Maximizing the acceleration and velocity of spherical particles levitated in ultrasonic acoustic fields

Abstract

Acoustic levitation provides a promising method for contactless transportation of objects in air. This opens opportunities, particularly in high-precision industries where mechanical contact is undesirable. For acoustic levitation to serve as a viable alternative, it is necessary to investigate the extent to which the operating speed can be increased while maintaining precise control.
Therefore, this thesis investigates the properties on which the acceleration and velocity limits depend and experimentally evaluates their influence. The study consists of two parts: an acceleration analysis and a velocity analysis.

In the first part, the maximum stable acceleration is set by the acoustic trap stiffness and expressed in terms of the measured eigenfrequency \(f_0\) and the wavelength \(\lambda\). Experiments are conducted on spherical particles of varying diameters (0.593 to 2.886 mm) and densities (30 to 2500 kg/m\(^3\)), driven sinusoidally at sub-resonant frequencies. The measured acceleration limits are compared with theoretical predictions based on a linearised small-particle (Rayleigh-limit) force description and a Taylor-expansion-based model. For most particles, the Taylor-based formulation reproduces the experimental acceleration limits within \(\pm 15\%\) in both directions. In contrast, the linearised model systematically overpredicts the achievable acceleration, with typical deviations of 40-50\% in the vertical direction and similar overestimation in the horizontal direction. The remaining discrepancies are attributed to cross-axis coupling and gravity-induced equilibrium offsets.

In the second part, the maximum achievable velocity is studied through a balance in forces between the acoustic radiation force and aerodynamic drag, using a nonlinear drag model. Velocity tests are performed using sinusoidal excitation with gradually increasing amplitude. The measured velocities are compared with analytically derived predictions and dynamic simulations. While agreement is good in the horizontal direction, the vertical direction shows larger phase lag and earlier loss of stability, indicating increased damping and nonlinear effects at high speeds.

The results demonstrate that maximum acceleration scales with \(f_0^2 \lambda\) and is direction dependent. Another result is that the particle density and diameter influence performance via eigenfrequency and drag. For acceleration, the Gor'kov-based model shows reasonable agreement, whereas for velocity, a Reynolds number-dependent increase in damping is observed, particularly in the vertical direction.

This work provides a validated experimental methodology for characterizing acceleration and velocity limits in acoustic transport, contributing to the design of faster and more reliable non-contact handling systems.