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

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 2 mu m 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 4 mu m and 6 mu m, 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 2 mu m. The equilibrium distance decreases when the shear modulus is increased. A simple relation between the two quantities is established.