Volume 104, Issue 5, November 1998
Index of content:
- NONLINEAR ACOUSTICS 
104(1998); http://dx.doi.org/10.1121/1.423848View Description Hide Description
The second-harmonic sound beam nonlinearly generated by a conical source is analytically described. It is shown that the radial second-harmonic beam is distributed as the Bessel function and independent of the propagation distance. Another important feature is that the beamwidth of the second-harmonic component is just equal to 1/2 times that of the fundamental, not 1/√ times in the general cases. A potential application of this beam in the acoustic nonlinearity parameter imaging or measurement is also discussed.
104(1998); http://dx.doi.org/10.1121/1.423849View Description Hide Description
In the present paper, the energy effects accompanying a strong sound disturbance of a medium are analyzed. The waves may be, in time, periodic — continuous or pulsed — or have the form of single pulses. The description is based on equations which are commonly applied in nonlinear acoustics. The Fourier analysis, elements of the theory of linear operators, and analytical functions are applied. A general method is given for the construction of the absorption operator in the domain of space–time coordinates to which the small-signal absorption coefficient corresponds. By analogy to linear equations and the corresponding dispersions equations, the quasi-dispersion equations in the case of nonlinear description are introduced. Simplification of the “classical” equation of nonlinear acoustics was performed. The relations between absorption operators in the space and time domains are shown. It is demonstrated that in nonlinear interactions, where terms of such type — nonlinear function of pressure — dominate, the power (energy) of the disturbance is conserved. Just as in the linear notation, the only reason why the total power (energy) changes is linear absorption, but that one which occurs under the conditions of nonlinear propagation. In consequence, the equations of power (and energy) balancing the disturbance have the same formal shape in nonlinear and linear descriptions. The equations provide a theoretical basis for different, easier, and more accurate methods than those used previously for determination (numerical and experimental) of, e.g., the power density of heat sources generated by sound. The function of the nonlinear gain of absorption and the function of effective absorption were also introduced. On the basis of quasi-dispersion equations the phenomenon of overtone generation (not harmonics) is shortly discussed.
104(1998); http://dx.doi.org/10.1121/1.423850View Description Hide Description
A one-dimensional model is developed to analyze nonlinear standing waves in an acoustical resonator. The time domain modelequation is derived from the fundamental gasdynamicsequations for an ideal gas. Attenuation associated with viscosity is included. The resonator is assumed to be of an axisymmetric, but otherwise arbitrary shape. In the model the entire resonator is driven harmonically with an acceleration of constant amplitude. The nonlinear spectral equations are integrated numerically. Results are presented for three geometries: a cylinder, a cone, and a bulb. Theoretical predictions describe the amplitude related resonance frequency shift, hysteresis effects, and waveform distortion. Both resonance hardening and softening behavior are observed and reveal dependence on resonator geometry. Waveform distortion depends on the amplitude of oscillation and the resonator shape. A comparison of measured and calculated wave shapes shows good agreement.
104(1998); http://dx.doi.org/10.1121/1.423851View Description Hide Description
The introduction of a strong acoustic field to an aqueous solution results in the generation of cavitationmicrobubbles. The growth and collapse of these microbubbles focuses and transfers energy from the macroscale (acoustic wave) to the microscale (vapor inside the bubbles) producing extremely high localized pressures and temperatures. This unique energy focusing process generates highly reactive free radicals that have been observed to significantly enhance chemical processing. This paper presents a model that combines the dynamics of bubble collapse with the chemical kinetics of a single cavitation event. The effects on sonochemical yields and bubbledynamics of gas composition and heat transfer are assessed and compared with previous theoretical and experimental studies. Results from this model are used to explain unusual experimentally observed sonochemical phenomena.