Equilibrium shapes of ferrofluid under different forces using continuum shape sensitivity analysis and level set method.

In this paper, a method for numerical simulation of the shape of a ferrofluid under external magnetic fields and the gravitational field is presented. The final shape is determined by an equilibrium condition of energy in a coupled system of electromagnetic fields and ferrofluid in the presence of gravity. The shape of the ferrofluid is captured by using the level set technique. The velocity field is calculated using continuum shape sensitivity analysis based on the material derivative concept. The numerical algorithm is implemented with a standard finite element procedure and tested on a shaping problem of ferrofluid located under an electromagnet. The numerical results showed that the proposed algorithm and numerical techniques are feasible and effective means of calculating ferrofluid shape variation under magnetic fields and the gravitational force. [ABSTRACT FROM AUTHOR]