Computational analysis of free surface magnetohydrostatic equilibrium: force versus energy formulation

A. A. Aristidopoulou - A. T. Papaioannu - A. G. Boudouvis

Department of Chemical Engineering, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

Abstract
The magnetohydrostatic equilibrium of free ferrofluid surfaces in an external magnetic field is formulated in terms of force balancing - the force formulation - as well as energy minimization - the energy formulation. Both formulations give rise to a nonlinear, free boundary problem that is solved by the Galerkin/finite element method. The governing equations in the two formulations are identical in the continuum. However, the discretized versions of the two formulations are not equivalent. Computations show that the dependence of the solutions of the governing equations on the applied field strength is not identical in the two formulations; their differences decrease with discretization refinement, but do not vanish. Tabl. 2, figs 4, refs 10.