title: Self-rotation in electrocapillary flows.
abstract: The mechanism of appearance of swirl in a certain class of converging flows is investigated numerically. The analysis is motivated by the spontaneous generation of swirl, which has been observed in electrified menisci (Taylor cones). The electrical stress acting on the cone surface drives these electrified millimetric fluid flows. Numerical results show that the primarily swirl-free meridian flow is unstable within an interval of values of the Reynolds number based on the surface stress. For values of the Reynolds number outside this interval, which depends on the forcing conditions and the geometry of the flow, the nonswirling meridian flow is stable. The instability mechanism of circulation amplification, which has nothing to do with the well-known increase of swirl velocity due to the vortex stretching mechanism, is due to a convection-diffusion effect. The circulation accumulated at the axis zone by the converging meridian motion is pumped by diffusion toward the conical surface. This feedback loop mechanism shoots the circulation amplification for values of the Reynolds number larger than a critical one. The same instability mechanism of swirl amplification could also appear in other converging flows generated by body forces (natural convection, electrical forces, etc.).