# Electrospray

Electrospray

The name electrospray is used for a device that employs electricity to disperse a liquid or for the fine aerosol resulted in this process. The method is sometimes improperly called electrohydrodynamic atomization. High voltage is applied to a liquid supplied through an emitter (usually a glass or metallic capillary). Ideally the liquid reaching the emitter tip forms a Taylor cone, which emits a liquid jet through its apex. Varicose waves on the surface of the jet lead to the formation of small and highly charged liquid droplets, which are radially dispersed due to Coulomb repulsion.

## History

In the late 16th century William Gilbert[1] set out to describe the behaviour of magnetic and electrostatic phenomena. He observed that, in the presence of a charged piece of amber, a drop of water deformed into a cone. This effect is clearly related to electrosprays, even though Gilbert did not record any observation related to liquid dispersion under the effect of the electric field.

In 1882, Lord Rayleigh theoretically estimated the maximum amount of charge a liquid droplet could carry;[2] this is now known as the "Rayleigh limit". His prediction that a droplet reaching this limit would throw out fine jets of liquid was confirmed experimentally more than 100 years later.[3]

In 1914, John Zeleny published work on the behaviour of fluid droplets at the end of glass capillaries.[4] This report presents experimental evidence for several electrospray operating regimes (dripping, burst, pulsating, and cone-jet). A few years later, Zeleny captured the first time-lapse images of the dynamic liquid meniscus.[5]

Between 1964 and 1969 Sir Geoffrey Ingram Taylor produced the theoretical underpinning of electrospraying.[6][7][8] Taylor modeled the shape of the cone formed by the fluid droplet under the effect of an electric field; this characteristic droplet shape is now known as the Taylor cone. He further worked with J. R. Melcher to develop the "leaky dielectric model" for conducting fluids.[9]

## Mechanism

To simplify the discussion, the following paragraphs will address the case of a positive electrospray with the high voltage applied to a metallic emitter. A classical electrospray setup is considered, with the emitter situated at a distance $d\,$ from a grounded counter-electrode. The liquid being sprayed is characterized by its viscosity $(\mu)\,$, surface tension $(\gamma)\,$, conductivity $(\kappa)\,$, and relative permittivity $(\epsilon_r)\,$.

### 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 $V\,$ will induce the electric field:[10]

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

where $r\,$ 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.[6] To meet both of these criteria the electric field must have azimuthal symmetry and have $R^{1/2}\,$ dependence to balance the surface tension and produce the cone. The solution to this problem is:

$V=V_0+AR^{1/2}P _{1/2} (\cos\theta _0)\,$

where $V=V_0\,$ (equipotential surface) exists at a value of θ0 (regardless of R) producing an equipotential cone. The magic angle necessary for $V=V_0\,$ for all R is a zero of the Legendre polynomial of order 1/2, $P _{1/2} (\cos\theta _0)\,$. There is only one zero between 0 and $\pi\,$ 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 infinitelly small. A singularity develops when the hydrodynamic relaxation time $\tau_H={\mu r \over \gamma}$ becomes larger than the charge relaxation time $\tau_C={\epsilon_r\epsilon_0 \over \kappa}$.[11] The undefined symbols stand for characteristic length $(r)\,$ and vacuum permittivity $(\epsilon_0)\,$. 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.[12]

## Applications

### 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.[13]

### 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 to control satellites, since the fine-controllable particle ejection allows precise and effective thrusts.

### Deposition of particles for nanostructures

Electrospray may be used in nanotechnology,[14] 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.

### Air purifiers

Particulates suspended in air can be charged by the aerosol generated by an 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.

## References

1. ^ Gilbert, W. (1628) De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth), London, Peter Short
2. ^ Rayleigh, L. (1882). "On the Equilibrium of Liquid Conducting Masses charged with Electricity". Philosophical Magazine 14: 184–186.
3. ^ Gomez, A & Tang, K (1994). "Charge and fission of droplets in electrostatic sprays.". Physics of Fluids 6 (1): 404–414. Bibcode 1994PhFl....6..404G. doi:10.1063/1.868037.
4. ^ Zeleny, J. (1914). "The electrical discharge from liquid points, and a hydrostatic method of measuring the electric intensity at their surfaces.". Physical Review 3 (2): 69. Bibcode 1914PhRv....3...69Z. doi:10.1103/PhysRev.3.69.
5. ^ Zeleny, J. (1917). "Instability of electrified liquid surfaces.". Physical Review 10 (1): 1–6. Bibcode 1917PhRv...10....1Z. doi:10.1103/PhysRev.10.1.
6. ^ a b Sir Geoffrey Taylor (1964). "Disintegration of Water Droplets in an Electric Field". Proc. Roy. Soc. London. Ser. A 280 (1382): 383. Bibcode 1964RSPSA.280..383T. doi:10.1098/rspa.1964.0151. JSTOR 2415876.
7. ^ Taylor, G. (1965) The force exerted by an electric field on a long cylindrical conductor. Proceedings of the Royal Society of London A: Mathematical, Physical & Engineering Sciences, 291, 145-158
8. ^ Tyalor, G. (1969) Electrically Driven Jets. Proceedings of the Royal Society of London A: Mathematical, Physical & Engineering Sciences, 313, 453-475
9. ^ Melcher, J. R. & Taylor, G. (1969) Electrohydrodynamics: A Review of the Role of Interfacial Shear Stresses. Annual Review of Fluid Mechanics, 1, 111-146
10. ^ L. B. Loeb, A. F. Kip, G. G. Hudson, W. H. Bennett (1941). "Pulses in negative point-to-plane corona". Physical Review 60 (10): 714–722. Bibcode 1941PhRv...60..714L. doi:10.1103/PhysRev.60.714.
11. ^ Fernández de la Mora, J.; Loscertales, I. G. (1994). "The current emitted by highly conductive Taylor cones.". Journal of Fluid Mechanics 260: 155–184. Bibcode 1994JFM...260..155D. doi:10.1017/S0022112094003472.
12. ^ Van Berkel, G. J.; Zhou, F. M. (1995). "Characterization of an electrospray ion source as a controlled-current electrolytic cell". Analytical Chemistry 67 (17): 2916–2923. doi:10.1021/ac00113a028.
13. ^ Fenn, J. B.; Mann, M.; Meng, C. K.; Wong, S. F.; Whitehouse, C. M. (2007). "Electrospray ionization for mass spectrometry of large biomolecules.". Science 79 (4926): 64–71. Bibcode 1989Sci...246...64F. doi:10.1126/science.2675315. PMID 2675315.
14. ^ Salata, O.V. (2005). "Tools of nanotechnology: Electrospray". Current Nanoscience 1: 25–33. Bibcode 2005CNan....1...25S. doi:10.2174/1573413052953192.

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