Heat transfer engineering an international journal, tập 31, số 2, 2010

Heat Transfer Engineering, 31(2):99–100, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903285294

editorial

Selected Papers on Improving Heat
Transfer via Electrohydrodynamic
Technique
MAJID MOLKI
Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA

Heat transfer processes may be substantially improved with
the aid of electrohydrodynamic (EHD) technique. The improvement may be in the form of enhanced convective heat transfer
coefficient, better mass removal in condensers, or it may lead to
a special cooling arrangement such as spot cooling of electronics components. The improvement may also be achieved when
the technique is used to control and change the thermal capacity
of a heat exchange device via a variable convective coefficient.
Regardless of the specifics of the application, EHD introduces
a novel approach in thermal engineering.
This special issue is devoted to thermal-fluid processes that
may benefit from electrohydrodynamics. There are six articles
in this issue. The cover photo is an application in which the
condensate drainage in evaporators is improved by the electrowetting technique. High voltage is applied to electrodes, and
the resulting electrostatic forces reduce the contact angle of the
condensate, leading to better condensate drainage. Electrowetting technique is discussed in the article by Kim and Kaviany,
which explains how it facilitates a more efficient removal of
condensate in heat exchangers.
The EHD technique has been shown to improve the twophase heat transfer. The article by Laohalertdecha et al. addresses the use of EHD in enhancing evaporation of refrigerant

R-134a inside smooth and micro-fin tubes. Despite the beneficial
effects of EHD on evaporation, there is a pressure drop penalty
associated with this technique. Using the enhancement factor, it

is shown in the article that, for the range of parameters of this
investigation, the heat transfer enhancement is sufficiently large
to compensate for the pressure drop penalty.
Another application of EHD is in the design of micropumps
for pumping liquid nitrogen. In the article by Foroughi et al.,
two designs of a micropump are presented which differ in the
shape of their emitters. The pump is intended to circulate nitrogen for the cryogenic spot cooling of electronics components.
With this technique, a cooling strategy may be devised to apply more cooling to locations which are likely to develop hot
spots.
The EHD technique is especially effective at low velocities,
such as flows driven by the buoyancy force. In the article by
Kasayapanand, the technique is applied to natural convection
in a finned channel where the flow and heat transfer are significantly influenced at lower values of Rayleigh number. The
effects of electrode arrangement and number of electrodes on
flow and heat transfer are discussed, and an optimum inclination
angle for the channel is recommended.
In the article by Kamkari and Alemrajabi we also see an
example of the EHD application for convective mass transfer. In
this case, high voltage is applied to a wire electrode positioned
above water surface to ionize the air and to generate corona
wind, which leads to a higher rate of evaporation from water.
The enhancement of water evaporation relies on disturbing the
saturated air layer over the water surface. At higher air velocities,
the layer is already disturbed and the enhancement effect of EHD
diminishes. Therefore, as is the case in buoyancy-driven flows,
this technique seems to be more effective in enhancement of

mass transfer at lower air velocities.

Address correspondence to Professor Majid Molki, Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville,
Edwardsville, Illinois 62026-1805, USA. E-mail:

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M. MOLKI

Another aspect of the EHD technique is that, under certain
operating conditions, the flow becomes unstable and oscillates,
because the electric bodyforce and inertia compete with each
other to control the flow. In the article by Lai and Tay, the
EHD technique is applied to gas flow in a parallel-plate channel
to investigate the oscillatory motions generated by EHD. It is
shown that heat transfer is improved under these conditions.
Moreover, heat transfer may be further improved if the primary
flow is excited at a frequency similar to those generated by the
EHD technique.
The articles presented in this issue are by no means exhaustive; they are intended to represent a limited set of examples
from a diverse list of possible applications in thermal engineer-

heat transfer engineering

ing. I hope you find the topics fascinating and helpful to your
own research and engineering practice.
Majid Molki is professor of mechanical engineering at Southern Illinois University Edwardsville. He

received his Ph.D. from University of Minnesota in
1982. With many years of teaching and research experience in thermal sciences, his research interests are
electrohydrodynamic enhancement of heat transfer,
electronics cooling, and flow boiling of refrigerants.
He has published extensively in technical journals
and conference proceedings. He is the Associate Editor of Heat Transfer Engineering, member of ASME,
member of the American Physical Society, and member of Alpha Chi Chapter
of Pi Tau Sigma honor society.

