Scaling Behavior of Field-Induced Aggregates in Ferrofluids

An ordered hexagonal array of aggregates can form in thin ferrofluid layers when an external magnetic field is applied. Using the Helmholtz free energy for this system, we calculate the optimum spacing for these aggregates. Results show excellent agreement with experimental findings as a function of field strength and layer thickness. Our analysis yields a crossover in the exponent for the scaling behavior of the aggregate spacing as a function of plate separation, in agreement with experiment. For the first time, we report a similar crossover in the scaling behavior of the aggregate spacing as a function of the magnetic field. The mechanisms responsible for both crossovers are introduced and discussed.