‘‘Induced transparency’’ of an acoustical waveguide containing a liquid with nonlinear viscosity

Abstract

Sound propagation in an acoustical waveguide containing a liquid that depends on a shear rate γ̇ viscosity is considered. A number of rheological models adequately representing such dependence in a wide range of γ̇ variation are well known (power law, Carreau model for stuctural viscosity, etc.). In most of the models viscosity decreases with the increase of γ̇. It can result from the destruction of some internal microstructures in the liquid and their self-reconstruction with a reduction of load (as, e.g., in a sol–gel transition). For such liquids the effect of ‘‘induced transparency’’ for intense sound waves is expected. In this work the effect is determined for harmonic waves, propagating in an acoustical waveguide with cross−section dimensions that are small in comparison with the sound wavelength. The dependence of viscosity on γ̇ is taken into account by retention of the first nonlinear term in the expansion of shear tension στ in shear rate γ̇: στ=ηγ̇−ξγ̇3, where η and ξ are linear and nonlinear parameters of viscosity, respectively. Sound attenuation in acoustical waveguides is due to the partial transmission of acoustical energy to the viscous waves being generated in the vicinity of waveguide walls. It is shown that the nonlinear viscosity gives rise to the effective viscous wave self-interaction, which results in the reduction of the energy dissipation. The application of the effect to the measurements of the nonlinear viscosity parameter is considered and the importance of this parameter for the evaluation of the oil quality is discussed. Work was partially supported by the Russian Foundation of Basic Research (project 97-08-17789).]