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. 2022 Oct 26;13:6370. doi: 10.1038/s41467-022-34167-y

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — a Randomly distributed tracer microparticles were attracted towards the capillary and exhibit out-of-plane circular streaming along the shaft of the glass capillary in the z-axis. The red arrow depicts the direction of movement of microparticles. See Supplementary Movie 2. Scale bar: 30 µm. b The acoustofluidic device generated a circular-flow field in the liquid surrounding its body, indicated by the PIV-generated velocity fields. The PIV was generated using MATLAB code and the blue arrows represent the velocity and direction of the microparticles. The green dot represents the position of capillary tip. See Supplementary Movie 2. Scale bar: 500 μm. c Average velocities of the tracer particles at the site indicated by the square box in b versus the voltage applied. Particle velocities were proportional to the square of the voltage used, thus satisfying the quadratic relation, as demonstrated in the log plot (inset). d Average velocities of tracer particles versus distance from the capillary boundary. Velocities scale to the power of negative two with distance. Each data point represents the average velocity measured from at least eight tracer particles. Error bars in both graphs c, d represent standard deviation (s.d.) as n ≤ 5. See Supplementary Data Files 2 and 3 for the source data for both graphs.