vol. 31 no. 2 2010


Heat Transfer Engineering, 31(2):101–107, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903285302

Electrowetting Purged Surface
Condensate in Evaporators
JEDO KIM and MASSOUD KAVIANY
Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA

Condensate electrowetting purge in evaporators (heat exchangers) based on the force balance at the three-phase contact
line (TCL) is used in a prototype heat exchanger. The electrowetting is described based on overcoming the static three-phase
contact line friction and detailed droplet physics is presented. Series of experiments was performed under various conditions
and it was found that electrowetting combined with hydrophobic coating improves the drainage rate by as much as factor of
three. Observations show that fins subjected to electrowetting are cleared of liquid droplets, in contrast to the fins which are
not. Based on the proposed physics and experimental data, optimized electrode designs for future reference are proposed.

INTRODUCTION

Dropwise condensation occurs when moist air flows in refrigeration or air-conditioning evaporators, and can block the air
passage and degrade the performance, thus requiring periodic
water surface droplet or frost purging (Emery and Siegel [1], Na
and Webb [2], and Ren et al. [3]). Surface modifications have
been devised to reduce the critical angle at which a given volume
surface droplet begins to slide under gravity. These include the
recent study by Adamson [4], who achieved a 50% reduction
in the volume needed for the onset of droplet sliding, using a
micro-grooved (directional) aluminum surface. However, these
passive surface modification techniques are not suitable for versatile operating conditions and active control of the condensate.
We examine theoretical and experimental aspects of purging
surface droplets by electrowetting, a phenomenon based on the
interaction of the electrostatic, gravity and surface forces. In
analyzing the electrowetting process a detailed description of
the dynamics at the three-phase contact line (TCL) is required.
However, the classical hydrodynamics cannot fully describe the
motion of the TCL. Several strategies have been introduced to
resolve the problem (deGennes [5], Oron [6], and Pismen [7]).
These approaches have been used exclusively for dynamic analysis by estimating the friction force as a product of the friction
We are thankful for useful discussions with Hailing Wu, Michael Heidenreich and Steve Wayne of Advanced Heat Transfer LLC, and Jeffrey Bainter of
Circle Prosco, Inc.
Address correspondence to Professor Massoud Kaviany, Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 481092125. E-mail:

coefficient and the velocity of the contact line. Little is known
about the static contact line friction just prior to initiation of
TCL motion. Nevertheless, since liquid droplets, unlike solid
objects, undergo significant topological changes in response to
external forces, it is possible to estimate the force necessary to
initiate motion of TCL by examining the topological observables (local radius meniscus curvature, local contact angle, etc.)
at the critical inclination angle. The dynamics of the static force

balance at the TCL have been investigated and the three regimes
(gravity dominated, intermediate and surface force dominated)
have been identified as shown in Figure 1 (Kim and Kaviany
[8]). It was found that the critical inclination angle at an applied potential follows the constant Bo line which suggests that
the electrostatic force reduces the contribution of the surface
forces. Here, we review the physics behind condensate purge
using electrowetting. Using this physical understanding, electrowetting technique is applied to enhance the drainage rate of
a prototype heat exchanger. Furthermore, ideal implementation
concepts are presented for future reference.

THEORETICAL ANALYSIS
Fundamentals of Surface Forces
Liquids form a spherical cap with a well-defined equilibrium
contact angle θc,o or spread across the surface as a thin film
when condensed or injected onto a solid surface. The precise
equilibrium that determines the topology of a droplet is the balance between the liquid–gas σlg , solid–liquid σsl , and gas–solid

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J. KIM AND M. KAVIANY

Figure 1 The critical inclination angle with respect to droplet volume for
three regimes (gravity dominated, intermediate and surface force dominated).
The theoretical curve fit of the experimental results are presented along with
data from [4].

