title: Width of a ferrofluid finger: hysteresis and a double energy minimum.
abstract: We study a ferrofluid in a horizontal Hele-Shaw geometry subjected to a vertical magnetic field. Specifically, we calculate the energy of a single ferrofluid finger using an idealized model for the finger. By minimizing this energy, we find the preferred finger width as a function of the applied field. Our model predicts a first order transition as the fluid abruptly transforms from a circular drop to a finite finger. This behavior arises because of a double energy minimum that yields two different stable configurations for the system. Interestingly, this system exhibits hysteresis as the circle-to-finger (increasing field) transition occurs at a different applied field than the finger-to-circle (decreasing field) transition. We carry out a simple experiment and observe good overall agreement with the theoretical predictions.
authors.affiliation: Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.
authors.forename: Narelle J
authors.initials: NJ
authors.lastname: Hillier
authors.forename: David P
authors.initials: DP
authors.lastname: Jackson