Ferrofluid drop in an off-centered radial magnetic field

We investigate the dynamic and morphological behaviors of a ferrofluid drop initially located at the center of a Hele–Shaw cell, under the influence of an off-centered radial magnetic field. Previous studies have demonstrated that when the center of the cell coincides with the center of the radial magnetic field, rotationally symmetric, stationary, starlike ferrofluid shapes may arise. In this work, we employ a perturbative, second-order mode-coupling approach to examine the changes in the emergent ferrofluid structures when the radial magnetic field is shifted off-center. Our results show that the symmetry and location of the applied radial magnetic field play a key role in determining the shape and dynamical response of the ferrofluid droplet, with the off-centered radial field leading to nonrotationally symmetric interfacial patterns that drift away from the magnetic field's center. Our early nonlinear findings indicate that stationary shapes only develop when the field's center is aligned with the center of the Hele–Shaw cell (i.e., with the center of the originally circular ferrofluid drop). We have also found that small misalignments between the center of the droplet and the center of the radial field can induce important changes in the pattern formation process, including modifications in the number of fingered protrusions formed. The influence of the ferrofluid's magnetic susceptibility on the interfacial shapes and drift velocity and the impact of random perturbations in the initial conditions are also scrutinized.