Ultrasonic Phased Arrays and Acoustic Streaming: A Physics-Based Prediction Framework

Airborne ultrasonic phased arrays have moved from laboratory curiosities to practical engineering components in less than a decade. These devices focus ultrasonic waves at specific points in mid-air, enabling applications that once seemed speculative: fingers detecting virtual textures without touching a screen, fragrance molecules steered through a room, and small objects suspended without any physical support. Yet a persistent obstacle has quietly limited their reliability - the focused sound fields produce not only the intended acoustic effects but also a secondary phenomenon, a steady, slow-moving airflow that persists as long as the sound is on.

This airflow, known as acoustic streaming, arises when high-intensity sound propagates through a viscous medium like air and transfers momentum to the surrounding fluid. The flow it creates is gentle - typically measured in centimeters per second - but that is precisely the problem. For mid-air haptic systems, even a few centimeters per second of unexpected airflow alters the tactile sensation a user perceives. For acoustic levitation, the same flow can destabilize a hovering particle. Despite the practical stakes, predicting the magnitude and spatial distribution of acoustic streaming from the operating parameters of a phased array had remained largely guesswork.

Visualizing Flow with Particle Image Velocimetry

A team led by Assistant Professor Tatsuki Fushimi at the University of Tsukuba's Institute of Library, Information and Media Science tackled this problem by combining two complementary approaches: direct experimental measurement and physics-based numerical simulation. On the experimental side, they used particle image velocimetry (PIV), a technique that seeds the air with fine tracer particles and tracks their motion between successive high-speed camera frames. PIV produces quantitative two-dimensional velocity maps of the airflow, capturing both where the streaming occurs and how fast the fluid moves.

The numerical side drew on established models of sound attenuation in air. When ultrasound propagates, two mechanisms progressively absorb energy from the wave: thermoviscous attenuation, which arises from heat conduction and viscous friction at the molecular level, and atmospheric attenuation, which reflects absorption by oxygen and nitrogen molecules. Both processes transfer energy to the fluid in a way that generates body forces capable of driving bulk flow. The team implemented these mechanisms in a simulation framework that takes in the key operating parameters of a phased array - focal length, beam shape, and input voltage - and outputs a predicted streaming velocity field.

Parameters That Govern Streaming Velocity

By systematically varying each operating parameter while holding the others fixed, the researchers mapped out how the streaming behavior changes. Focal length determines where in space the acoustic energy concentrates, and with it, where the streaming-driving body force is strongest. Beam shape - whether the array steers a tight focused beam or a broader pattern - controls the spatial extent of the high-intensity region. Input voltage sets the overall acoustic pressure amplitude, which scales directly with the magnitude of streaming.

The experimental PIV measurements showed consistent agreement with the numerical predictions across all configurations tested. Crucially, the simulated streaming velocities fell within the range predicted by considering only thermoviscous and atmospheric attenuation, without requiring any empirical correction factors. This agreement indicates that the dominant physics governing acoustic streaming in mid-air phased arrays is already captured in established acoustic theory - it simply had not previously been applied to this configuration in a systematic way.

Streaming velocities observed in the experiments ranged from roughly 5 to 30 centimeters per second depending on the configuration, with higher voltages and tighter focal geometries producing stronger flows. The spatial structure of the streaming showed a characteristic pattern: a forward jet along the acoustic beam axis, accompanied by slower return flows off to the sides. This structure remained qualitatively consistent across the parameter range tested, though its spatial extent scaled with focal length.

Honest Limitations of the Framework

The study was conducted under controlled laboratory conditions with a specific commercial transducer array supplied by Murata Manufacturing Co., Ltd. The numerical model treats air as a linearly responding medium and does not account for nonlinear acoustic effects that become relevant at very high drive voltages. Whether the predictions remain accurate at the extreme ends of the operating envelope - very short focal distances or maximum input voltages - has not yet been established. The PIV measurements also provide two-dimensional velocity slices through what is fundamentally a three-dimensional flow field, so some detail about the full volumetric streaming structure is inferred rather than directly measured.

Real deployments of ultrasonic phased arrays often operate in the presence of obstacles, hands, or other objects that would redirect or modify the streaming. The framework as presented does not incorporate such boundary conditions, meaning that direct application to complex operating environments will require additional work.

Practical Consequences for Interface Design

The value of this framework is most apparent for engineers designing haptic interfaces, odor delivery platforms, and acoustic levitation systems. Previously, accounting for acoustic streaming in the design process meant either ignoring it (and accepting unpredictable behavior) or running expensive experimental campaigns for each new configuration. The validated simulation model reduces that burden significantly: a designer can now compute the expected streaming pattern for a given array configuration before building hardware.

For haptic applications, this means quantifying the airflow artifact that users will feel alongside the intended acoustic radiation pressure sensation. For levitation, it enables predicting whether a given beam configuration will produce streaming strong enough to destabilize the target particle. In both cases, the framework supports iterative design optimization in software rather than hardware.

The research was supported by the Japan Science and Technology Agency under the Adopting Sustainable Partnerships for Innovative Research Ecosystem program, grant number JPMJAP2330.