Interfacial instability of thin ferrofluid films under a magnetic field

We study magnetically induced interfacial instability of a thin ferrofluid film subjected to an applied uniform magnetic field and covered by a non-magnetizable passive gas. Governing equations are derived using the long-wave approximation of the coupled static Maxwell and Stokes equations. The contact angle is imposed via a disjoining/conjoining pressure model. Numerical simulations show the patterning resulting from unstable perturbations and dewetting of the ferrofluid film. We find that the subtle competition between the applied field and the van der Waals induced dewetting determines the appearance of satellite droplets. The results suggest a new route for generating self-assembled ferrofluid droplets from a thin film using an external magnetic field. An axisymmetric droplet on a surface is also studied, and we demonstrate the deformation of the droplet into a spiked cone, in agreement with experimental findings.