[Paper Review] Acoustic propulsion of nano- and microcones: dependence on particle size, acoustic energy density, and sound frequency

Johannes Voß, Raphael Wittkowski|arXiv (Cornell University)|Jul 2, 2023

Microfluidic and Bio-sensing TechnologiesEngineering3 citations

TL;DR

This study uses acoustofluidic simulations to investigate how the propulsion of cone-shaped nano- and micro-particles depends on particle size, acoustic energy density, and ultrasound frequency. Results show propulsion velocity increases linearly with size and energy density, rises with frequency up to ~1 MHz, then decreases, revealing a non-monotonic frequency dependence critical for optimizing acoustic particle delivery systems.

ABSTRACT

Employing acoustofluidic simulations, we study the propulsion of cone-shaped nano- and microparticles by a traveling ultrasound wave. In particular, we investigate how the acoustic propulsion of the particles depends on their size and the energy density and frequency of the ultrasound wave. Our results reveal that the flow field generated around the particles depends on all three of these parameters. The results also show that the propulsion velocity of a particle increases linearly with the particle size and energy density and that an increase of the sound frequency leads to an increase of the propulsion velocity for frequencies below about 1 MHz but to a decrease of the propulsion velocity for larger frequencies. These findings are compared with preliminary results from the literature.

Motivation & Objective

• To understand the dependence of acoustic propulsion on particle size, acoustic energy density, and ultrasound frequency in cone-shaped nano- and microparticles.
• To resolve discrepancies between experimental and theoretical findings on size-dependent propulsion speed.
• To identify optimal acoustic parameters for maximizing propulsion velocity in nano- and microcones.
• To provide a quantitative simulation framework for guiding future experimental design in acoustofluidic particle manipulation.

Proposed method

• Acoustofluidic simulations were performed using the finite volume method on a structured, mixed rectangular-triangular mesh with 300,000–800,000 cells.
• The Navier-Stokes equations for viscous, compressible fluid flow were solved numerically with adaptive time-stepping and a Courant-Friedrichs-Lewy condition to ensure stability.
• Dimensionless numbers including Euler number (Eu), Helmholtz number (He), and Reynolds numbers (Re_b, Re_s, Re_p) were used to characterize the system, with Re_p < 10⁻⁵ indicating highly viscous flow.
• Simulations covered frequencies from 0.5 to 5 MHz, particle sizes from 100 nm to 10 µm, and acoustic energy densities corresponding to Eu = 2.20×10⁴ to 2.20×10⁶.
• The system was initialized with a traveling ultrasound wave, and particle velocity was extracted after steady-state flow was achieved.
• Data from simulations were validated against literature and used to derive scaling laws for propulsion velocity.

Experimental results

Research questions

• RQ1 How does the propulsion velocity of cone-shaped nano- and microcones scale with particle size?
• RQ2 How does the acoustic energy density of the ultrasound wave affect propulsion velocity?
• RQ3 How does the sound frequency influence propulsion velocity, and is there an optimal frequency?
• RQ4 Why do experimental and theoretical studies report conflicting trends in size-dependent propulsion?
• RQ5 What is the role of fluid viscosity and wave parameters in determining the flow field around the particle?

Key findings

• Propulsion velocity increases linearly with particle size, confirming theoretical predictions for symmetric particles.
• Propulsion velocity increases linearly with acoustic energy density, indicating a direct proportionality to input power.
• For frequencies below approximately 1 MHz, propulsion velocity increases with frequency; above 1 MHz, it decreases, indicating a non-monotonic frequency dependence.
• The flow field structure around the particle is strongly dependent on all three parameters: size, energy density, and frequency.
• The particle Reynolds number remains below 10⁻⁵, confirming that inertial effects are negligible and viscous forces dominate the dynamics.
• The results reconcile conflicting literature findings by showing that the frequency-dependent behavior is critical and that the optimal frequency window lies below 1 MHz for maximum propulsion.