IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 51, NO. 2, MARCH/APRIL 2015
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Electrically Enhanced Condensation I:
Effects of Corona Discharge
Michael Reznikov, Senior Member, IEEE
Abstract—The effect of a corona discharge in the steam on the
rate of nucleation and condensation of a liquid phase is theoretically and experimentally investigated by means of implementation
with a steam condenser for an improved phase-change rate. The
phenomena considered include the nucleation of water vapor on
mobile charge carriers, the electrohydrodynamic vapor flow toward the condenser wall, and the thermodynamics of the charged
microdroplet. The dielectrophoretic interaction of droplets and
vapor is presented in terms of additional potential that adds to
the evaporation energy barrier on the surface of the droplets.
Experimental results obtained on the effect of a corona discharge
confirm a 16% improvement in the condensation rate.
Index Terms—Corona, dielectrophoresis (DEP), thermal
engineering.
N OMENCLATURE
EEC
DEP
EHD
CV
E
F
G
H
U
R
T
e
q
k
l
n
p
r
v
Φ
Electrically enhanced condensation.
Dielectrophoresis or dielectrophoretic.
Electrohydrodynamic.
Heat capacity at a constant volume.
Electric field.
Force.
Gibbs (free) energy.
Enthalpy.
Potential energy.
Radius of a droplet.
Absolute temperature (Kelvin scale).
Single electron charge.
Electric charge.
Boltzmann’s constant.
Index of the liquid phase.
Concentration.
Pressure.
Radial coordinate.
Volume.
Induced DEP potential.
Manuscript received February 6, 2013; revised March 31, 2014 and June 27,
2014; accepted August 18, 2014. Date of publication September 9, 2014; date
of current version March 17, 2015. Paper 2013-EPC-082.R2, presented at the
2012 IEEE Industry Applications Society Annual Meeting, Las Vegas, NV,
USA, October 7–11, and approved for publication in the IEEE T RANSACTIONS
ON I NDUSTRY A PPLICATIONS by the Electrostatic Processes Committee of
the IEEE Industry Applications Society. This work was supported by U.S.
Department of Energy Grant DE-EE0005130.
The author is with Physical Optics Corporation, Torrance, CA 90501 USA
(e-mail: mreznikov@poc.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIA.2014.2354734
α
β
γ
ε
ε0
μ
ρ0
Polarizability of a water molecule.
Index of the gas (vapor) phase.
Surface tension (surface energy).
Dielectric constant.
Absolute dielectric permittivity of vacuum.
Chemical potential.
Dipole moment of a water molecule.
I. I NTRODUCTION
P
HASE-CHANGE heat exchangers are widely used, from
miniature heat pipes in notebooks to steam condensers in
power plants, where liquefying typically occurs due to passive
thermal exchange. The temperature on the condensing wall
is lowered below the dew point, and the depletion (due to
condensation) of the vapor phase is constantly compensated
for by diffusion. Because the mass flow rate (and the heat
flux carried) depends on the gradient of the vapor pressure, a
high thermal flux is achieved by the intensive cooling of the
condenser, which is energy consuming (in the best case) or even
impossible with air convection cooling in the summer. In fact, a
geothermal power plant’s output drops to less than two-thirds of
the rated capacity during the hotter portions of the year, which
is primarily due to an increased condenser pressure and which
decreases the heat extraction from the geothermal brine to lower
the temperature. In general, air-cooled condensers significantly
contribute to the cost of generating electrical power; therefore,
the intensification of condensation potentially results in additional generated power.
The presented paper describes the concept of electrostatically
enhanced condensation, which has been also considered in our
previous work [1]–[3].
EEC is based on the combination of three phenomena: 1) the
DEP nucleation of the vapor on electrically charged centers;
2) the EHD flow of the vapor due to the drag by electrically
charged droplets; and 3) the temporal (until droplets are discharged) storage of heat energy in electrically charged droplets.
II. BACKGROUND
DEP [4] is an electrostatic effect that occurs when a highgradient electric field interacts with a neutral particle. The
interaction of the gradient field with the dipole moment, which
is induced in this particle, creates the net force that moves the
particle. The direction of this force is dependent on the relative
polarizability of the particle and that of the medium. If the
polarizability of the particle is higher than that of the medium,
the force is applied to the particle and directed toward a higher
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electric field (positive DEP). If the polarizability of the medium
is higher than that of the particle, the space charge of the interfacial Maxwell–Wagner polarization is formed in the medium,
and the DEP force moves the medium toward the higher field.
