Two-Dimensional Magnetic Liquid Froth

Abstract

We present a new cellular structure, obtained in a pseudo two-dimensional (2D) layer of magnetic fluid (MF) submitted to a perpendicular magnetic field. This froth is analogous to 2D soap froths, because its energy contains an interfacial contribution. Nevertheless, whereas a soap froth coarsens in time to minimize the surface of its interface, the 2D MF froth can be stable in time. Indeed it also has a magnetic energy, which allows the cellular pattern to reach an equilibrium state. The properties of such a froth in its equilibrium state are thus driven by competition between the surface energy and the magnetic energy. The latter depends on the amplitude of the applied magnetic field, which is a control parameter of this system. An evolution of the structure is obtained on decreasing the amplitude of the field: the number of cells decreases so that the pattern turns into a single drop of MF in zero field. We present here a study of this coarsening with decreasing of the field. For high amplitudes of the applied field, we have observed out of equilibrium states of the 2D MF froth: the area of the cells evolves in time, depending on their number of sides. This behaviour looks like a Von Neumann one (which drives the time-evolution of 2D soap froths), but with the opposite sign: 5-sided cells grow in time, 7-sided cells shrink, whereas 6-sided cells do not evolve. In section 6, the 2D MF froths are shown to obey the Aboav and Weaire law which describes the topological interactions between cells, as all the 2D cellular structures. Finally, we present a potential application of the 2D MF froth, for the study of topology in 2D cellular patterns.