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Mechanisms and modeling of electrohydrodynamic phenomena
(“Maxwell”) forces to pull the liquids from the nozzle tip, a function of the nature of the solvent, high voltage and
rather than apply thermal or acoustic energy to push liquid pressure of the liquid at the tip of the tube (which is linked
from a fine capillary. The EHD inkjet printing can be a to the flow rate in modern electrospray experiments) [12,14] .
high-resolution inkjet printing technology because there Before1960s most work focused on the behavior of perfect
is a large “neck-down ratio” between the inner diameter conductors (mercury or water) or perfect dielectrics (a polar
of the nozzle and the jet: The jet diameter is about two liquid such as benzene), but Allan and Mason (1962) started
orders of magnitude smaller than the nozzle diameter. to study on poorly conducting liquids - and established
Thus, in EHD jet printing the nozzle inner diameter can the leaky dielectrics model or ohmic model [15,16] . In 1969
be much larger than that used in thermal or piezoelectric Taylor derived a pioneering theory to adequately explain
inkjet printing (about 20 μm); this makes blockages much the peculiar form of meniscus cones, referred as Taylor
less likely and makes it easy to employ a highly viscous cone, and the related concept is only recently extended
liquid . EHD ink-jet printing is a mask-less, non-contact, for use in micro patterning . Then, Cloupeau and Prunch
[5]
[17]
direct-write, and additive process, and it is used in the proposed a classification of EHD jetting modes on the basis
field of micro or nanomanufacturing for patterning of of their observations in the air at atmospheric pressure .
[18]
a large class of materials on a variety of substrates Specially, Cloupeau and Prunet-Foch organized EHD
without adversely affecting the chemical properties of jetting modes according to liquid flows from the meniscus
the deposited materials. Park developed an EHD inkjet in a continuous or pulsating manner into: (1) Continuous
[6]
printing system, and they used a microcapillary with manner including cone-jet, multi-jet, simple jet, and
diameter from 0.3 to 30 µm to produce single droplet ramified jet modes and (2) pulsating manner including
with sub-micrometer size. Followed by their seminal dripping, micro dripping produced at the end of the
work, a series of applications appear in recent years, and capillary or meniscus, pulsed cone-jet produced by breakup
applications include varied electronics, biotechnology, of a jet, and spindle mode . In terms of location where
[18]
and three-dimensional (3D) printing. Liang used drops are formed, spraying modes can also be divided into
[7]
the coaxial nozzle to print microscale 3D cell-laden two different groups: Electrified droplets pinched off either
constructs, and Liu investigated that influence of EHD from a protruding meniscus or from a jet emerging from a
[8]
jetting parameters on the morphology of PCL scaffolds. conical meniscus [18,19] . It should be noted that the release
Designs of EHD printing system and recent applications of charged droplets directly from the apex of a cone is not
of high-resolution printing will be introduced in the possible in competition with the formation of a cone-jet .
[20]
following paper due to the limitation of length. In the Fenn et al. found that flowing solution of large polymers
remaining sections of this paper, we provide a brief and proteins can be formed by electrostatic atomization of
account of the history of EHDs and related technology. their solutions from a Taylor cone in a bath gas, and this
Then, we review the known theories and principles led to the 2002 Nobel Prize in Chemistry received by Fenn
related to EHD printing, especially the theory of Taylor et al. [21,22] . Early reports on the use of this phenomenon
cone formation, mechanism of cone-jet transition, and for the controlled deposition of materials drew inspiration
criteria for jet stability. from electrospray techniques for the generation of charged
droplets [23-25] . De la Mora and Loscertales explored the
2 History of EHDs and Jet Formation relationship between the various parameter and emitted
Technology current and jet diameter for high conducting liquid. Ganan-
Calvo proposed six different scaling laws to define cone-
The phenomenon of a liquid drop subject to sufficiently jet transition . Chen performed a series of studies on the
[26]
strong electric forces adopting a roughly conical shape generation and placement of droplets with a high positioning
has been reported by Gilbert in 1600 [9,10] . The electrically accuracy about 4±2 µm [27,28] . Park et al. used the EHD
induced formation of a cone-jet and its breakup into method to eject different types of ink from microcapillary
droplets were first reported by Grey in the 1700s . In 1882, nozzles of different sizes and obtained printing resolution
[11]
Rayleigh conducted research on the theoretical analysis of up to 1 µm [6,29] . Maginean et al. and Chen separately
[28]
[30]
the breakup of a spherical liquid droplet under electrical investigated pulsating cone-jet formation and summarized
stress and derived an instability condition for an electrically scaling law for oscillation frequency in the two different
charged spherical droplets . His result implies that (for scenarios.
[12]
a spherical droplet) the stability criterion is equivalent to
the condition that the electric stress outward is equal to the 3 Theory and Mechanism of EHD Inkjet
surface tension stress inwards. The rapid EHD pulsation Printing
of the electrified liquid surface, now known as the cone-jet
transition that a thin liquid jet is ejected from the tip of an The mechanisms of EHD jetting are complicated, and
electrified cone shape, is discovered first time by Zeleny the physics behind this phenomenon is not completely
in 1915 . Zeleny also characterized the resulting spray as known. This paper summarizes some of the contributions
[13]
2 International Journal of Bioprinting (2019)–Volume 5, Issue 1