thumb|right|250 px|Photograph of a meniscus of polyvinyl alcohol in aqueous solution showing a fibre drawn from a Taylor cone by the process of electrospinning.
A Taylor cone refers to the cone observed in electrospinning, electrospraying and hydrodynamic spray processes from which a jet of charged particles emanates above a threshold voltage. Aside from electrospray ionization in mass spectrometry, the Taylor cone is important in field-emission electric propulsion (FEEP) and colloid thrusters used in fine control and high efficiency (low power) thrust of spacecraft.
History
This cone was described by Sir Geoffrey Ingram Taylor in 1964 before electrospray was "discovered". This work followed on the work of Zeleny who photographed a cone-jet of glycerine in a strong electric field and the work of several others: Wilson and Taylor (1925), Nolan (1926) and Macky (1931). Taylor was primarily interested in the behavior of water droplets in strong electric fields, such as in thunderstorms.
Formation
thumb|right|300 px|Electrospray diagram depicting the Taylor cone, jet and plume
When a small volume of electrically conductive liquid is exposed to an electric field, the shape of liquid starts to deform from the shape caused by surface tension alone. The liquid becomes polarized and as the voltage is increased the effect of the electric field becomes more prominent. This causes an intense electric field surrounding the liquid droplet
Theory
Sir Geoffrey Ingram Taylor in 1964 described this phenomenon, theoretically derived based on general assumptions that the requirements to form a perfect cone under such conditions required a semi-vertical angle of 49.3° (a whole angle of 98.6°) and demonstrated that the shape of such a cone approached the theoretical shape just before jet formation. This angle is known as the Taylor angle. This angle is more precisely <math>\pi-\theta _0\,</math> where <math>\theta _0\,</math> is the first zero of <math>P _{1/2} (\cos\theta _0)\,</math> (the Legendre function of order 1/2).
Taylor's derivation is based on two assumptions: (1) that the surface of the cone is an equipotential surface and (2) that the cone exists in a steady state equilibrium. To meet both of these criteria the electric field must have azimuthal symmetry and have <math>\sqrt{R}\,</math> dependence to counter the surface tension to produce the cone. The solution to this problem is:
:<math>V=V_0+AR^{1/2}P _{1/2} (\cos\theta _0)\,</math>
where <math>V=V_0\,</math> (equipotential surface) exists at a value of <math>\theta _0</math> (regardless of R) producing an equipotential cone. The angle necessary for <math>V=V_0\,</math> for all R is a zero of <math>P _{1/2} (\cos\theta _0)\,</math> between 0 and <math>\pi\,</math> which there is only one at 130.7099°. The complement of this angle is the Taylor angle.