Two-dimensional magnetic liquid froth: Coarsening and topological correlations

Abstract

We present an experimental study of a cellular system which may be formed in a two-dimensional (2D) layer made of an immiscible mixture of a magnetic fluid and an oil. We obtain a wet or a dry 2D froth, the characteristics of which are determined by the strength of an externally applied magnetic field. The froth is formed in an equilibrium state; the topological and geometrical features of the froth are fixed by the value of the applied field. The cellular pattern of the froth is stable in time, and a coarseninglike behavior is observed on decreasing the amplitude of the field. This cellular system can be used as a model to study topological processes in the equilibrium state, contrary to soap froths which are nonequilibrium systems because gas diffusion occurs. We show that the topological characteristics are statistically reversible after a magnetic-field cycle, and we present a statistical study of the froth features as a function of the amplitude of the field. The topological correlations between neighboring cells are well described by the Aboav-Weaire law. Finally, we consider the area of an $n$-sided cell, and show that its growth rate (magnetic field dependent) is, in a surprising manner, proportional to $n\ensuremath{-}6,$ similarly to the Von Neumann law.