Labyrinthine instabilities of a magnetic droplet in a Hele--Shaw cell

C.-Y. Wen¹ - Ching-Yao Chen² - C.-H. Tsai¹ - D.-C. Kuan¹

¹ Department of Mechanical and Automation Engineering, Da-Yeh University, Chang-Hwa, Taiwan, Republic of China
² Department of Mechanical Engineering, National Yunlin University of Science and Technology, Yunlin, Taiwan, Republic of China

Abstract
We have qualitatively and quantitatively analyzed the labyrinthine instability of an immiscible droplet under a perpendicular field. Interesting reverse-growing fingers are recorded for the situation with an extremely vigorous fingering instability. The experiments further confirm the strong correlation between the fastest growing mode by theoretical predictions and the final number of fingers within a wide range of modes. Also validated is the dependence of a critical magnetic Bond number for the 2-lobe mode on the dimensionless diameter. Verifications of the theoretical results have given more reliable supports to the correctness of the applied mathematical model and the following up simulations based on the model. Figs 5, Refs 12.