Shape formation of ferrofluid under external magnetic fields using level set method

The shape formation of ferrofluid under magnetic field has been considered to be one of most difficult problems to analyze. In this paper we present a numerical implementation of the level set method for the equilibrium shape calculation of ferrofluid under magnetic field. The magnetic-fluid coupled system has an extremum value of electromagnetic system energy. When the system is composed of magnetic permeable material and current sources, the system energy is a maximum at the equilibrium state. The level set method is adopted for shape capturing since it can easily handle shape variations of fluid including topological changes such as merging, splitting, and even disappearing of connected material regions. The velocity field for the level set method is calculated using a shape derivative of continuum sensitivity analysis that is derived by employing the material derivative concept. The numerical results for a model problem of some ferrofluid on a glass plate show that the level set method works well for the ferrofluid shape formation.