Numerical simulations of a ferrofluid drop on a substrate under an applied magnetic field

Understanding the behavior of a ferrofluid drop on a surface is of direct relevance to applications such as adaptive liquid lens optics. Here, we consider a ferrofluid drop on a horizontal substrate subjected to an applied uniform magnetic field with a non-magnetizable passive gas atop. Governing equations are the static Maxwell equations coupled with the incompressible Navier-Stokes equations. We use the long wave approximation to derive the equation that governs the non-linear evolution of the drop interface. Contact angles are imposed through the disjoining pressure model. The evolution equation is solved numerically and the results are compared with data from experiments.