Marco Fontelos (Departamento de Matemáticas, Universidad Autónoma de Madrid, Espagne). Drops in an electric field: instabilities, bifurcations and phase field modelling.

The influence of electric fields on the shape and evolution of drops is an important problem in the context of technological applications such as electrowetting. The term electrowetting is commonly used for some techniques to change the shape and wetting behaviour of liquid droplets by the application of electric fields and charges. First, we describe the presence of symmetry breaking bifurcations and their physical role in the development of instabilities. We also discuss the possible formation of singularities at the liquid surface. We then develop and analyze a model for electrowetting that combines the Navier-Stokes system for fluid flow, a phase-field model of Cahn-Hilliard type for the movement of the interface, a charge transport equation, and the potential equation of electrostatics. A critical role in the deduction of suitable couplings between phase field and other physical fields is played by variational principles involving suitable energies.