Nonlinear viscoelastic effects on the harmonic generation of a finite-amplitude acoustic wave

The effect of fluid viscoelasticity on the second-harmonic wave generated by a planar acoustic wave is considered. It is shown that the growth, decay, wavenumber, phase, and amplitude of the second-harmonic wave are all modified by fluid viscoelasticity. The effect on the amplitude, the most readily measured property, is discussed in detail. It is found that viscoelasticity in the form of frequency thinning causes a shift in the maximum of the second-harmonic amplitude to distances further from the acoustic source. Finite linear and nonlinear viscoelasticity are found to cause both harmonic suppression and harmonic enhancement, depending on the properties of the fluid and the dimensionless frequency of oscillation. The harmonic suppression predicted here may be associated with changes in the noise spectrum of cavitation that have been observed for dilute polymer solutions.