Experimental studies of labyrinthine instabilities of miscible ferrofluids in a Hele-Shaw cell

The first systematic experimental studies on the labyrinthine instabilities of miscible ferrofluids in a Hele-Shaw cell are presented. Two distinct features of instabilities are observed: (i) the miscible labyrinthine fingers caused by the magnetic dipolar forces; (ii) the secondary waves dominated by the third-dimensional effects. Prominence of the labyrinthine fingers is confirmed to be affected significantly by both the magnetic field strength and the cell gap width. On the other hand, wave selection of the secondary wave numbers is mainly dominated by the gap width. The characteristic wavelength λ of the secondary waves follows a nearly linear correlation with the gap width h, which is consistent with earlier findings on the viscous fingering instability. The wavelength can be approximated as λ≈(7±1)h.