As a result, the particle moves away from the high field region
(negative DEP). Due to the polar nature of a water molecule
(the dipole moment, i.e., ρ0 = 6.2 · 10−30 C · m) and the low
polarizability of these molecules (α = 1.45 · 10−30 m3 ), the
polarization of the water vapor or the steam is mostly related
to the rotational orientation of water molecules. In addition,
because the surrounding medium is the less polarizable gas or
vacuum, only positive DEP should be considered in the matter
of interaction between electrically charged nuclei and the polar
molecules of the vapor.
The phenomenon of water vapor nucleation on electrically
charged particles, e.g., ions, was first noticed by C.T.R. Wilson
[5] in 1897. He also noted that the nucleation of the water
vapor depends on the signs of ions, i.e., the negative ions are
more efficient [6]. Later, this dependence on the ion charge was
attributed to the mostly negative charge in the external shell
of the droplet surface’s double layer [7]. In fact, the electric
field across this double layer may increase or decrease the
Coulomb field of the electric charge in the nuclei but only
inside the double layer. This phenomenon would affect the
energy barrier for evaporation (or the corresponding latent heat
of condensation) but not the electric field outside the droplet.
Moreover, the experimental evidence for a lower concentration
of hydrogen ions than hydroxide ions at the surface of the water
droplet at a neutral pH [7] may be the result of evaporation.
Hydrogen ions (protons) in the water always associate with
water molecules and form hydronium ions, i.e., H3 O+ , which
may be ejected together with a salvation shell of approximately
ten water molecules per ion [8]. The condensation on an electrically charged nucleus was intensively researched in connection
with the matter of atmospheric physics [9], [10]. Initially, the
reduction of the critical radius of a droplet or the saturated
vapor pressure over the droplet surface (the Kelvin effect [11])
was essentially treated as reduced surface tension due to the
presence of electric forces. In other words, the alternation of the
thermodynamic potential of droplets by the electric charge was
attributed to the surface interfacial (Maxwell–Wagner) polarization due to the Coulomb interaction with the electric charge
carried by droplets. Only in 2002 [12] was the interaction between gas-phase water dipoles and charged droplets accounted
for, followed by a demonstration that the effect of DEP forces
in the gas (vapor) phase may prevail over the surface tension
effect on the surface of the liquid phase. The modeling of
water droplets [13] accounted for the dipole moment of water
molecules but as a means of binding energy for the molecules
of the outer layer. This parameter determines the value of the
surface tension but not the DEP interaction of a droplet with
the water vapor outside the droplet.
It was experimentally demonstrated that water droplets are
easily generated on ions [14], [15], with an average droplet size
of ∼10 nm. The notable influence of electrostatic charges on
the condensation of the steam in a turbine of a power plant was
investigated [16], with the conclusion that the application of
an electrostatic corona can produce an increase in the turbine
Fig. 1. Attraction of the vapor molecule with a native dipole moment ρ0 to
the charged droplet.
output power. Regarding the physics of condensation, this paper
demonstrated two types of droplet development, i.e., the heterogeneous nucleation on ions and the homogeneous nucleation
from supercooling at a higher expansion ratio. No conclusions
regarding the mechanism of heterogeneous nucleation besides
that proposed by Wilson [5] were drawn. The later study by
Bakhtar et al. [17] demonstrated that the introduction of a
charge into a flowing steam can affect its nucleation behavior
downstream of the turbine, whereas the extent to which it
affects the steam flow and condensation depends on the field
and fluid conditions.
Recent related works [18], [19] considered the effect of
dipole–ion interaction in the matter of the stability of water
droplets [18] and the nucleation [19], [20] of water on charged
nuclei. Although the model considered in [20] accounted for
the dipole moment of the water molecule, it was limited to
the orientation of dipoles in the electric field of charged nuclei, which is the extension of J.J. Thomson’s approach [21].
The correlation of numerical modeling with experimental data
demonstrated a reduced vapor pressure compared with that predicted by the Kelvin equation, which is essentially a diminution
of the surface tension effect due to the presence of electric
charges. Nevertheless, the conditions considered were related
to the atmospheric science, i.e., to the low pressure of the
vapor and low temperatures. Therefore, a better understanding
of processes related to the EEC is of interest in both scientific
theory and engineering practice.
