The shape evolution of small droplets attached to a conducting surface and subjected to relatively strong electric fields is studied both experimentally and numerically. The problem is motivated by the phenomena characteristic of the electrospinning of nanofibres. Three different scenarios of droplet shape evolution are distinguished, based on numerical solution of the Stokes equations for perfectly conducting droplets. (i) In sufficiently weak (subcritical) electric fields the droplets are stretched by the electric Maxwell stresses and acquire steady-state shapes where equilibrium is achieved by means of the surface tension. (ii) In stronger (supercritical) electric fields the Maxwell stresses overcome the surface tension, and jetting is initiated from the droplet tip if the static (initial) contact angle of the droplet with the conducting electrode is $\alpha_{s}\,{<}\,0.8\pi $; in this case the jet base acquires a quasi-steady, nearly conical shape with vertical semi-angle $\beta \,{\leq}\, 30^{\circ}$, which is significantly smaller than that of the Taylor cone ($\beta_{T}\,{=}\,49.3^{\circ}$). (iii) In supercritical electric fields acting on droplets with contact angle in the range $0.8\pi \,{<}\,\alpha_{s}\,{<}\,\pi $ there is no jetting and almost the whole droplet jumps off, similar to the gravity or drop-on-demand dripping. The droplet–jet transitional region and the jet region proper are studied in detail for the second case, using the quasi-one-dimensional equations with inertial effects and such additional features as the dielectric properties of the liquid (leaky dielectrics) taken into account. The flow in the transitional and jet region is matched to that in the droplet. By this means, the current–voltage characteristic $I\,{=}\,I(U)$ and the volumetric flow rate $Q$ in electrospun viscous jets are predicted, given the potential difference applied. The predicted dependence $I\,{=}\,I(U)$ is nonlinear due to the convective mechanism of charge redistribution superimposed on the conductive (ohmic) one. For $U\,{=}\,O(10kV)$ and fluid conductivity $\sigma \,{=}\,10^{-4}$ S m$^{-1}$, realistic current values $I\,{=}\,O(10^{2}nA)$ were predicted.

The shape evolution of small compound droplets at the exit of a core-shell system in the presence of a sufficiently strong electric field is studied both experimentally and theoretically. It is shown that the jetting effect at the tip of the shell nozzle does not necessarily cause entrainment of the core fluid, in which case the co-electrospinning process fails to produce core-shell nanofibers. The remedy lies in extending the core nozzle outside its shell counterpart by about half the radius of the latter. The results also show that the free charges migrate very rapidly from both fluids and their interface to the free surface of the shell. This reflects the fact that most of the prejetting evolution of the droplet can be effectively described in terms of the perfect conductor model, even though the fluids can be characterized as leaky dielectrics. The stress level at the core-shell interface is of the order of 5×103g∕(cms2), the relevant value in assessing the viability of viruses, bacteria, DNA molecules, drugs, enzymes, chromophores, and proteins to be encapsulated in nanofibers via co-electrospinning.

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The capillary-dominated regime of dynamics of electrified jets of a viscous leaky dielectric liquid is studied numerically. In this regime the effective force in the direction of an applied field due to tangential electric stresses is balanced by the gradient of liquid pressure governed by the surface-tension stresses. As is characteristic of this regime, the electric current and the characteristic jet radius are dependent on the surface-tension coefficient and not on viscosity. In the scope of this work, the conditions of the existence of this regime are determined. A qualitative order-of-magnitude analysis gives the power-law dependences of the jet radius and electric current on the parameters of the problem (conductivity, applied electric field, flow rate, and surface-tension coefficient). Numerical results are obtained for low conductive liquids for a large range of the dimensionless flow rate (capillary number, Ca). The order-of-magnitude estimations of electric current are in agreement with the numerical results given a small Ca. The corresponding numerically obtained jet shapes are discussed and explained.

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