Low and high Reynolds number flows inside Taylor cones

Abstract

Liquid motions inside Taylor cones exhibit interesting features which are not well understood yet. In addition to the flow rate injected through the electrified needle to which the conical meniscus is anchored, the action of the tangential electrical stress on the cone surface induces a recirculating meridional motion, towards the apex along the generatrix and away from it along the axis. Sometimes, a vigorous swirl is observed. The characteristic value of the liquid velocity is found to be highly dependent on both the electrical conductivity and the viscosity of the liquid, so that the Reynolds number of the liquid flow varies from very small values (creeping flow) for the case of highly conducting and viscous liquids to relatively large values for liquids with sufficiently low values of the liquid conductivity and viscosity. Theoretical conical flows for low and high values of the Reynolds number show qualitatively good agreement with photographs of real flows inside Taylor cones. In particular, the existence of a vigorous swirl which is observed in the electrospraying of paraffins and other poorly conducting and low viscosity liquids can be explained as bifurcation of a primarily nonswirling meridional flow when the Reynolds number reaches a critical value.