Compressibility effects on steady streaming from a noncompact rigid sphere.

Area of Science:

• Fluid Dynamics
• Acoustics
• Acoustofluidics

Background:

• Steady streaming is a phenomenon occurring around objects in oscillating fluid flows.
• Existing models often assume compact spheres and neglect fluid compressibility.
• Understanding streaming is crucial for applications involving acoustic manipulation of particles.

Purpose of the Study:

• To generalize existing results for steady streaming around a rigid sphere in a plane standing acoustic field.
• To incorporate the effects of fluid compressibility and non-compactness of the sphere.
• To analyze the influence of sphere position and fluid properties on streaming behavior.

Main Methods:

• Theoretical analysis of fluid flow around a rigid sphere in an acoustic field.
• Inclusion of compressibility effects through fluid properties like Prandtl number and ratio of specific heats.
• Visualization of flow streamlines to demonstrate streaming patterns in low Reynolds number regimes.

Main Results:

• The steady slip velocity at the boundary layer exhibits complex variations dependent on sphere position, compactness, and fluid compressibility.
• Compressibility effects are significant in gases but negligible in liquids.
• High-frequency acoustic fields lead to the strongest streaming effects.

Conclusions:

• The study provides a generalized framework for understanding steady streaming around spheres, accounting for compressibility.
• Sphere position and compactness are critical factors in determining streaming patterns.
• The findings are relevant for designing acoustic devices and understanding microfluidic transport phenomena.