TAYLOR CONE ELECTROHYDRODYNAMICS. THE MINIMUM AND MAXIMUM FLOW RATES IN ELECTROSPRAYING

The surface charge at the liquid–gas interface in cone-jet electrospraying, almost relaxed from an electrochemical point of view, is driven by the radial electric field created to supply the current to the cone tip that the microjet withdraws. The electric stress applied on the liquid surface provokes a low or high Reynolds number motions in the electrified meniscus depending on a dimensionless parameter which relates the liquid viscosity and its electrical conductivity. The analysis of the surface motion is essential to quantify the surface current convected to the cone’s tip, which is shown to be negligible compared to the one driven by bulk conduction. In the case of high Reynolds number motions, we show mathematically, and also experimentally, the emergence of an interesting self-rotation phenomenon. In addition, an analysis of the equations governing the electrohydrodynamics of the charged liquid ligament issuing from the tip of an electrified meniscus in a steady cone-jet suggests the mechanisms which set the stability limits of this steady regime. It is shown that for low and moderate liquid polarities (less than 40 times the vacuum permittivity), the minimum liquid flow rate that can be electrosprayed in a steady cone-jet is reached when the surface tension stress at the cusp from which the jet issues, which provokes a resulting pressure gradient against the flow, overcomes the electrostatic “suction” effect. To show the role of the different forces involved, we have carried the calculation of the intervening ones in the momentum equation using the digitized shape of a cone-jet close to the minimum flow rate in the case of a permittivity 6.5 times larger than the vacuum one. For larger polarities, which impose large electrical conductivities as well, the role of viscous forces, polarization forces, and charge relaxation effects is discussed. In addition, we have carried out experimental measurements of the minimum flow rate using several different liquids. These results are discussed and compared with the experimental data from different authors, as well as with other previously given scaling laws and estimations of the minimum flow rate in cone-jet electrospraying.