Abstract
We investigate the dynamics of ferrofluidic wavy vortex flows in the counter-rotating Taylor-Couette system, with a focus on wavy flows with a mixture of the dominant azimuthal modes. Without external magnetic field flows are stable and pro-grade with respect to the rotation of the inner cylinder. More complex behaviors can arise when an axial or a transverse magnetic field is applied. Depending on the direction and strength of the field, multi-stable wavy states and bifurcations can occur. We uncover the phenomenon of flow pattern reversal as the strength of the magnetic field is increased through a critical value. In between the regimes of pro-grade and retrograde flow rotations, standing waves with zero angular velocities can emerge. A striking finding is that, under a transverse magnetic field, a second reversal in the flow pattern direction can occur, where the flow pattern evolves into pro-grade rotation again from a retrograde state. Flow reversal is relevant to intriguing phenomena in nature such as geomagnetic reversal. Our results suggest that, in ferrofluids, flow pattern reversal can be induced by varying a magnetic field in a controlled manner, which can be realized in laboratory experiments with potential applications in the development of modern fluid devices.
Highlights
Reversal of a fluid flow upon parameter changes or perturbation is closely related to intriguing phenomena such as geomagnetic reversal, a drastic change in a planet’s magnetic field where the positions of magnetic north and south are interchanged[1]
We report magnetic-field induced flow pattern reversals in the classic Taylor-Couette system (TCS)[8], which can exhibit a large number of flow structures of distinct topologies and has been an experimental and computational paradigm for investigating many fundamental phenomena in fluid dynamics for decades[9,10,11,12,13]
The TCS with conventional fluid or with ferrofluid but without external magnetic field typically possesses a large number of solutions with distinct dynamical properties, some of which can coexist in a wide range of parameters[11]
Summary
Reversal of a fluid flow upon parameter changes or perturbation is closely related to intriguing phenomena such as geomagnetic reversal, a drastic change in a planet’s magnetic field where the positions of magnetic north and south are interchanged[1]. The TCS with conventional fluid or with ferrofluid but without external magnetic field typically possesses a large number of solutions with distinct dynamical properties, some of which can coexist in a wide range of parameters[11]. With variation in the strength of either axial or transverse magnetic field, the fluid motion can change from pro-grade to retrograde wavy flow patterns separated by stable interim, standing-wave solutions with zero angular velocities. These standing waves are part of an other class of flow states, mixed-ribbon[28]. Our results suggest that flow pattern reversals in the ferrofluidic TCS can be controlled through an external magnetic field, which is fundamentally interesting and relevant for practical development of novel fluid devices
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