Contribution to the dynamics of a deformable interface between two immiscible electromagnetically controllable fluids

We consider the case of a deformable material interface between two immiscible moving media, both of them being magnetizable, stressing the time dependence of the metric at the interface. This introduces a nonlinear term, proportional to the mean curvature, in the surface dynamical equations of mass momentum and angular momentum. That term intervenes also in the singular magnetic and electric fields inside the interface which lead to the influence of currents and charge densities at the interface. Also, we give the expression for the entropy production and of the different thermodynamical fluxes.