Liu Li(李柳)1,2, Decai Li(李德才)1,3,†, Zhiqiang Qi(戚志强)1,2, Lu Wang(王璐)1,2, and Zhili Zhang(张志力)1,2
1 School of Mechanical, Electronic, and Control Engineering, Beijing Jiaotong University, Beijing 100044, China; 2 Beijing Key Laboratory of Flow and Heat Transfer of Phase Changing in Micro and Small Scale, Beijing 100044, China; 3 State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
Abstract The explicit analytical solution of Rosensweig instability spikes' shapes obtained by Navier-Stokes (NS) equation in diverse magnetic field H vertical to the flat free surface of ferrofluids are systematically studied experimentally and theoretically. After carefully analyzing and solving the NS equation in elliptic form, the force balanced surface equations of spikes in Rosensweig instability are expressed as cosine wave in perturbated magnetic field and hyperbolic tangent in large magnetic field, whose results both reveal the wave-like nature of Rosensweig instability. The results of hyperbolic tangent form are perfectly fitted to the experimental results in this paper, which indicates that the analytical solution is basically correct. Using the forementioned theoretical results, the total energy of the spike distribution pattern is calculated. By analyzing the energy components under different magnetic field intensities H, the hexagon-square transition of Rosensweig instability is systematically discussed and explained in an explicit way.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 51735006, 51927810, and U1837206) and Beijing Municipal Natural Science Foundation (Grant No. 3182013).
Corresponding Authors:
Decai Li
E-mail: lidecai@tsinghua.edu.cn
Cite this article:
Liu Li(李柳), Decai Li(李德才), Zhiqiang Qi(戚志强), Lu Wang(王璐), and Zhili Zhang(张志力) Wave nature of Rosensweig instability 2024 Chin. Phys. B 33 034701
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