σgs interfacial tensions. This balance of forces is represented by

the free energy at the contact line
Fif =

Ai σi − λV

(1)

where λ is the Lagrangian multiplier for the constant volume
constraint, A is area, V is the liquid volume and λ is equal to
the capillary pressure p across the liquid-gas interface. Minimization of the free energy leads the following two conditions
which govern the topology (meniscus) of droplet (Adamson [4]
and Israelachvili [9]). The first is the meniscus Laplace equation
which states that p is constant over the entire interface
p = σlg

1
1
+
r1
r2

(2)

where r1 and r2 are the two principal radii of curvature of
the meniscus. The Laplace equation shows that for homogeneous substrates, liquid droplets adopt a spherical cap shape
in mechanical equilibrium. The other is the contact line Young
equation
cos θc,o =

σsg − σsl

σlg

(3)

This relates the interfacial tension to the apparent contact angle θc,o . Figure 2a shows the contact angle and the surface tension in equilibrium for liquid droplet on a horizontal surface. For
the relevant scale, often, it is possible to adopt a one-dimensional
model of the contact line, where the three interfacial tensions are
pulling on TCL. For a liquid on an inclined surface, the ratio of
the surface forces to gravity is represented by the Bond number
(Bo = ρgD2 sin ϕ/σlg ), where ρ is the density of the liquid,
heat transfer engineering

Figure 2 Balance of forces at the TCL for (a) ϕ = 0◦ and (b) ϕ > 0◦ .

g is the gravitational constant and D is the droplet diameter.
We consider moderate Bond numbers (Bo = 0.8–2.5), so the
droplet motion is moderately influenced by gravity. For a plate
inclination angle ϕ, the mass center of the droplet shifts towards
the advancing side, giving rise to the local capillary pressure p
at the liquid–gas interface. The opposite phenomenon exits on
the receding side. TCL of the advancing side is pinned due to
the contact line friction and is not allowed to advance until a
critical inclination angle is reached. Then at the advancing side,
according to Eq. (2), reduction in the radius of curvature occurs
and causes the contact angle to increase. At the receding side,
reduction of the local capillary p requires a larger radius of
curvature and this results in a smaller contact angle. This difference between the advancing and receding contact angles is
referred to as the contact angle hysteresis and is shown in Figure
2b. As seen in the figure, the force balance at the TCL is modified due to the presence of contact line friction. From the point
of surface tension equilibrium at the TCL, the contact angle hysteresis can be modeled as the addition of friction, fs (per unit

length), to the σsl at the advancing side and subtraction of friction, fs , at the receding side. The radial component of fs varies
along the azimuthal angle ζ, thus, the contact angle varies from
θc,a,max to θc,o then to θc,r,min . The contact angle hysteresis and
the retention force (the sum of fs over the entire contact line)
can be related using following equation for circular droplets,
Fs = kσlg R(cos θc,r − cos θc,a )

(4)

where k is a constant, R is the length scale representing the
size of the meniscus, and θc,r and θc,a are the receding and
advancing contact angles. Here k depends on the topology of the
droplet and is found empirically using the measured receding
vol. 31 no. 2 2010


J. KIM AND M. KAVIANY

and advancing contact angles at the critical inclination angle.
Knowing k and using the droplet force balance, the critical
inclination angle can be found. Elsherbini and Jacobi [10, 11]
have performed a comprehensive empirical analysis of droplets
on aluminum substrates, with commercially available coatings.
They propose an empirical relation between the Bond number
and the ratio of the receding and advancing contact angles, i.e.,
θc,a
= 0.01Bo2 − 0.155Bo + 0.97
θc,r

(5)

This relationship is used to estimate the retention force over
the entire range of Bond numbers.

