Investigation of a three-phase medium with a negative parameter of nonlinearity

Abstract

Nonlinear acoustic properties of a composite medium, consisting of hollow microspheres suspended in Castor Oil, at elevated hydrostatic pressure are experimentally investigated. The acoustic nonlinear parameter B / A of the medium is found to be highly dependent upon hydrostatic pressure. B / A varies from a small negative value near ambient pressure to a very large negative value ͑around −6000͒ in the vicinity of 7 ϫ 10 4 Pascals, above ambient pressure. With a further increase in hydrostatic pressure the magnitude of B / A decreases passing through zero and finally becomes positive. Finite amplitude wave propagation in this medium at low hydrostatic pressures is characterized by waveform steepening in the backward direction leading to rarefactive shockwaves and, at high hydrostatic pressures, by steepening in the forward direction leading to compressive shockwaves. Estimates of B / A are obtained from both the measurement of thermodynamic properties and from waveform distortion during propagation.

Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

“…In contrast to the above-mentioned bubbly liquids, for which the bubbles have the same contrast ς in compressibility with the liquid and the existence of a clear maximum of the non-linear parameter in its dependence on bubble concentration is a known fact (Trivett et al, 2006;Zaitsev et al, 2009b), for cracked rocks, the fact of maximal non-linearity at an intermediate concentration of cracks is not typical. Bearing in mind that for the bulk modulus K of rocks under hydrostatic compression, the 1-D description is applicable as far as the normal compliance of cracks is concerned (see below for more details); we note that pressure dependences of K(P ) usually demonstrate an ever-increasing slope dK(P )/dP (i.e.…”

Axial compression of hollow elastic spheres

“…These range in diameter from 20 to 55 µm with shell thicknesses of approximately 0.1 µm. In [Trivett et al 2006], when the behaviour of these microspheres was studied in castor oil, the Young's modulus of the shell was estimated to be ∼3 GPa from the sound speed of the mixture, but in this case the spheres are formed by a chemical reaction in-situ and it is not possible to obtain a test sample of the shell polymer to confirm this estimate.…”

Acoustic Waves in Bubbly Soft Media

“…Second, the EMM is developed under quadratic approximation by employing a simple perturbation approach, and the nonlinearity of medium is studied by inspecting the second harmonic wave with no harmonics of orders higher than 2 involved. Finally, the present model could not enable full incorporation of all the practical effects that affect the acoustical properties of a bubbly medium, such as the buckling of bubbles [46]. These problems will be the focus of a future study.…”