On combined spatial and temporal instabilities of electrically driven jets with constant or variable applied field

We investigate the problem of combined spatial and temporal instabilities of electrically driven viscous jets with finite electrical conductivity in the presence of either constant or variable applied electric field. A mathematical model leads to a lengthy equation for the unknown spatial growth rate and temporal growth rate of the disturbances. This equation is solved numerically using Newton's method. We investigated two cases of water jets and glycerol jets. For water jets and in the case of either constant or variable applied field, we found two new modes of instabilities which grow simultaneously in time and space and lead to significant reduction in the jet radius. However, in the case of glycerol jets, we found two new modes of instabilities in the presence of constant applied field but only one mode of instability in the presence of variable applied field. For the glycerol jets, the combined temporal and spatial instabilities are less stronger and lead to an increase in the jet radius. The instabilities for both types of water and glycerol jets were found to be restricted to particular domain in their wavelength and were enhanced with the strength of the electric field.