Taylor cone

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A Taylor cone refers to the cone observed in electrospray 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 colloid thrusters used in fine control and high efficiency (low power) thrust of spacecraft.

1 History
2 Theory
3 External links
4 References

[edit] History

This cone was described by Sir Geoffrey Ingram Taylor in 1964 before electrospray was "discovered". This work followed on the work of Zeleny where in 1917 he photographed a cone-jet of glycerine under high electric field and the work of several others, Wilson & 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.

[edit] 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 $π - θ 0$ where $θ 0$ is the first zero of $P 1 / 2 (c o s θ 0)$ (the Legendre polynomial 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 $R 1 / 2$ dependence to counter the surface tension to produce the cone. The solution to this problem is:

V = V 0 + A R 1 / 2 P 1 / 2 (c o s θ 0)

where $V = V 0$ (equipotential surface) exists at a value of $θ 0$ (regardless of R) producing an equipotential cone. The magic angle necessary for $V = V 0$ for all R is a zero of $P 1 / 2 (c o s θ 0)$ between 0 and $π$ which there is only one at 130.7099°. The complement of this angle is the Taylor angle.