Sessile and pendant droplets of polymer solutions acquire stable shapes when they are electrically charged by applying an electrical potential difference between the droplet and a flat plate, if the potential is not too large. These stable shapes result only from equilibrium of the electric forces and surface tension in the cases of inviscid, Newtonian, and viscoelastic liquids. In liquids with a nonrelaxing elastic force, that force also affects the shapes. It is widely assumed that when the critical potential φ_(0*) has been reached and any further increase will destroy the equilibrium, the liquid body acquires a conical shape referred to as the Taylor cone, having a half angle of 49.3°. In the present work we show that the Taylor cone corresponds essentially to a specific self-similar solution, whereas there exist nonself-similar solutions which do not tend toward a Taylor cone. Thus, the Taylor cone does not represent a unique critical shape: there exists another shape, which is not self-similar. The experiments of the present work demonstrate that the observed half angles are much closer to the new shape. In this article a theory of stable shapes of droplets affected by an electric field is proposed and compared with data acquired in our experimental work on electrospinning of nanofibers from polymer solutions and melts.
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