Small acoustically forced symmetric bodies in viscous fluids

Area of Science:

• Acoustic physics
• Fluid dynamics
• Particle dynamics

Background:

• Acoustic forces on particles are crucial in various physical phenomena.
• Previous calculations often simplified particle shapes or fluid properties.
• Understanding these forces is key for applications in acoustics and material science.

Purpose of the Study:

• To analytically determine the total acoustic force on small rigid bodies in a viscous fluid.
• To investigate the influence of particle shape on acoustic forces in low-frequency regimes.
• To extend existing models to more complex particle geometries.

Main Methods:

• Utilizing an analytical approach in the low-frequency limit, where particle size is less than viscous diffusion length and acoustic wavelength.
• Employing Eulerian linear expansion of Lagrangian hydrodynamic quantities (velocity and pressure).
• Calculating forces for progressive and standing acoustic waves on spheres and then extending to symmetric bodies.

Main Results:

• The acoustic force calculation is valid when acoustic steady streaming effects are negligible.
• For progressive waves, particle shape significantly affects the leading-order acoustic force on symmetric bodies.
• For standing waves, the leading-order acoustic force on a symmetric body is independent of its shape, depending only on volume and density.

Conclusions:

• The study provides an analytical framework for calculating acoustic forces on small particles of various shapes in viscous fluids.
• Particle shape is a critical factor for progressive waves but not for standing waves at leading order.
• The findings offer insights into acoustic manipulation and transport of small objects in complex fluids.