Annular flow instabilities and large-scale vortices in electromagnetically driven horizontal soap films

We study the conditions under which large-scale vortex flow patterns appear in electromagnetically driven conducting horizontal soap films created between two coaxial cylindrical electrodes and placed in a vertical magnetic field. For large Marangoni and Peclet numbers, the two-dimensional flow in a flat free film is effectively incompressible and the surface concentration of an insoluble surfactant plays the role of the pressure away from the boundaries. If the direct radial electric current flows through the film, the Lorentz force arising in a uniform field drives the azimuthal flow. Its stability is investigated in cases of slip and no-slip boundary conditions at the edges of the film in the limit of a small Hartmann number. Flow stability changes nontrivially depending on the slip length, and the flow stabilizes for perfect-slip boundaries. In contrast, if the vertical axisymmetric field is strongly nonuniform, the flow may become linearly unstable at much smaller Reynolds numbers than the critical value for no-slip boundaries,- leading to the formation of large-scale circulation cells. Our experiments conducted using a piecewiseconstant magnetic field detect the formation of vortex structures that are in qualitative agreement with those predicted by the performed analysis.<p></p>