A paper titled “Measurement of traveling pressure waves inside a droplet,” with Sayaka Ichihara as the lead author, has been accepted for publication in "Experimental Thermal and Fluid Science".

In this study, we proposed a background-oriented schlieren (BOS) measurement method for the noncontact, quantitative measurement of pressure waves propagating inside a droplet. Although droplets are transparent, it is not easy to quantitatively measure internal pressure waves because light is refracted at the droplet interface. In this study, we reconstructed the density gradient field and pressure field inside the droplet by combining projected background BOS, ray-tracing correction, fast checkerboard demodulation, and vector tomography.

In the experiments, we applied a laser-induced shock wave to a perfluorohexane (PFH) droplet suspended in water and measured the pressure waves propagating inside and outside the droplet in both space and time. The obtained density gradient and pressure fields were compared with numerical calculations, confirming good agreement in the speed of sound, focal position, maximum pressure, and other parameters. Furthermore, we successfully observed experimentally the sign reversal of pressure waves associated with shock wave focusing inside the droplet.

This research is also the result of ongoing international collaboration between TUAT and ETH Zürich. The starting point for this study was Sayaka Ichihara’s visit to Prof. Outi Supponen’s group at ETH Zürich from January to March 2023, during which she applied the BOS method to various high-speed pressure wave phenomena. Subsequently, following Prof. Outi’s visit to the Tagawa Laboratory at the end of March 2023, regular online meetings began between the two laboratories.

In June 2024, Ms. Ichihara returned to ETH Zürich and acquired the core data for this paper through two weeks of intensive experiments. The quantitative validity of the experimental results was then verified through comparison with numerical simulations of the interior of the droplet being conducted at ETH Zürich. Furthermore, in February 2025, we invited co-author Samuele Fiorini to the Tagawa Laboratory to discuss the paper. Through these ongoing exchanges and discussions, this paper was completed.

This work provides a new measurement method for understanding the interaction between shock waves and droplets. It is expected to contribute to the understanding of high-speed pressure wave phenomena occurring inside transparent droplets and spherical objects, such as in atomization, aircraft combustion, raindrop collisions, and medical applications. Furthermore, this achievement is the result not merely of a single joint experiment, but of the international exchange of young researchers, ongoing discussions between laboratories, and the integration of experimental and numerical simulations.

Paper Information：

Sayaka Ichihara, Samuele Fiorini, Yoshiyuki Tagawa, and Outi Supponen,

“Measurement of traveling pressure waves inside a droplet,”

Experimental Thermal and Fluid Science, accepted.

DOI/URL: https://doi.org/10.1016/j.expthermflusci.2026.111800