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

16.2 Relaxation Processes 445from irregular surfaces. The process of relaxation, which represents the lag betweenthe introduction of a perturbation and the adjustment of the molecular energydistribution to the perturbation, requires a finite time; and the energy interchangeapproaches equilibrium in an exponential fashion. Considerable information regardingthe nature of matter can be derived from the study of relaxation phenomena.High-intensity ultrasound can result in energy absorption that yields considerableamount of heat, to the extent that glass or steel can be melted quickly.Ultrasonic waves can also generate stresses, resulting in cavitation in fluids.Cavitation is also capable of producing free chemical radicals, thus fosteringspecific chemical reactions. The stresses produced in the cavitation process aresufficiently concentrated to erode even extremely sturdy materials. Cavitation alsoprovides the mechanism of ultrasonic cleaning.16.2 Relaxation ProcessesRelaxation entails molecular interactions in gases and liquids. These interactionsaffect absorption and velocity dispersion, both of which depend on frequency(and on pressure, in the case of gases). Chemical reactions also entail relaxationprocesses on their own, but they will not be considered in this chapter, except forthe effect of ultrasound on reaction rates.To better understand the phenomenon of relaxation, let us consider an ideal gasmade up of diatomic molecules. The individual molecules move translationwisein three principal directions in a nonquantitized fashion, i.e., any translational energyis allowable. In addition, the molecules rotate about three perpendicular axes(actually two, since one axis has zero moment of inertia, hence zero rotationalenergy), and the molecules also vibrate along the direction of the bond joining theatoms. These molecules collide with one another in translation motion, exchangingenergy among themselves. A single collision is usually sufficient to transfertranslational energy from one molecule to another, but a certain period of time isneeded to randomize the energy associated with excessive velocity in a particulardirection. This amount of time is referred to as the translational relaxation time(Herzfeld and Litovitz, 1959), and it is given byτ tr = η p = 1.25 τ cwhere τ tr is the translational relaxation time, p is the gas pressure, η is the viscosityof the gas, and τ c is the interval between collisions. As the gas pressure is lowered,the rate of collisions decreases in the same proportion.Unlike the case of translational motion, rotation and vibration are quantitized.When a collision occurs, a change in rotational or vibrational state will occuronly when the change of energy of another state is sufficient to permit at least onequantum jump. For rotational energy transfer the spacing between energy levelsis given by 2(J + 1)B, where J denotes the rotational quantum number (whichmust be an integer), B = ¯h 2 /2I , I is the effective moment of inertia and ¯h isthe