Simultaneous multi-frequency excitation for environmentally robust 2D acoustic focusing in cylindrical tubes

Acoustic focusing in cylindrical tubes based on bulk acoustic waves (BAWs) enables two-dimensional (2D) focusing with a single transducer, but its performance strongly depends on the match between the driving frequency and the resonance condition of the coupled transducer–tube–fluid system. Environmental variations in temperature and solution properties shift the resonance frequency, making it difficult to maintain acoustic focusing. This study demonstrates that simultaneous multi-frequency excitation of a single transducer can achieve robust 2D acoustic focusing of 15-µm polystyrene microparticles in a stainless steel tube at around 1080 kHz. Temperature variation (20–30 °C) caused a center frequency shift of 13.5 kHz, which was compensated by dual-frequency excitation. NaCl concentration variation from 0% to 3.5% produced a shift of 20.5 kHz that was also covered by dual-frequency excitation. When temperature and NaCl concentration varied simultaneously (total shift of 37 kHz), triple-frequency excitation achieved 2D focusing under all conditions. The center frequency was well described by a linear function of temperature and NaCl concentration, providing an interpolation-based guideline for frequency selection. Electrical spectrum measurements confirmed that the intended frequency components dominated the multi-tone excitation. Power and thermal measurements showed that PZT self-heating increased with the number of frequency components, while its temperature remained below 40 °C. After prior characterization for fixed-frequency selection, the method operates with one amplifier and one transducer without real-time active feedback control and can be extended by adding frequencies. These findings offer practical design guidelines for robust cylindrical acoustic focusing devices operating under predefined environmental windows.