The normal field instability in ferrofluids: hexagon–square transition mechanism and wavenumber selection

Abstract

When a ferrofluid layer is subjected to a uniform and vertically oriented magnetic field, an interfacial instability occurs, above a critical value of the magnetic field, giving rise to a hexagonal array of peaks. On increasing the magnetic field, a smooth morphological transition from the hexagonal array to a square array was observed above a second threshold. The hexagon–square transition phenomenology, in addition to the role of penta–hepta defects initially present in the hexagonal pattern, was investigated. Furthermore, the pattern and wavenumber selection was studied by two different procedures: first by imposing jumps in field intensity and second by varying the magnetic field in a quasi-static way. The results obtained were very different for the two procedures. They indicated that the square pattern was a metastable state induced by the compression of the hexagonal pattern on increasing the control parameter. This hypothesis was confirmed by performing an additional experiment where the pattern was isotropically compressed. In this experiment, the transition was induced at a constant magnetic field lower than the transition onset value. However, the theoretical values for stability domains of hexagons and squares proposed in the literature were found to not agree with the experimental values.