THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

16.3 Cavitation 451where δ j k s /ks∞ is a relaxation adiabatic compressibility (which has a negativevalue) and j denotes that there may be more than a single-relaxation processentailed. In such complex cases, τ s, j and δ j k s /ks∞ can no longer be respectivelyassociated with a single-transfer reaction and relaxation energy of a specific mode,because the various modes and reaction pathways are coupled. So the sums inEquations (16.12) and (16.13) should cover all eigenvalues of the energy transfermatrix, which also accounts for all reactions. These two equations constitute thestandard equations for calculating sound absorption in moist air as function offrequency and temperature. Equations (16.12) and (16.13) can also be used inthe reverse manner, where the measured values of absorption and velocities canbe used to derive the transition rates. But when the number of relaxation modesincreases, the number of possible relaxation paths multiplies very rapidly, thuslimiting this procedure to only a few special cases.While relaxation processes similar to the energy exchanges in gases occur in liquids,there are important differences that arise from the greater density of moleculesinherent in liquids and the consequential multibody interactions. The concept of arate equation is less applicable, but the existence of relaxation time as a measure ofthe time for a system to revert to an equilibrium state in sustaining a perturbationremains valid.In a few cases such as CS 2 and a number of organic liquids, the relaxationmechanism appears to be the same as that for gases, i.e., the internal energy ofthe individual molecules is excited by “collisions.” These types of liquids arecalled Kneser liquids, and they generally have a positive temperature coefficientof absorption. With other liquids, the molecules bond temporarily to form largegroups that reconfigure themselves when an ultrasound wave passes through. Suchfigurative relaxations tend to be very rapid, and there is the possibility of thefrequency dependence of absorption and dispersion, which results in a distributionof relaxation times. Such liquids are termed associated liquids. Water is a primeexample of such a liquid.Chemical reactions complicate matters even more: in a reversible chemicalreaction with heat of reaction H. H plays a role in the relaxation equationsin the same manner as E for vibrational relaxation. Because chemical reactionsincrease the possibility of the number density of the molecules changing, additionalrelaxation absorption and dispersion tend to occur.16.3 CavitationThe phenomenon of cavitation, the rupture of liquids, is readily observed in boilingwater, turbines, hydrofoils, and in seawater in the vicinity of a ship’s rotatingpropeller. It occurs in those regions of liquids that are subject to high-amplitude,rapidly vacillating pressures. Cavitation also occurs in a liquid irradiated withhigh-energy ultrasound.Consider a small volume of liquid through which sound travels. During thenegative half of the pressure cycle the liquid undergoes a tensile stress, and during