The secondary Bjerknes force between two oscillating bubbles in Kelvin-Voigt-type viscoelastic fluids driven by harmonic ultrasonic pressure

Abstract

The interaction between two small bubbles experiencing transient cavitation in a nonlinear Kelvin-Voigt fluid is investigated. The time-delay effect in the interaction is incorporated in the coupled Keller-Miksis model. The refined model predicts that bubbles with radii smaller than 2µm will be repelled by large bubbles, in contrast to predictions from previous models. The matching pressure needed to obtain same level of transient cavitation in different Kelvin-Voigt fluids is shown to depend mainly on the shear modulus and is insensitive to other parameters, which makes it a useful parameter to correlate the results. When the radii of the bubbles fall between 4µm and 6µm, the secondary Bjerknes force obtained with matching pressures shows only weak dependence on the shear modulus. For the pressure amplitudes investigated, equilibrium distances can be found between two bubbles when the equilibrium radius of one of the bubbles is in a narrow range around 2µm. The equilibrium distance decreases when the shear modulus is increased. A simple relation between the two quantities is established.

Nonlinear dynamics and acoustic emissions of interacting cavitation bubbles in viscoelastic tissues

“…Specifically, the expansion ratios of bubbles can be suppressed or enlarged, which largely depends on the ultrasound parameters, the ambient bubble radii, the distances between bubbles and the number of bubbles [35] , [39] , [40] . Recently, several studies have attempted to clarify the impacts of the viscoelasticity of the surrounding medium on the translational and/or radial motions of bubbles with considering bubble–bubble interactions [41] , [42] . It was found that increasing elasticity, viscosity or both would significantly reduce the translational and radial motions of bubbles and consequently reduce the bubble–bubble interactions [42] .…”

Rectified Diffusion of Gas Bubbles in Molten Metal during Ultrasonic Degassing

“…For example, the wave will be greatly attenuated by the oscillating bubbles within a short distance [33][34][35], leading to the frequency locking of the wave [34]. On the contrary, the acoustic wave could also manipulate the distributions of the bubbles through inducing the Bjerknes forces between them [36][37][38][39], leading to the coalescence of the bubbles. In the present model, for the sake of the simplicity, those effects are not accounted with neglecting the strong interactions between the waves and bubbles.…”

Modulation of the secondary Bjerknes force in multi-bubble systems

“…The pressure wave travels with a finite speed c, so the time for the pressure to propagate from bubble i to j is D i j /c. If this time-delay effect is taken into account in the pressure coupling term, [7] shows that Eq. 3becomes…”

“…Note that the two summations on the right hand side include every term from j = 1 to N. Eq. (5) was given in a slightly different form in [7]. Eq.…”

“…By definition, F i j is the time-averaged pressure force on bubble i generated by the oscillations of bubble j. As is explained in [7], the time-delay effect introduces an additional force on each bubble, but the forces do not contribute to the relative motion of the two bubbles. Therefore the timedelay effect on F i j can be neglected.…”