103

where, T is the Maxwell stress tensor which is written as
1
T ik = εo ε − δik |E|2 + E i E k
2

where δik is the Kronecker delta and n is the normal direction.
The tangential component of the electric field at the surface
vanishes and the normal component is related to the local surface
charge density through ρs = εo ε E • n. Now noting that every
term except the component directed along the outward surface
normal vanishes, Eq. (7) becomes

Electrowetting

1
ρ E ds
2 s

Fe =

Extensive electrowetting studies have been done with spatial
dimensions where gravity effects are negligible (Bond number tending to zero) in the areas such as microfluidics or microelectronics (Berge and Peseux [12], Srinivasan et al. [13],
and Yun et al. [14]). Figure 3 renders the contact angles affected by electrowetting. To relate the applied voltage to the
change in the effective surface tension, the thermodynamicelectrochemical, energy minimization, and electromechanical

approach have been used (Berge [15], Jones [16], and Jones
[17]. All of these approaches converge to a single well-accepted
electrowetting relation which is presented subsequently. Here
the electromechanical approach is reviewed which was first introduced by Jones [16] and starts from the Korteweg-Helmholtz
body force density (Landau and Lifschitz [18])
F k = ρf E −

ε0 2
ε0 2 ∂ε
E ∇ε + ∇
E
ρ
2
2
∂ρ

(6)

where E is the electric field vector, ρf is the fluid charge density, ρ and ε are the mass density and the dielectric constant of
the liquid. The last term in Eq. (6) describes the electrostriction
and can be neglected. If we assume that the liquid is perfectly
conductive, integrating Eq. (6) over the entire volume is equivalent to integrating the Maxwell stress tensor over the liquid-gas
interface
Fe =

T • n ds

(8)

(9)

The field and charge distribution are found by solving the
electrical Laplace equation for the electrostatic potential with
the appropriate boundary conditions. Both the field and charge
distributions diverge upon approaching the contact line [19].
Therefore, the Maxwell stress is maximum at the contact line
and exponentially decays with distance from the contact line.
After integration using ϕ = − E • n ds, where ϕ is the
voltage drop across the interface, the horizontal component of
the Maxwell stress is
fe =

εo ε
ϕ2
2d

(10)

Since this force acts only on the contact line and is perpendicular to TCL, it is used in the force balance and the Young
equation, i.e.,

σeff
sl,e = σsl −

ε0 ε
ϕ2
2d

cos θc,e = cos θc,o +

ε0 ε
ϕ2
2σlg d

(11)
(12)

(7)

Figure 3 Rendering of electrowetting of the surface droplet on a dielectric
coated substrate. The net charge distribution is also shown.

heat transfer engineering

where θc,e is the electrowetted contact angle, θc,o is the neutral
contact angle, ε is the dielectric constant of the dielectric layer
underneath the water droplet, d is the thickness of the dielectric
layer, and ϕ is the applied potential between the liquid and the
electrode underneath the dielectric layer. Ideally, as the potential
is increased, the electrowetted contact angle approaches zero.
However, it is found that the contact angle saturates at a value
θc,sat varying between 30◦ and 80◦ , depending on the system
(Moon et al. [20] and Peykov et al. [21]). This contact angle
saturation can be explained as an electron-discharge mechanism,
together with the vertical component of the electrostatic force
acting on the contact line (Kang [22]).
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J. KIM AND M. KAVIANY

Physics of Droplet Purge Initiation
Physics of the electrowetting assisted purge of droplets can be
analyzed using a simple force balance at TCL. At TCL, a force
of per unit length is applied in the radial direction as predicted
by Eq. (10). As a result, the x component of the electrowetting
force will vary as the cosine of the azimuthal angle ζ. In contrast,
the contact line friction is constant along TCL in the x direction,
since it is assumed that the friction is a reaction force existing
only in the x direction and that droplet weight is uniformly
distributed at liquid–solid interface. Note that the integral of the
contact line friction at the critical inclination angle is equal to
the retention force, which is given by Eq. (4). By curve fitting the
data points under no electrowetting conditions, the magnitude of
k from the experiment was found to be 1.845. Then according to
the classical droplet mechanics and by using the retention force
data, the sum of the forces at the critical inclination angle can
be written as
Fx =

