Effect of small electric fields on liquid menisci

Under the effect of surface tension, the liquid meniscus assumes a semi-spherical shape at the tip of the emitter. Application of the positive voltage ${\displaystyle V\,}$ will induce the electric field:^[11]

${\displaystyle E={2V \over r\ln(4d/r)}}$

where ${\displaystyle r\,}$ is the liquid radius of curvature. This field leads to liquid polarization: the negative/positive charge carriers migrate toward/away from the electrode where the voltage is applied. At voltages below a certain threshold, the liquid quickly reaches a new equilibrium geometry with a smaller radius of curvature.

The Taylor cone

Voltages above the threshold draw the liquid into a cone. Sir Geoffrey Ingram Taylor described the theoretical shape of this cone based on the assumptions that (1) the surface of the cone is an equipotential surface and (2) the cone exists in a steady state equilibrium.^[7] To meet both of these criteria the electric field must have azimuthal symmetry and have ${\displaystyle R^{1/2}\,}$ dependence to balance the surface tension and produce the cone. The solution to this problem is:

${\displaystyle V=V_{0}+AR^{1/2}P_{1/2}(\cos \theta _{0})\,}$

where ${\displaystyle V=V_{0}\,}$ (equipotential surface) exists at a value of ${\displaystyle \theta _{0}}$ (regardless of R) producing an equipotential cone. The magic angle necessary for ${\displaystyle V=V_{0}\,}$ for all R is a zero of the Legendre polynomial of order 1/2, ${\displaystyle P_{1/2}(\cos \theta _{0})\,}$. There is only one zero between 0 and ${\displaystyle \pi \,}$ at 130.7099°, which is the complement of the Taylor's now famous 49.3° angle.

Singularity development

The apex of the conical meniscus cannot become infinitely small. A singularity develops when the hydrodynamic relaxation time ${\displaystyle \tau _{H}={\mu r \over \gamma }}$ becomes larger than the charge relaxation time ${\displaystyle \tau _{C}={\epsilon _{r}\epsilon _{0} \over \kappa }}$.^[12] The undefined symbols stand for characteristic length ${\displaystyle (r)\,}$ and vacuum permittivity ${\displaystyle (\epsilon _{0})\,}$. Due to intrinsic varicose instability, the charged liquid jet ejected through the cone apex breaks into small charged droplets, which are radially dispersed by the space-charge.

Closing the electrical circuit

The charged liquid is ejected through the cone apex and captured on the counter electrode as charged droplets or positive ions. To balance the charge loss, the excess negative charge is neutralized electrochemically at the emitter. Imbalances between the amount of charge generated electrochemically and the amount of charge lost at the cone apex can lead to several electrospray operating regimes. For cone-jet electrosprays, the potential at the metal/liquid interface self-regulates to generate the same amount of charge as that lost through the cone apex.^[13]

Electrospray ionization

Electrospray became widely used as ionization source for mass spectrometry after the Fenn group successfully demonstrated its use as ion source for the analysis of large biomolecules.^[14]

Liquid metal ion source

A liquid metal ion source (LMIS) uses electrospray in conjunction with liquid metal to form ions.^[15][16] Ions are produced by field evaporation at tip of the Taylor cone. Ions from a LMIS are used in ion implantation and in focused ion beam instruments.

Electrospinning

Similarly to the standard electrospray, the application of high voltage to a polymer solution can result in the formation of a cone-jet geometry. If the jet turns into very fine fibers instead of breaking into small droplets, the process is known as electrospinning .

Colloid thrusters

Electrospray techniques are used as low thrust electric propulsion rocket engines to control satellites, since the fine-controllable particle ejection allows precise and effective thrust.

Deposition of particles for nanostructures

Electrospray may be used in nanotechnology,^[17] for example to deposit single particles on surfaces. This is done by spraying colloids on average containing only one particle per droplet. The solvent evaporates, leaving an aerosol stream of single particles of the desired type. The ionizing property of the process is not crucial for the application but may be used in electrostatic precipitation of the particles.

Deposition of ions as precursors for nanoparticles and nanostructures

Instead of depositing nanoparticles, nanoparticles and nano structures can also fabricated in situ by depositing metal ions to desired locations. Electrochemical reduction of ions to atoms and in situ assembly was believed to be the mechanism of nano structure formation.

Fabrication of drug carriers

Electrospray has garnered attention in the field of drug delivery, and it has been used to fabricate drug carriers including polymer microparticles used in immunotherapy^[18] as well as lipoplexes used for nucleic acid delivery.^[19] The sub-micrometer-sized drug particles created by electrospray possess increased dissolution rates, thus increased bioavailability due to the increased surface area.^[20] The side-effects of drugs can thus be reduced, as smaller dosage is enough for the same effect.

Air purifiers

Electrospray is used in some air purifiers. Particulate suspended in air can be charged by aerosol electrospray, manipulated by an electric field, and collected on a grounded electrode. This approach minimizes the production of ozone which is common to other types of air purifiers.