Self-forming, quasi-two-dimensional, magnetic-fluid patterns with applied in-plane-rotating and dc-axial magnetic fields

We report flow instabilities with simultaneous, in-plane-rotating and dc-axial uniform magnetic fields. In uniform dc-axial magnetic fields, a ferrofluid drop in a Hele-Shaw cell with an ~1.0-mm gap forms the familiar labyrinth pattern. With subsequent application of an ~100-G rms in-plane, 20-40-Hz rotating uniform magnetic field, smooth spirals form. If the rotating magnetic field is applied first, the drop holds together for low dc-axial magnetic fields and no labyrinth pattern develops. If the dc magnetic field is subsequently increased above a threshold value, the ferrofluid drop abruptly transforms into many ferrofluid droplets arranged in a regular pattern.