Instability patterns of ferrofluids immersed in a fluid layer

We present a systematic experimental study of a different pattern-forming instability occurring when a ferrofluid droplet is immersed in a thin layer of a nonmagnetic fluid and subjected to a uniform perpendicular magnetic field. For a miscible droplet with various initial diameters or field strengths, we demonstrate the development of a hybrid-type ferrohydrodynamic instability, where peak and labyrinthine ferrofluid patterns coexist and share a coupled dynamic evolution. For the cases of a smaller initial droplet, the fluids are confined within the layer and result in a regime of labyrinthine dominant instability. If the volumes of ferrofluids are sufficiently large, the third dimensional peaks would exceed to layer's surface and the Rosensweig instability is the dominant behaviour. On the other hand, no labyrinthine instability is triggered for an immiscible droplet in the present experiments due to significant constraints of the surface tension. Only the Rosensweig instability with several distinct stages is observed. An interesting dual Rosensweig instability is observed if the magnetic field is turned off and reapplied in the immiscible cases.