Magnetic field induced labyrinthine structures in ferrofluid emulsions

Jing Liu¹ - G. A. Flores¹ - M. Mohebi² - N. Jamasbi²

¹ Department of Physics and Astronomy, California State University, Long Beach, CA 90840, USA
² Center for Scientific Investigation and Higher Education of Ensenada, Ensenada, Baja California, MEXICO

Abstract
Using optical microscopy, we studied magnetic-field-induced structures in a confined ferrofluid emulsion where the magnetic field is applied quickly as a step function. Columnar, bent-wall-like and labyrinthine structures in 3D are observed, corresponding to disks, "worms" and branch-like patterns in cross-sectional area normal to the magnetic field direction. These 2D structures are characterized by both the ratio of "worms" vs. total aggregates and the average complexity () of the aggregates in a given image. "Phase" diagrams are obtained to characterize disk (columnar) to "worm" (bent-wall) structural transitions as a function of the thickness of the cell used to confine the sample along the field direction, the particle volume fraction, and the rate of the magnetic field application. The distributions of aggregate complexity for a given image is characterized by skewness and quality factor to describe the symmetry and width of complexity distribution. The results show that increasing either cell thickness (L), particle volume fraction (F), or magnetic field ramping rate (R), increases the average complexity of the formed patterns as = 1.8(F^3.11)L ++ 141 log(R) + 0.83, as well as the symmetry and the range of the complexity. This relation can be understood qualitatively. At fast ramping rate R or increasing F (decreasing the inter-particle distance and thus increases the particle interaction), strong magnetic interaction between particles does not allow particles enough time to explore the lowest energy state (columnar structures) before locked into local energy minima (labyrinthine structures). The L-dependence of the complexity supports molecular dynamics simulation results: chains form first and then aggregate to form complex structures; longer chains have larger range of attraction. Figs 9, Refs 25.