Calculated properties of field-induced aggregates in ferrofluids

We have calculated the critical radius of aggregates in thin layers of ferrofluid, assuming a cylindrical aggregate shape, as a function of external field and plate separation. Results are obtained by minimizing the Helmholtz free energy, and can be used to predict aggregate radius and spacing. The model, with entropy included, provides reasonable predictions for the onset of the labyrinth pattern. These results show good agreement when compared with data from experiments on Fe3O4 kerosene-based ferrofluids and magnetorheological fluids.