III. T HEORY
The EEC considered is based on the combination of three
phenomena: 1) the DEP nucleation of the vapor on electrically
charged centers; 2) the EHD flow of the vapor due to the drag by
electrically charged droplets; and 3) the temporal (until droplets
are discharged) increment of the heat capacity of electrically
charged droplets.
A. DEP Nucleation
DEP nucleation centers are ions generated by the corona
discharge or electrically charged droplets produced by the
electrospray atomization. The DEP force is directed toward the
charged center, as shown in Fig. 1.
REZNIKOV: EEC I: EFFECTS OF CORONA DISCHARGE
1139
If a water molecule is placed in a gradient electric field
of magnitude E, such a polar molecule experiences DEP
force Fdp = ρo gradE, which is directed to the side of the
increased field E. Due to this force, water molecules drift in
the gradient electric field and produce a gradient of the vapor
concentration. The steady state occurs when the DEP drift and
the local diffusion flows are equal, which leads to the classic
Maxwell distribution of the vapor concentration, i.e., n(r0 ) =
n∞ exp(U (r0 )/kT ), where k is Boltzmann’s constant, T is the
absolute temperature, and the potential energy of a molecule at
distance r0 from point charge q is U (r0 ). This energy can be
calculated by the integration of the DEP force from distance r0
to infinity as follows:
∞
U = ρ0
gradEdr = ρ0 q/ 4πε0 r02 .
(1)
r0
Here, 1/4πε0 ≈ 9 × 109 N · m2 /C2 is Coulomb’s constant,
where ε0 is the absolute dielectric permittivity of vacuum.
Therefore, the gradient electric field induces the enrichment of
the water vapor, i.e., nR /n∞ = pR /p∞ = exp(UR /kT ) (kT =
0.026 eV), near the charged particle or the very thin wire
electrode of radius R = r0 , where nR and n∞ are the concentrations of vapor molecules near the surface of curvature 1/R
and far from this surface, respectively. When the vapor density
exceeds the saturation level, nucleation occurs.
The saturation level is the equilibrium of droplets with the
surrounding vapor. In terms of thermodynamics, this equilibrium occurs when the chemical potentials (Gibbs free energy
per molecule) in the droplet and in the vapor are equal because
the energy barrier for the evaporation is diminished by the
surface energy due to the surface tension, i.e., γ. This leads to
the classic Kelvin equation [11] for the saturated vapor pressure
pβ near the surface of a drop with radius R as follows:
pβ = p∞ exp
2γv l
kT R
(2)
where v l is the volume per single molecule in the liquid, and
p∞ is the pressure of the saturated water vapor above a flat
surface at temperature T . If the droplet is electrically charged,
traditionally, the saturated vapor pressure is defined by the
classic Kelvin–Thomson (CKT) equation [21] in the following
modern form:
pβ = p∞ exp
2γv l
q2 vl
−
2
kT R 32π kT ε0 R4
1
1
− l
εβ
ε
(3)
which is the modification of (2) to account for the interfacial
polarization of water in the droplet and the vapor near this
droplet. This polarization may be treated as an example of
the DEP [4], which considers the vapor as a uniform medium
with dielectric constant εβ ≈ 1. Equation (3) does not account
for the DEP, which was introduced 90 years after 1888 when
Sir J. J. Thomson [21] (not to be confused with Sir W. Thomson,
Baron Kelvin of Largs) noted that the electric charge “increases
Fig. 2. Decrement of the effective surface tension due to the DEP forces for
a single charged droplet of varied radius: 1—by the combined MKT equation
(4); 2—only by the additional component in the MKT equation (4); 3—by the
CKT equation (3).
the tendency of the vapour to deposit on the liquid.” If the
additional potential energy due to the drift of dipoles, as in (1),
is accounted for, the classic (3) for pβC is modified to
pβM = pβC exp −
ρ0 q
.
4πkT R2
(4)
Therefore, the electrical charge decreases the pressure of the
vapor, which is in equilibrium with the droplet. In terms of the
Kelvin (2), this may be considered decreased surface tension.
