We investigate the linear stability threshold of a dielectric liquid subjected to unipolar
injection in a 2D rectangular enclosure with rigid boundaries. A finite element formulation
transforms the set of linear partial differential equations that governs the system into a set
of algebraic equations. The resulting system poses an eigenvalue problem. We calculate
the linear stability threshold, as well as the velocity field and charge density distribution,
as a function of the aspect ratio of the domain. The stability parameter as a function
of the aspect ratio describes paths of symmetry-breaking bifurcation. The symmetry
properties of the different linear modes determine whether these paths cross each other
or not. The resulting structure has important consequences in the non-linear behavior of
the system after the bifurcation points.Ministerio de ciencia y tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458
