https://doi.org/10.1140/epje/s10189-024-00420-z
Regular Article - Flowing Matter
Free surface oscillation driven by rotating stirrer
1
Graduate School of Engineering, The University of Tokyo, 7-3-1, Hongo, 113-8656, Bunkyo-ku, Tokyo, Japan
2
Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, 560-8531, Toyonaka, Osaka, Japan
a
watamura@g.ecc.u-tokyo.ac.jp
Received:
19
December
2023
Accepted:
25
March
2024
Published online:
13
April
2024
To gain insights into the mechanisms of free surface oscillation in a rotating mixing container, we observe the free surface deformation and measure the torque acting on the bar. The container was half-filled with liquids. Periodic surface oscillation occurs. At the rotational speed where the amplitude of the oscillation reaches its maximum, the time-averaged torque also takes the local maximum values. To account for the sloshing mechanism, an equation of motion is derived using the Lagrangian mechanics; we found that the sloshing occurs when the collision frequency of bar on the surface is consistent with the natural frequency of the system and the damping coefficient is sufficiently smaller than unity. The time-averaged torque increases when the sloshing becomes violent. We conclude that the hydrodynamics of oscillation is successfully modeled using point-mass mechanics, and thus we can reasonably capture the rotation speed at which violent oscillation occurs.
© The Author(s) 2024
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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.