Indeed, the surface tension is the result of the asymmetry of
the cohesive forces acting on a molecule on the surface of a
liquid droplet. Therefore, the surface tension also depends on
the interaction with the media on the other side of the surface,
i.e., air or vapor. As a result of additional electrical energy,
which increases the energy barrier for the molecule to leave a
droplet, the evaporation of a charged droplet is suppressed. This
shifts the equilibrium between evaporation and condensation
toward condensation and thus decreases the equilibrium vapor
pressure if compared with that of a neutral droplet of the same
radius or allows for the growth of the droplet at the same vapor
pressure.
Thus, the charged droplet acquires additional negative potential energy, which may be interpreted either as the increased
latent heat of evaporation or the decreased effective surface
tension as follows:
1
q2
1
ρ0 q
− l −
(5)
γel (R) = γ∞ −
16πε0 R3 εβ
ε
8πRv l
in the basic Kelvin (2). The relative decrement of the surface tension (−Δγ/γ) due to the electric charge in the droplet is shown
in Fig. 2 for both the CKT and modified Kelvin–Thomson
(MKT) equations, i.e., (3) and (4), respectively.
When the decrement of the surface tension reaches 100%, the
effect of the surface curvature is completely diminished, and the
droplet disintegrates, which is exactly the Rayleigh limit, i.e.,
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Fig. 3. Oversaturation of the vapor pressure near the droplet of radius R,
i.e., pR , relative to the saturated vapor pressure over the flat surface of the
water p∞ : 1—the neutral droplet; 2 and 3—the droplets with single and double
electron charges, respectively, according to the CKT equation (3); 4 and 5—the
droplets with single and double electron charges, respectively, according to the
MKT equation (4). Circles show the Rayleigh limits according to (6).
Fig. 4. Enrichment of the vapor versus the radial distance from the center of a
droplet, which carries the electric charge: 1—the single electron charge; 2—the
double electron charge.
the maximal charge carried by the droplet qR , at which fission
occurs as follows:
qR = 8π
ε0 γ · R 3 .
(6)
Curve 3 in Fig. 2 shows the correct result, i.e., 0.4 nm, for a
single electron charge according to (6) because this equation
was delivered from the CKT equation (3). Accounting for
additional DEP forces (curve 1 in Fig. 2) shows a notable
increase of 88% in this critical radius. This result may be
explained after the consideration of Fig. 3, which shows the
“oversaturation” of the vapor pressure near the surface of a
droplet, i.e., pR , relative to the saturated vapor pressure over
the flat surface of the water p∞ .
Considering the droplet growth from the single ion nucleus,
Fig. 3 shows that the CKT equation predicts energy barriers
at radii of ∼0.7 and ∼1 nm, which prevents this growth if
critical oversaturation, i.e., ∼3.5 p∞ and ∼2.2 p∞ , for single
and double electron charges, respectively, is not reached. In
contrast, the MKT equation shows that the chemical potential
of a charged droplet is always lower than that of the vapor over
the flat water surface. As a result, the growth of these droplets
is always thermodynamically favorable because this decreases
the Gibbs energy of the system. That is consistent with the
experimental data [14], [15]. Therefore, the diminishing effect
of the electric charge on the surface tension (the Rayleigh limit)
is not applicable to the growing droplet, which quickly exceeds
the critical radius. On the other hand, it is perfectly valid for the
evaporating droplet when the chemical potential of the liquid in
the droplet is higher than that in the surrounding vapor.
Of course, if the vapor pressure near the surface of the
droplet is considered the same as that far from the droplet, the
droplet would very slowly grow when the radius of a single
charged droplet exceeds ∼6 nm, and the decrement of the free
energy is diminished. However, the DEP force moves the vapor
Fig. 5. Effective DEP radius, i.e., Reff , for the droplets that are carrying
electric charge q in units of single electron charge e: 1—the effective DEP
radius; 2—the Rayleigh critical radius.
toward the droplet and thus creates the local enrichment of the
vapor. Fig. 4 shows this enrichment as elevated vapor pressure,
i.e., p(r)/p∞ , as a function of distance r from the center of
a charged droplet. The dramatic enrichment shown in Fig. 4
for small distances from the center of the droplet is purely
theoretical because the Maxwell distribution assumes the steady
state. In reality, the charged droplet immediately starts to grow,
which will not allow the vapor pressure near the droplet surface
to increase more than a few times over that in the ambient vapor.
