Modeling fast acoustic streaming: Steady-state and transient flow solutions.

Area of Science:

• Fluid Dynamics
• Acoustics
• Microfluidics

Background:

• Acoustic streaming is traditionally modeled as a slow, steady fluid response to acoustic waves, a simplification known as the slow streaming assumption.
• This assumption, established by Lord Rayleigh over a century ago, is often inaccurate in microacoustofluidics where fluid and acoustic velocities are comparable.
• Current microacoustofluidic research often relies on this invalid assumption due to the lack of suitable alternatives.

Purpose of the Study:

• To introduce a novel mathematical method for accurately analyzing acoustic streaming in microfluidic devices.
• To address the limitations of the traditional slow streaming assumption in microacoustofluidics.
• To provide a framework for understanding the spatiotemporal scale disparities between acoustic fields and fluid dynamics.

Main Methods:

• Developed a mathematical approach to decouple fast acoustic scales from slow hydrodynamic scales in governing equations.
• Applied the method to Navier-Stokes equations for semi-infinite problems, preserving unsteady fluid behavior.
• Derived Burgers and Riccati equations to model unsteady and steady acoustic streaming, respectively.

Main Results:

• The new method naturally separates acoustic and hydrodynamic scales without arbitrary assumptions.
• Unsteady streaming field equations provide physical insight into bulk flow temporal evolution.
• Derived Burgers and Riccati equations offer concise insights into acoustic streaming nonlinearity.
• An absolute upper bound of 50% for energy efficiency in converting acoustic to streaming energy was established.

Conclusions:

• The proposed mathematical method offers a valid alternative to the long-standing slow streaming assumption.
• This work provides a foundation for modeling and understanding unsteady acoustic streaming phenomena.
• The findings offer crucial insights into the energy conversion efficiency of acoustic streaming in microfluidic applications.