Labyrinthine instabilities of miscible magnetic fluids in a rotating Hele-Shaw cell

Abstract

This study presents the first experimental results of confining miscible magnetic fluids in a rotating Hele-Shaw cell. Variations in the prominence of labyrinthine instabilities are observed under a range of experimental conditions, with different magnetic field strengths, gap depths, and rotation speeds. These instabilities are characterized by two modified Péclect numbers, namely, Pem (the ratio of the characteristic magnetic advection rate and the diffusion rate) and Pec (the ratio of characteristic rotation advection and the diffusion rate). The magnetic effect is characterized by dipolar repulsion, which triggers a distinctive fingering pattern differing from the progressive diffusion pattern that occurs without magnetic fields or rotation. Under the same rotation speed, the magnetoviscous effect will hinder the growth rate of the magnetic drops at the later stage. However, both the rotation effect and the gap depth greatly enhance the growth rate of the magnetic drops, as these conditions help to intensify the labyrinthine instabilities. In contrast, the countering pressure gradient produces an opposite force that constrains the trend toward expansion. Two major phases in the growth of instabilities are defined: a magnetization phase and a rotation phase, which are dominated by the magnetic and the rotation effect, respectively. The significance of the rotation effect is confirmed by the linear regression between the rotation growth rate and Pec. Finally, main fingering structures that evolve from the secondary waves are verified as having a wavelength λ to gap depth h relation of λ≈(7±1)h.