Viscous effects on the interaction force between two small gas bubbles in a weak acoustic field

Area of Science:

• Fluid dynamics
• Acoustics
• Bubble dynamics

Background:

• The secondary Bjerknes force governs the interaction between oscillating bubbles in an acoustic field.
• Classical theories predict attraction between bubbles driven below resonance.
• Previous models often neglect viscous effects and acoustic streaming.

Purpose of the Study:

• To investigate the relative motion of two gas bubbles in an acoustic field.
• To derive a refined formula for the secondary Bjerknes force considering viscous effects and acoustic streaming.
• To explore conditions under which bubble repulsion occurs.

Main Methods:

• Calculation of the time-averaged secondary Bjerknes force.
• Modeling of an incompressible viscous liquid medium with large bubble separation.
• Application of a slippage boundary condition at the gas-liquid interface.
• Inclusion of translational oscillations and scattered field vorticity.

Main Results:

• A refined formula for the interaction force was derived, incorporating translational oscillations, vorticity, and acoustic streaming.
• Viscous effects were shown to induce repulsion between small bubbles driven below resonance across a broad parameter range.
• This repulsion contrasts with the attraction predicted by classical Bjerknes theory.

Conclusions:

• Classical Bjerknes theory has limitations regarding bubble interactions in viscous fluids.
• Viscous effects play a crucial role in determining bubble relative motion, potentially leading to repulsion.
• The derived formula provides a more comprehensive understanding of bubble-bubble interactions in acoustic fields.