Page 62 - IJB-5-1

Mechanisms and modeling of electrohydrodynamic phenomena
claimed the dependence of jet diameter on nozzle diameter Wettability of capillary may cause a liquid ridge over
from their study, and this different result from above can the entire periphery of the nozzle outlet or only on the
be attributed to the lower electrical conductivity of ink . small part of it. During the growth of the ridge, the flow
[64]
At this circumstance, smaller droplets can be the outcome rate of the atomized liquid is lower than the total rate,
of using a thinner nozzle. In a stable cone-jet transition, causing the electric field to decrease due to the increase in
smaller nozzle diameters will extend both the low and the section of the capillary . Wettability can be reduced
[57]
high flow rate limit for a given liquid conductivity . The by coating non-wettable substance around nozzle except
[57]
electric field strength near the nozzle depends on both on the outlet section .
[57]
the applied voltage and the nozzle diameter. Thus, with
decreasing outer diameter, the field strength increases 3.2.2 Characteristic Dimensions and Scaling Law
and the resulting electrostatic forces, as well as the Related to Cone-jet Transition
entrance velocity, raise up . Furthermore, a smaller 3.2.2.1 Ganan-Calvo’s Scaling Law for Four Different
[20]
nozzle diameter or distance between two electrodes, the Conditions
required onset voltage is lower [44,65] . It is favorable for In the model of Ganan-Calvo , EHD spraying in
[66]
high-resolution printing and precise placement to keep a steady cone-jet mode is a quasi-electrostatic quasi-one-
short distance “l” (usually smaller than 5 mm) between dimensional (1D) condition based on two assumptions:
nozzle and ground electrode due to reduction of lateral (1) The inner electric displacement  E , is small
i
0r
n
variations . As printing complex feature with sharp turns compared to the displacement,  E , where E and
[6]
o
o
0
n
n
or small corners, a small distance “l” enables the process E are the normal outer and inner electric fields on the
i
n
to response promptly to the abrupt path change. Another jet’s surface, respectively; (2) the radial variations of
key factor for high-resolution printing is plotting speed, the liquid velocity are small compared to the average
and it is also important to consider compatibility between velocity for most liquids and EHD spraying conditions.
plotting speed and jetting speed. As a stable jet emits from Since the transverse section of the cone region is very
the tip of the cone, the speed of jetting depends on flow large compared to that of the emitted microjet, and the
rate and electrical potential. The plotting speed is the liquid velocity is small compared to that in the microjet,
movement speed of the substrate. If two speeds match the bulk ohmic electric conduction is dominant in the
each other, a straight jet appears, and a uniform continuous cone with very small inner electric fields [55,60,67] . Thus, the
plotted line is deposited on the substrate. In the pulsating cone region is considered as perfectly electrostatic [35,60] .
mode, it shows an equal space between droplets. Material The axial electric field E should be of the order of the
z
properties also need to be added into consideration in normal electric field at the cone:
regard to the matching process. γ
Finally, the effect of surface tension needs to be E ~( ε ) . 05 (7)
z
considered. In Taylor’s theory, the formation of a jet in the o L o
cone-jet transition only occurs when the stress induced by In the ohmic model or “leaky dielectric” model [5,16] ,
the electrical field (ε E /2) is larger than the stress induced an ohmic constitutive law for the current in the cone-jet
2
0
by surface tension (2γ/r), and a square dependence exists transition region is assumed [53,66] .
between the onset voltage and the surface tension. If the I = + = 2 ε 0 n + πξ 2 (8)
QE
surface tension of the liquid is too high, triggering of corona I scv I ocd ξ KE z
discharges prevents electrostatic atomization in the air . where I is surface convection current, I is ohmic
[57]
The effect of lowering surface tension stress at the liquid scv ocd
apex by adding surfactants is the same as an increase of bulk conduction current, Q is emitted flow rate, is normal
the Maxwell stress . The suppression of low-frequency electric field on the jet’s surface, ξ is radius of jet, and
[20]
K is liquid electric conductivity
. The point where
[66,68]
spray and the reduction of cone length at low surfactant the surface convection current equals the ohmic bulk
concentrations is probably related to a weak reduction of conduction current is located close to the jet’s origin .
[67]
the surface tension of the liquid cone . The phenomenon
[20]
of corona discharge usually occurs with liquids having QE 0 no ~ RKE (9)
2
a high surface tension and thus requiring high fields to R o o zo
overcome the surface tension stress . The corona can The pressure difference across the jet’s surface
[57]
be suppressed by increasing the dielectric strength of the is balanced by the normal electrostatic stress. The
surrounding medium, such as Freon 12, CO , and SF 6 [41] polarization stress  − ) 2 2 [66]
(
 E / is negligible .
2
or lowering the temperature of the ambient air [31,57] . The Thus, 0 r 0 z
hysteresis phenomenon that the minimum voltage needed to
maintain the cone-jet mode is lower than the voltage needed ε (E ) ~ ρQ 2 (10)
2
to initiate the cone-jet mode needs to be considered . 0 no R 4
[57]
o
8 International Journal of Bioprinting (2019)–Volume 5, Issue 1