The nucleation and growth of the charged droplets depletes
the vapor phase near a droplet, which is compensated for by the
DEP flow and diffusion. The DEP flow involves the surrounding
vapor at a distance shorter than the effective DEP radius, where
the DEP potential decreases below kT . This radius is ∼1.5 nm
for the single electron charge in the droplet. Fig. 5 shows the
effective radius for the droplets that are charged to the Rayleigh
limit (e.g., by an electrospray).
As Fig. 5 clearly illustrates, the effective DEP radius really
exceeds the Rayleigh critical radius for droplets smaller than
REZNIKOV: EEC I: EFFECTS OF CORONA DISCHARGE
1141
120 nm in diameter. The growth of larger droplets is only
supported by the diffusion of the vapor.
B. Thermodynamics of Charged Droplet
Equations (2)–(4) are derived from the condition of the
equilibrium of a water droplet of radius R with the vapor. At
this condition, the chemical potential of the molecule in the
neutral droplet, i.e., μl (R, T ), is equal to the chemical potential
of a gas phase (vapor) water molecule near the surface of this
droplet as follows:
μβ (R, T ) = μ0 (T ) + kT ln(p∞ ) +
2γv l
kT R
(7)
where μ0 (T ) is the standard chemical potential of the vapor,
and p∞ is the ambient vapor pressure. Equation (7) leads
to the Kelvin (2) because μβ (R, T ) = μ0 (T ) + kT ln(p(R)).
Similarly the Kelvin–Thomson equation is derived from
μβ (R, T, q) = μβ (R, T ) − ΔμDEP
(8)
Fig. 6. Dimensionless heat capacities for (o) positively and (x) negatively
charged clusters [22]. The lines represent the literature values for the bulk
ice at P = 1 atm and T = 0 ◦ C (topmost ice line), −63 ◦ C (middle line),
and −123 ◦ C (bottom line); and for the bulk liquid water at P = 1 atm and
T = 0 ◦ C, 50 ◦ C, and 100 ◦ C. The liquid water lines almost coincide.
where ΔμDEP = (q 2 v l /32π 2 ε0 R4 ) + (qρ0 /4πε0 R2 ) is the
decrement of the chemical potential due to the DEP forces, i.e.,
ΔμDEP . Due to the low polarizability of the water molecules,
i.e., α, and the relatively low electric field, we are neglecting
here the impact of vapor polarization Δρ0 (r) = αE(r). The
Born energy corresponding to the change in the electric potential energy of the charged nuclei due to the polarization of the
vapor as a dielectric shell, i.e.,
Δμβpol =
q2
8πεβ ε0 R
was also neglected because it is ∼ 10−20 J for R = 10 nm and a
single electron charge, i.e., q = e = 1.6 · 10−19 C, whereas the
DEP contribution to the chemical potential is ∼ 0.9 · 10−12 J
under the same conditions.
The outcome from (8) is that the heat capacitance of the
charged droplet is decreased. At a constant droplet volume of
4πR3 /3, the heat capacitance is proportional to the second
derivative of the Gibbs energy, i.e., G = N · μl , where N
is the number of molecules in the cluster (the droplet), and
the chemical potential in the liquid μl is defined by (8) if
the equilibrium with the vapor is established. Therefore, the
isochoric heat capacitance of the droplet is defined as
2 2
∂ G
∂ (μn −ΔμDEP )
CV, N =−T
=−T · N
∂T 2 V, N
∂T 2
V
(9)
where μn is the chemical potential in the neutral droplet according to (7). As (9) indicates, the electric charge should decrease
the heat capacitance of the droplet. This speculative conclusion
is supported by the experimental data from the work in[22],
where the effect of the electric charge on CV,N was investigated
by measuring the evaporation rate of the charged clusters. Fig. 6
presents the results of this work for positively charged pure
water clusters and water clusters formed on negative ions (O2 ),
(CO3 ), or (NO3 ). The experimental data are plotted for CV,N /k
as a function of N . Therefore, the linear plot corresponds to the
Fig. 7. Standard stepwise enthalpy changes for the clustering of water on
hydronium ions, i.e., H3 O+ [19]. The symbols are the experimental values
from various measurements (see [19, Refs. 16, 17, 21, and 25]). The dashed
line 1 is the prediction based on the CKT equation (3), and the solid line 2
represents the calculation based on the MKT equation (4). The rectangle bar on
the right of the plot indicates the enthalpy of vaporization for water at the given
temperature.
constant heat capacity per molecule, i.e., cV,N , in the cluster, and
the higher inclination of the line means a higher heat capacity.
