TÍTULO IV: Disposiciones reguladoras de la transferencia de créditos
NIVEL 2: Medias cautelares y proceso penal 5.5.1.1 Datos Básicos del Nivel 2
For the wave propagation and scattering phenomena considered thus far in this chap-ter, the wave amplitudes have been implicitly assumed to be of small amplitude. This implies that for an ultrasound wave that is introduced as a sine wave, it will, with the exception of some viscoelastic absorption phenomena, remain in that form, even when there are scattering phenomena, which are encountered.
When the energy in the applied wave is increased, there is a diverse range of ultrasound phenomena that can be involved. These high-power interactions can in general be classed as “nonlinear” interactions. Such interactions may involve shock waves, harmonic generation, and a wide range of other phenomena that are thermal, mechanical, and chemical in nature.
Elastic Wave Propagation and Associated Phenomena 95
2.12.1 caVitation
Many of the useful effects of ultrasonic energy are associated with cavitation, a term used to describe the formation of cavities, or bubbles, in a liquid medium.
During the rarefaction portion of the cycle, when the pressure in the wave is below ambient, gas pockets may form and expand with the impressed field. These gases may be of two types: (1) those that have been dissolved or trapped in minute bub-bles in the liquid or on surfaces in contact with the liquid and (2) vapors of the liquid itself. The first of these produces gaseous cavitation, and this form is of relatively low intensity. The second type, called vaporous cavitation, is of fairly high intensity.
Not all phenomena associated with cavitation appear to be explained completely by either vaporous or gaseous cavitation. If the pressure within the cavity is lower than the vapor pressure of the liquid during the expansion phase, the bubble is a result of fragmentation due to the tensile stress imposed by the ultrasonic wave being equal to the tensile strength of the liquid. This type of cavitation is very intense. The tensile strength of the liquid imposes an upper limit on the amplitude of the stress of the ultrasonic wave used to produce cavitation.
It is unlikely that the true tensile strength of the liquid is ever reached in practice because most liquids contain nuclei about which cavitation bubbles originate. These nuclei may consist of dispersed dust particles, prominences on immersed surfaces, or minute gas bubbles.
High localized stresses are developed during the formation and subsequent col-lapse of cavitation bubbles. Free chemical ions are produced within the vicinity of the bubble walls. High localized temperatures may also be present. Sometimes, weak flashes of light are produced—an effect called sonoluminescence. The peak values of either the temperature, sometimes estimated to be as high as 7200°C (1300°F), or the pressures (possibly as high as 520 MPa (75,00 psi) can be determined only theoretically because if these temperatures and pressures are obtained, their duration is extremely brief and they are minutely localized.
Some effects produced in the presence of cavitation include increased chemical activity (including reactions that would not occur in the absence of cavitation), ero-sion of surfaces, rupture or fragmentation of suspended particles, emulsification of liquid mixtures, and dispersion of small particles in the liquid. Applications based on these phenomena will be discussed in later chapters.
The importance of cavitation in ultrasonic processing has prompted a consider-able amount of research and many publications with respect to the physics and asso-ciated effects of this phenomenon [7,64,65].
The onset of cavitation occurs at intensities, or cavitation thresholds, that depend upon such factors as the sizes of nuclei, ambient pressure, amount of dissolved gases, vapor pressure, viscosity, surface tension, and the frequency and duration of the ultrasonic energy.
When cavitation occurs, it not only dissipates the ultrasonic energy but also impedes transmission of the sound past it. Each bubble is a scattering site, and the scattering cross section includes both the bubble and the surrounding medium that is most directly affected by the bubble oscillations.
To be effective, that is, to cause the effects associated with the expansion and violent collapse of cavitation bubbles, the bubble must be capable of expanding with the rarefaction part of the cycle of the impressed field and of collapsing before the total pressure reaches its minimum value. That is, the bubble must reach the size where it will collapse catastrophically in less than one-quarter cycle of the impressed wave. Therefore, generation of intense cavitation depends upon the relationship between the dimensions of the nuclei, the wavelength of the sound field, and the intensity of the sound field. Bubbles larger than a critical radius, Rc, will not expand to an unstable size for catastrophic collapse before the pressure in the wave starts to increase. Frederick [64] gives the following relationships for Rc:
R P ratio of specific heats of the gas in the bubble, σ is the surface tension of the liquid (dyn/cm), P0 is the hydrostatic pressure (atm), and ρ is the density of liquid (g/cm3).
The intensity, or violence, of the cavitation bubble is a function of the ratio of the bubble radius at the instant before collapse to the minimum radius before expansion.
The effect of surface tension on bubble size is indicated by the equation P P
i= 0+2R
0
σ (2.137)
where Pi is the vapor pressure inside the bubble and R0 is the radius of a bubble, which is stable under these conditions.
Viscosity affects the rate of growth and collapse of cavitation bubbles. For this reason, very high viscosities may preclude the generation of cavitation.
In some applications, high ambient pressures have been used to suppress cavita-tion in coupling fluids used to transmit focused energy into specimens located in the focal region. This technique eliminates losses due to scattering from cavities.
Figure 2.34 is a photograph of ultrasonic horns designed to produce high intensi-ties for processing in liquids (a) after very little service, (b) after exposure to ultra-sonic cavitation for approximately four hours in detergent and water, and (c) after exposure to ultrasonic cavitation for only a few minutes in an acidic environment.
Figure 2.34b is an example of cavitation-induced erosion. Figure 2.34c is an example of cavitation-induced corrosion. The frequency was 20 kHz.
In addition to cavitational phenomena in fluids, high-power ultrasound can also cause phenomena such as acoustoplasticity, or softening, in metals [66]. The topics relating to high-power ultrasound interactions in both industrial and medical appli-cations are discussed in subsequent chapters of this text.
Elastic Wave Propagation and Associated Phenomena 97
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