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Gao D, et al.
high and low pulsation frequencies weakly increase electrode and distance between two electrodes . With
[57]
with the increase of electrical conductivities, since the the increase of electric field strength, there are many
dielectric relaxation time of liquid without the addition different forms of cone-jet transition . Within the regime
[18]
of electrolyte concentration is already shorter than the of the steady cone-jet transition, the liquid meniscus
time scale of a single pulse period . The addition of the of a Taylor cone recedes toward the nozzle base as the
[20]
electrolyte causes decreases of capillary potential, and as electric field strength is increased . Within the operating
[44]
a result the measured average capillary current increases envelope, the range of applied voltage for steady cone-
due to an increase of emitted electric charges during a jet transition is <7% for a given flow rate , which is
[55]
single pulse . small in comparison with the changes due to the liquid
[20]
The first one (Q/Q ) in the dimensionless group is the flow rate. Since the range of electric field strengths for the
0
ρKQ steady cone-jet transition is fairly narrow, this group can
dimensionless flow rate ( ) and the jet diameter can
γε be considered as an invariant .
[55]
0
be varied by two orders of magnitude by changing the The third is the relative permittivity of fluid ε which is
flow rate . The potential required for the formation of determined by the amount of the alignment of dipoles .
[55]
r,
[33]
steady cone-jet transition is affected by flow rate and the When two liquids have a similar value of the fourth
resulting shape of the liquid cone . The minimum flow dimensionless group, the liquid with higher relative
[38]
rate and its associated electric field are considered as a permittivity has a smaller charge relaxation length,
stability boundary of cone-jet , and Q is of the order of and thus a larger potential is required to achieve lower
[5]
0
the minimum flow rate for a given liquid . The minimum threshold for cone-jet formation .
[60]
[33]
flow rate is not, simply, the flow rate due to the upstream ρε γ 2 1
pressure, but rather the specific flow rate that causes The fourth dimensionless group is ( 0 3 ) , which
3
µ
K
electrical stress to strip off (or shear) the surface charge only depends on the liquid properties. It can be considered
layer of the fluid [33,61] . The cone-jet mode only appears as the ratio of the propagation velocity of a perturbation
within a limited range of values of flow rate for a given Q
conductivity . The value of the current and diameter of across the jet by the velocity of liquid 0 2 and viscous
[18]
jet grow with the increase of flow rate . Chen provided µ D 0
[57]
operating modes of steady cone-jet in the E-Q diagram for diffusion [55] . The axial velocity profile of the liquid
the conductivity of liquids above 10 S/m when other ρD 0
−4
materials and geometry parameters are kept fixed . In the jet depends on the viscous dimensionless parameter.
[5]
experiment of Juraschek and Rollgen, the “low” frequency Viscosity does not explicitly affect the jet diameter. The
of the appearance of current pulse sequence increases with viscosity of the liquid mainly affects the stability of the
the increase of liquid flow rate, since a shorter time is jet, especially with polymer jets where the huge
needed to build up the required large cone volume with a viscoelastic effects and elongational viscosity associated
critical radius for the onset of a liquid emission process . with polymers prevent the capillary instability [62,63] . Thus,
[20]
The number of pulses in a sequence also slightly increases higher viscosity liquids form thicker jets under the cone-
[38]
due to the extension of emission time by raised liquid jet transition . In the cone-jet mode, the length of the
supply . The “high” pulsation frequency is weakly jets increases with the viscosity, the resistivity, and the
[20]
[18]
changed by liquid flow rate, but the amplitude and width flow rate of the liquid .
of the pulse increase with flow rate accordingly. In The following dimensionless group relates to the nozzle
conclusion, the duty cycle of the “high” frequency diameter D , which has a small influence on the diameter
n
pulsations is affected by liquid supply to the apex region of jet D , particularly for conductive liquids. For high
j
−4
of the cone and weakly affected by liquid supply to the conductivity liquids (10 S/m and above), De la Mora
bulk of the cone. et al. demonstrated that the current is independent of the
The second is dimensionless electrical voltage needle voltage and geometry of the electrodes as long as a
stable cone is formed . This conclusion is consistent with
[31]
V
related to Taylor’s critical voltage 05 . [55] . The the result that current becomes decreasingly dependent on
γ  D  needle voltage at increasing conductivities in I-Q curves .
[57]
 ε 0  The jet diameter becomes irrelevant to nozzle diameter
0 

electric field promotes the charge migration away from when the ratio of the two diameters approaches to zero .
[60]
the electrode partly through the solution bulk after the Under these conditions, the dynamic effect due to the jet
charge is produced electrochemically at the emitter liquid emission is negligible and limited to the vicinity of the
interface, partly along the liquid surface . The value conical apex (e.g., d /d >>1 in the derivation). However,
[19]
0
n
of an electric field on the liquid is not only depends on this simple behavior does not hold for liquids with
value of voltage but also varied with a dimension of small electrical conductivities and area of stable conical
the capillary, the shape, and dimensions of the bottom meniscus depends on electrode geometry . Choi et al.
[31]
International Journal of Bioprinting (2019)–Volume 5, Issue 1 7