As Fig. 6 shows, the heat capacity of the small charged
droplets (clusters) is notably lower than that of water. There is
an almost identical increase in CV,N with the size for both the
negatively and positively charged clusters. Very small clusters
(less than 20 molecules) behave similarly to the ice near the
melting temperature. There is an increase in cV,N in the range
from 20 to ∼70 molecules per cluster, which may be associated
with the transition to the liquid structure. Nevertheless, cV,N
notably decreases for clusters in the range from ∼70 to ∼200
molecules, which confirms our conclusion from (9).
On the other hand, the enthalpy of the charged droplet is
higher than that of the same number of molecules in the bulk
neutral water. The excess enthalpy is stored as the energy of the
electric polarization. This is supported by numerical modeling
[19], [20] and experimental data, as shown in Fig. 7. Therefore,
despite the lower heat capacity of a small charged droplet,
it notably carries (2–3 times) higher enthalpy than a neutral
droplet of the same size. This energy is extracted from the vapor
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In the interelectrode gap, the charge carriers collide with neutral
molecules, thus passing their kinetic momentum to the neutral fluid. This creates a pumping action that moves the fluid
through the system. Because the collision rate is very large,
the charge carriers reach a steady-state (terminal) velocity in
a very short distance; thus, all additional kinetic energy is
passed to the neutral molecules by collision. In the moist gas
or pure steam, the DEP-stimulated nucleation further increases
the pumping action due to the increased cross section for collisions. Therefore, the EHD flow is the EEC component, which
inherently accompanies the DEP nucleation due to the injection
of charge carriers. It should be noted that the direct injection
of electrically charged droplets, e.g., by the electrospray [24],
produces a similar effect.
Fig. 8. Effective DEP radius for capturing the aerosol particles of varied sizes
calculated for the radii of electrospray droplets: (1) 10 nm, (2) 100 nm, and (3)
1000 nm.
phase during DEP nucleation and released when the droplet
reaches the grounded electrode (the condensing surface).
C. DEP Collection of Aerosol
The significant electric charge of electrospray droplets also
allows for the attraction of an electrically neutral aerosol due
to the induced dipole moment. The polarizability of a dielectric
sphere, i.e., α, of radius r with dielectric permittivity ε is α =
3ε0 Vr (ε − ε0 )/(ε + 2ε0 ), where Vr = 4πr3 /3 is the volume of
a sphere. The DEP force, i.e., Fdp , acting on the aerosol droplet
at distance R from the center of a droplet carrying charge q is
Fdp = α · E · grad|E| =
2
α
2αq
gradE 2 =
.
2
εε0 R5
(10)
Assuming that the threshold value for DEP potential Φdp is
equal to kT , the equation for the effective DEP radius rp ,
i.e., the radius of a sphere that limits the space around the
electrospray droplet of radius r where all neutral particulates
will be collected, is as follows:
∞
Φdp =
F (qr , rp )dx = kT.
(11)
R
The solution of (11) accounting for (10) at varied radii of
electrospray droplets R and at the radius of an aerosol particle
rp is presented in Fig. 8; assuming the water-based aerosol,
dielectric constant ε was set to 80. It is not surprising that the
larger charged droplets collect the aerosol at greater distances.
Fig. 8 shows that the tenfold increase in the electrospray radius
elevated the effective DEP radius ∼5 times, which is due to the
increased charge carried by the droplet.
D. EHD Flow
The EHD flow is a well-known phenomenon [23]. When
a corona discharge is initiated between the emitter and the
grounded electrode, the generated ions migrate to the ground
electrode with an average drift velocity on the order of 100 m/s.
E. Corona Discharge in Steam
The application of a negative corona discharge in the steam
[25] revealed a lower starting (inception) voltage than that in
the air and an anomalous weaker current at low voltages if the
steam is sufficiently close to saturation. The positive corona was
investigated for air at varied humidity levels [26] up to 15 g/m3 .
The lower inception voltages and the lower currents were found
for the higher humidity case that was attributed by the authors
to the greater values of the ionization coefficients and the lower
mobility of ions than that of electrons. Both these results are
consistent with the EHD nucleation of the water droplet that
decreases the mobility of charge carriers and extends the cross
section for collisions.
