Viscoelastic bubbly media and ultrasonic shear-mode effects

Abstract

Here we show that in ultrasonic fields the phenomenon of reconversion of shear-modes into an effective compressional wave has a significant effect for bubbles in a medium viscosity liquid or weak gel. We present the consequent extra terms in the effective wavenumber and find the changes in sound velocity for different bubble radii. At high concentrations of bubbles the inclusion of shear-mode effects in the multiple-scattering model can help identify bubble sizes where additional resonance signatures emerge.Rayleigh gave the first mathematical description of compressible oscillations of bubbles in a liquid in 1917 [27] without inclusion of surface tension or viscous effects. The Rayleigh model was later applied to the dynamics of bubble cavitation by Plesset [25]. The first consideration of the collapse or growth of a bubble in a viscous fluid was carried out by Poritsky in 1952 [26]. For low concentrations of bubbles the Foldy model of 1945 is successful for describing the attenuation and sound velocity [11]. However, it does not take into account inter-bubble coupling effects. Importantly, no examination of the high concentration phenomena has been carried out and consequences linked to the recombination of energy fluxes in the compressional wave have been disregarded on dissipation arguments. Historically, the approaches taken to describe bubble acoustics have fallen under two categories: linear and non-linear modelling, where traditionally linear models have formed the initial understanding to develop more complex dissipative arguments. The Foldy model is based upon linear bubble dynamics. In the work of Commander and Prosperetti [6], based on the findings by van Wijngaarden [31] and Caflisch et al [4], linear bubble oscillations were examined against available data. We consider the bubbles to have a monodisperse size distribution and identical initial conditions. Technologies have been developed that can produce bubbles of uniform size distribution and have been reported as having high stability. A stable bubble is more durable against pressure changes and does not implode or expand rapidly. From this perspective a linear model is applicable. Bubbles may dissolve quite rapidly and for this reason small nuclei can be coated in nanoparticles to increase their lifetime [28] and to slow or prevent Ostwald-Ripening and convergence to a larger bubble. Low excitation pressures may lead to a linear approximation to the oscillations. The bubbles at higher pressures are, however, deformable, sensitive to changes in the continuous phase, and can fuse or fission under perturbation. Bubble growth and collapse can occur in a flow which is important for a range phenomena. The stable bubbles can also be dispersed in a liquid medium. When the number of bubbles becomes larger than a few percent by volume concentration, i.e. there is a high bubble fraction in the continuous phase, some degree of shear-mode conversion back to the primary compressional wave can occur. Multiple scattering formulations have until the present day b...