Bubbles and stripes in dipolar fluids

Dipolar fluids exhibit phase behavior as a function of the dimensionless magnetic energy ${\mathit{N}}_{\mathit{B}}$ (‘‘magnetic Bond number’’) and concentration. I propose a phase diagram for such fluids, in an infinite-aspect-ratio cell, for large Bond numbers. For concentrations φ≪${\mathit{N}}_{\mathit{B}}^{\mathrm{-}1/2}$, a two-dimensional lattice of magnetic bubbles should appear, while for higher concentrations, a striped phase has a lower energy. The aspect ratio of the stripes, while asymptotically constant at high concentrations or Bond numbers, shows significant variation near the transition. I expect these results to be relevant to pattern formation in magnetorheological fluids, and possibly to ferrofluids as well.