F. Cumulative Model for Electrostatically
Enhanced Condensation
Summarizing the detailed considerations provided earlier,
the EEC is the cumulative and inherently synergetic result
of multiple processes, which may be briefly summarized as
follows.
• The electric charge increases the stability of a charged
water droplet, which grows until the DEP energy in the
vapor phase is reduced below kT or until the equilibrium
with the vapor phase is reached.
• The drift of the droplet toward the water surface due to
the electrostatic force involves the flow of the vapor and
leads to the direct deposition of the dispersed (droplets)
condensed phase on the bulk condensate.
• When a charged droplet reaches the boundary region with
the flat liquid surface (e.g., the surface of the condenser)
and discharges, the stored DEP energy is directly transferred to the condensing surface.
Therefore, the EEC process allows for highly localized condensation in the volume of the vapor, with the subsequent
acquisition of water clusters at the condenser surface. This is
exactly the desired effect of the EEC.
IV. P RELIMINARY E XPERIMENTS
A. Experimental Setup and Results
To evaluate the effect of the EEC of the steam, we assembled an experimental setup that utilizes a cooled multichannel
REZNIKOV: EEC I: EFFECTS OF CORONA DISCHARGE
Fig. 9.
1143
Scheme of the experimental apparatus.
Fig. 12. Increment of the temperature in the condenser with a constant high
voltage (8 kV) applied to the corona wires and the variable power applied to the
thermoelectric coolers: 0—without the corona discharge; 1—positive corona
discharge; 2—negative corona discharge.
Fig. 10. Scheme of the installation for corona electrodes.
Fig. 11. Experimental setup.
aluminum condenser where each channel was equipped with
an array of corona wires, as shown in Fig. 9. The steam was
generated by boiling water in the closed vessel.
The steam exhaust was open to the ambient air; thus, the pressure in the condenser and the boiler was constant, i.e., 1 atm,
and the temperature of the supplied steam was 100 ◦ C.
Corona wires (75 μm in diameter and 90 mm long, tungsten)
are installed in the cavities of the condenser channels, as Fig. 10
illustrates. The purpose of these cavities was to decrease the
average velocity of the steam along the channel.
Fig. 11 shows the experimental setup used in these preliminary tests.
Both positive and negative coronas were evaluated. All of the
electrodes were energized to the same high voltage (8 kV), producing a corona current ∼1 mA across the condenser channels
through which the steam passed on its way to the apparatus.
The temperature of the condensing surface was monitored with
a thermocouple.
To detect the change in the steady-state temperature in the
condenser, the measurements were made after the temperature
was fully established. The power of the thermoelectric cooler
Fig. 13. Relative increment of the temperature in the condenser with a
constant high voltage (8 kV) applied to the corona wires and the variable
power applied to the thermoelectric coolers: 1—positive corona discharge;
2—negative corona discharge.
was varied, and the temperature was measured both upon
the application of the corona voltage and without the corona
voltage. As Fig. 12 shows, the increment of the temperature
with a high voltage applied is systematic, and the absolute
difference in the temperature increases with the power applied
to the thermoelectric coolers. The effect of the negative corona
was notably smaller than that of the positive corona.
Fig. 13 presents the same data as the relative increment of the
temperature.
The most efficient performance of the EEC is reached at
higher cooling power and a positive corona discharge. The
effect of the negative corona was smaller, and the corona current
was less stable. In fact, we have investigated the fact that
the water collection on the isolators of the corona electrodes
was more intensive with the negative corona. This resulted in
random sparks over the isolators and, finally, in the destruction
of the corona electrodes.
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 51, NO. 2, MARCH/APRIL 2015
B. Discussion of Experimental Results
The purpose of this preliminary qualitative test was to reveal if the corona discharge really affects the performance
of steam condensers. Because the rate of condensation and,
correspondingly, the release of latent heat depend on multiple
interdependent factors such as the temperature of a condensing
surface, the gradient of the steam pressure near this surface, the
heat exchange through the layer of condensed water, etc., the
setup used only allowed for the detection of the temperature
change on the condensing surface. Therefore, Fig. 13 presents
the relative effect of the EEC on this steady-state temperature
established at varying cooling power values.
