Very viscous electrically forced jets

The dynamics of an axisymmetric jet of a very viscous liquid issuing into a region of uniform electric field, which is of interest for electrospinning, is described numerically using the leaky dielectric model. The jet is continuously strained by surface electric stresses. The flow depends on a capillary number Ca based on the liquid flow rate; an electric Bond number that measures the ratio of electric to surface tension stresses; the dielectric constant of the liquid; and the ratio T of a mechanical (viscous-capillary) time to the electric relaxation time required for the charge that is brought to the surface by the electric field to screen the liquid from the field. The electric current and the radius of the jet increase with Ca and tend to well defined limits for large values of this parameter, whereas a stationary jet ceases to exist when Ca decreases below a certain minimum. The radius of the jet decreases when the electric Bond number increases, due to the increased straining, and also when the time ratio T increases, which suggests that charge relaxation effects are always important in the formation of the jet.