Experimental and Numerical Study of Acoustic Streaming in Mid-Air Phased Arrays

Mid-air acoustic streaming, where ultrasound induces steady fluid motion, could significantly affect the perception of haptic sensations, stability of levitation systems, and enable controlled transfer of odours (smells) through air by directing volatile compounds to specific locations. Despite its importance, the streaming behavior in airborne phased-array transducers remains poorly understood. Here, we use particle image velocimetry and numerical simulations to investigate streaming dynamics in single- and multi-focus acoustic fields. Experimental measurements reveal streaming velocities exceeding $0.4~\text{m/s}$ in single-focus configurations and up to $0.3~\text{m/s}$ in multi-focus setups, with distinct grating lobe-induced lateral jets. While multi-physics finite-element models effectively capture central streaming, they exhibit subtle differences and perform poorly in capturing flow in the side lobes. These findings provide valuable insights into the interplay between acoustic field design and streaming dynamics, offering guidance for optimizing ultrasonic technologies in haptics and levitation applications.

💡 Research Summary

This paper presents a combined experimental and numerical investigation of acoustic streaming generated by a 40 kHz flat phased‑array (PA) transducer operating in air. The authors use particle‑image velocimetry (PIV) to obtain high‑resolution velocity fields and develop a multi‑physics finite‑element model in COMSOL to predict the streaming forces.

The experimental platform consists of a 16 × 16 Murata MA40S4S open‑type air‑coupled transducer array driven at 5 V, 8 V and 10 V. Smoke particles seeded in a 1 m³ enclosure are illuminated by a 5 W green laser sheet and recorded with a Sony α9 camera at 240 fps (1000 frames per case). PIVlab (MATLAB) processes the image pairs, and the resulting velocity fields are low‑pass filtered (10 Hz Butterworth) and spline‑smoothed to remove high‑frequency noise. The authors examine three beam configurations: (i) a single focused beam at various axial focal distances (e.g., z = 80 mm), (ii) Bessel‑type beams generated by imposing a conical phase distribution, and (iii) multi‑focus fields created with an iterative back‑propagation (IBP) algorithm that places two or three focal spots simultaneously.

For the acoustic field, a 3‑D Huygens‑principle model superposes the contribution of each element, using the directivity function D(k,θ) and phase shifts φₙ chosen to achieve the desired beam shape. The complex pressure p yields the particle velocity v₁ = (1/jωρ)∇p, from which the time‑averaged acoustic intensity I = ½ Re(p·v₁*) is computed. The streaming body force per unit volume is then F = 2αIc, where α is the attenuation coefficient and c the speed of sound. Two attenuation models are considered: (a) thermoviscous attenuation derived from the Stokes‑Kirchhoff relation (including shear viscosity, bulk viscosity, thermal conductivity and specific heat), and (b) atmospheric attenuation that accounts for oxygen and nitrogen relaxation processes and depends on temperature, humidity and pressure.

The force field is exported as a CSV file and imported into COMSOL Multiphysics 6.2. A 2‑D axisymmetric domain (200 mm × 400 mm) with a mirror symmetry plane at x = 0 is used. Laminar flow is assumed, the bottom boundary (the array surface) is a no‑slip wall, and all outer boundaries are set as pressure outlets. Mesh details and convergence criteria are provided in the supplementary material.

Experimental results show that a single focus can generate a central jet with peak streaming velocities up to 0.4 m/s, while the array’s grating lobes produce pronounced lateral jets that can reach 0.2–0.3 m/s. Multi‑focus configurations generate multiple jets that interact, creating complex flow patterns. Bessel beams produce a more distributed jet whose peak velocity depends on the cone angle; larger angles broaden the jet and reduce the maximum speed. The measured streaming velocity increases with both focal distance and drive voltage, consistent with the quadratic dependence of acoustic intensity on pressure amplitude.

Numerical simulations capture the central jet reasonably well, especially when the atmospheric attenuation model is used; the thermoviscous model tends to underestimate the central velocity. However, both models substantially underpredict the strength of the lateral jets caused by grating lobes. This discrepancy is attributed to the 2‑D simplification, which cannot fully represent the three‑dimensional interference pattern of the array, nor the nonlinear coupling between high‑amplitude acoustic fields and the surrounding air.

Transient measurements reveal that the streaming flow does not appear instantaneously. Rise times of 0.8–1.2 s are observed after the array is switched on, with higher voltages yielding slightly longer rise times but higher steady‑state velocities (mean velocities of 0.15 m/s at 5 V, 0.21 m/s at 8 V, and 0.30 m/s at 10 V). Decay times after the drive is turned off range from 2.5 s (10 V) to 5.1 s (5 V). Acceleration and deceleration peaks increase with voltage, indicating that nonlinear viscous effects become more significant at higher acoustic intensities.

The authors discuss several implications. First, the presence of strong grating‑lobe jets means that simple beam steering strategies may unintentionally generate lateral forces that could affect haptic perception or destabilize levitated objects. Second, the limited accuracy of 2‑D models for side‑lobe flows suggests that full 3‑D CFD, possibly coupled with nonlinear acoustic propagation, is required for precise design of multi‑focus or high‑resolution haptic displays. Third, the measured transient response provides a guideline for control algorithms that need to account for the finite build‑up and decay times of streaming‑based forces.

In conclusion, the paper demonstrates that mid‑air acoustic streaming from phased‑array transducers can reach velocities comparable to those used in tactile feedback (≈0.3–0.4 m/s) and that the streaming pattern is strongly influenced by array geometry, focal distance, drive voltage, and beam type. While the central jet can be reliably predicted with existing attenuation models, the lateral jets arising from grating lobes remain a modeling challenge. These findings offer practical design insights for emerging ultrasonic technologies such as haptic interfaces, acoustic levitation platforms, and directed‑odor delivery systems.