Due to the constant thermal resistance of the condensing
heat sink, the higher heat flow requires a higher temperature
difference between the condensing and cooled surfaces. The
hot-side temperature in the thermoelectric coolers was stabilized by the enforced convection heat exchange with the
ambient air. As a result, the increased electrical power applied
to the thermoelectric coolers leads to the lowered temperature
of the condensing surface, as curve 0 in Fig. 12 shows. At
each applied cooling power, if the released latent heat of the
condensation increases, the heat flow through the condensing
heat sink increases as well, as the differences between curves 0,
1, and 2 in Fig. 12 indicate.
Fig. 13 shows that, initially, the effect of the EEC is diminished with increased cooling power when the temperature of the
condensing surface is above the ambient temperature (22 ◦ C).
At temperatures lower than ambient, the effect of the EEC
increases, at least for the positive corona. This indicates that
the enhanced condensation requires not only the nucleation and
delivery of the vapor to the condensing wall but also the ability
of this wall to extract the latent heat.
The lesser efficiency of the negative corona discharge may
be attributed to the longer free pass of emitted electrons than
that of ions. Because the effective radius for the DEP capture
of the steam molecules is limited, most of the nucleation in the
unipolar region occurs on negative ions. In addition, because
the ionization region for the negative corona is thinner than that
for the positive corona, the gradient of the electric field around
the negative corona electrode is correspondingly higher. As a
result, this electrode (a thin wire) works as a DEP nucleation
center itself, and the deposition of water on the electrode affects
the corona current emission.
Because a constant voltage was applied to the corona electrodes in this experiment, the increment of the condenser temperature cannot be attributed to the deposited corona discharge
power, which is ∼8 W, because the relative effect of this power
on the increased cooling power should decrease, whereas the
opposite is observed.
Of course, such components of the EEC as the effect of the
corona wind (the EHD effect) and the drag of the steam by
droplets were present in this experiment. In fact, these processes
support the diffusion of the vapor toward the condenser and
should improve condensation. Nevertheless, when the cooling
power is raised and the condensation rate is correspondingly increased, the relative impact of the corona wind should decrease
due to the higher pressure gradient and the correspondingly
improved diffusion of the vapor without a corona discharge.
In this case, the relative increment of the temperature should
decrease, whereas Fig. 13 shows the opposite effect of the
corona. Therefore, the tests carried out demonstrated that the
DEP nucleation is a significant part of the corona effect on
vapor condensation.
Although the 16% enhancement of the steam condensation
by the corona discharge is confirmed in the experiment presented, this improvement is rather limited by the charge of a
single ion. The major problem is that the high-gradient electric
field near the corona electrode also attracts the vapor, which
condenses on the electrode, which finally leads to the discharge
over the insulators.
V. C ONCLUSION
The feasibility of the basic model developed for electrostatically enhanced condensation has been demonstrated by a
preliminary conceptual test. The investigated effect is limited
by the charge of a single ion. Further research will be directed
toward the use of an electrospray to produce nucleation centers
with a high density of the electrical charge.
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1145
Michael Reznikov (M’99–SM’05) was born in Kiev,
Ukraine, in 1948. He received the M.S.E.E. degree
with a major in semiconductors and dielectrics from
Kiev Polytechnic University, Kiev, Ukraine, in 1972
and the Ph.D. degree in physics and mathematics,
majoring in solid-state physics, from the National
Academy of Sciences of Ukraine, Kiev, Ukraine,
in 1980.
During his Ph.D. studies, he researched the field
emissions from silicon interfacial polarization in
composites and the electrostatic coalescence of metal
clusters that resulted in the development of technologies for dielectric spectroscopy for the nondestructive testing of thin films and for electrostatic
imaging. Since 2001, he has been a Principal Scientist with Physical Optics
Corporation, Torrance, CA, USA, where he initiated and managed a number
of projects in electrostatic dehumidifying, polymer-gel-based electrolyte thermoelectric conversion, capacitive electrostatic sensing, electrically supported
spray and evaporation technologies, and thermal management. He is the author
or coauthor of more than 40 publications in refereed international and national
journals and proceedings of international conferences. He is the holder of
12 patents.
Dr. Reznikov is a member of the American Physical Society and the Electrostatics Society of America. He was the recipient of the Ukrainian State Prize
for Sciences and Technology in 1986 for his research on material degradation
on board space stations.