debonding and (5) tearing of rubber particles (6) transparticle fracture (7) debonding of hard particles (8) crack deflection by hard particles (9) voided/cavitated rubber particles (10) crazing (II) plastic zone at craze tip (12) diffuse shear yielding (13) shear band/craze interaction. After Garg and Mai (1988a).

When ultrasound is used as energy carrier, a sound intensity in the range from 5-10 W cm-2 is employed. This energy is sufficient to heat the material up to or even above its melting point. As a result, the diffusion velocity of the free radicals in turn increased. In addition, in the fluid phase of the matrix, sonochemical reactions are possible, based on cavitation. Such cavitation is associated with... 

The chemical effects of ultrasound do not arise from a direct interaction with molecular species. Ultrasound spans the frequencies of roughly 15 kHz to 1 GHz. With sound velocities in liquids typically about 1500 m/s, acoustic wavelengths range from roughly 10 to 10 4 cm. These are not molecular dimensions. Consequently, no direct coupling of the acoustic field with chemical species on a molecular level can account for sonochemistry or sonoluminescence. Instead, sonochemistry and sonoluminescence derive principally from acoustic cavitation, which serves as an effective means of concentrating the diffuse energy of sound. 

According to the hot-spot theory (Neppiras Noltingk 1950), the homogeneous ultrasound reaction takes place in the collapsing cavitation bubble and in the superheated (ca. 2,000 K) liquid shell around it. Species with sufficient vapor pressure diffuse into the cavity, where they undergo the effect of adiabatic collapse. 

It seems that the cavities enclose a vapor of the solute because of the high vapor pressure of these compounds. The primary reaction pathway for these compounds appears to be the thermal dissociation in the cavities. The activation energy required to cleave the bond is provided by the high temperature and pressure in the cavitation bubbles. This leads to the generation of radicals such as hydroxyl radical, peroxide radical, and hydrogen radical. These radicals then diffuse to the bulk liquid phase, where they initiate secondary oxidation reactions. The solute molecule then breaks down as a result of free-radical attack. The oxidation of target molecules by free radicals in the bulk liquid phase under normal operating pressures and temperatures can be presented by a second-order rate equation ... 

Hence, in practical flow situations the water is not pure gas bubbles and small impurities are embedded within the liquid. Small gas bubbles can stay in suspension for a long time, because the relative motion in an upward direction due to gravity is opposed by transport in the downwards direction by turbulent diffusion (ref. 57). These microbubbles are initially trapped in the liquid mostly by jet entrainment, cavitation, and/or strong turbulence at a gas/liquid (usually air/water) interface (ref. 58). 

Fig. 11a-d TEM of a section through part of the fracture surface of a third generation HDPE tested with an initial K of 0.12 MPa m1/2 in Igepol. a Overview, b localised interla-mellar cavitation behind the fracture surface, c region of relatively diffuse deformation behind the fracture surface, showing both relatively coarse cavitation (i) and finer inter-lamellar cavitation (it) and d detail of deformation at the fracture surface (embedded in epoxy and stained in Ru04, tensile axis as indicated by the arrows) [73]... 

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