=

π
2

−π
2

1
2Rfe cos ζdζ − Fsx
2

π
2

R
−π
2

εo ε
ϕ 2 cos ζdζ − 0.923σlg R(cos θc,r − cos θc,a )
d
(13)

We have assumed that the applied forces are concentrated at
TCL, as graphically represented in Figure 4. From the figure we
see that the contact line of the advancing side will start to slip
when the electrowetting overcomes the local static contact line
friction value at the location of θc,a,max . As fe becomes larger
with increase in potential, the portion of the contact line which

begins to slip increases. Also, as the contact line begins to slip,
it causes an instantaneous reduction in the advancing contact
angle. When the advancing contact angle is reduced, according
to Eq. (12), the retention force is reduced which results in lowering of the critical inclination angle (for given liquid volume).
When a sufficient portion of the contact line friction is removed,
the bulk liquid motion is initiated. In sum, the sequence of
liquid motion under electrowetting can be described as first,

at the onset of motion, the droplet is charged and experiences
electrowetting which overcomes the static TCL friction. When
the sum of the gravity and electrowetting force is larger than
the static friction over the entire contact line of the droplet, the
bulk condensate motion is initiated. As the droplet advances,
the electrostatic energy is dissipated and dewetting becomes
apparent. When the droplet recovers its original topology, it experiences a rise in electrostatic energy due to its proximity to
the over-hanging electrode and this sequence is repeated. Using
the preceding droplet physics, prediction of the electrowetting
reduction of the critical inclination angle is possible by using
a simple force balance at the TCL. The observation indicates
minimum or no advancing of receding contact line until the advancing contact line has well advanced, thus, it is reasonable to
assume that the dominant criteria for the initiation of the droplet
motion is the force balance at the advancing contact line (Kim
[8]). As long as the droplet is not separated, this treatment of
the force on the contact line is valid. The retention force can be
estimated using Eq. (4) with the empirical contact angle relation
(5). The electrowetting force can be calculated by integrating
the x component acting on TCL over the azimuthal angle for
the advancing portion of the droplet. Then by solving for the
inclination angle which the gravity balances, the resultant of
the retention force and the electrowetting force, it is possible
to obtain a theoretical prediction of the variation of the critical
inclination angle with the applied potential. This angle is found
by solving the following equation
φ = sin−1
⎛
⎝

π

2
−π
2

R εdo ε ϕ 2 cos ζdζ − 0.923σlg (cos θc,a − cos θc,r )
ρgV

⎞
⎠

(14)
Note the underlying assumptions that friction force at the rear
TCL does not contribute to the initiation of the droplet motion
and that the weight of the droplet is applied to the front half of
the droplet.
EXPERIMENTAL ANALYSIS
Implementation of Electrowetting in Heat Exchangers
Figure 4 Graphical representation of balance between the retention and electrowetting forces, at the advancing TCL.

heat transfer engineering

The theoretical analyses in the preceding sections have indicated that by using electrowetting droplet motion initiation at
vol. 31 no. 2 2010


J. KIM AND M. KAVIANY

low Bond numbers is possible. This would significantly increase
the drainage rate in heat exchangers. To extend the theoretical
prediction to practical application, a series of experiments were

designed and performed. Figure 5 presents a detailed picture
of an electrowetting assisted droplet purge in prototype heat exchangers manufactured by AHT (Advanced Heat Transfer). The
heat exchangers were coated with a dielectric layer (polymer
based electric insulation coating ε = 2.4 and θc,o = 70◦ ) with
200 µm in thickness. A second polymer-based P4 (ε = 3.0 and
θc,o = 110◦ ) hydrophobic coating (Circle Prosco, Bloomington,
IN, USA) with 300 µm in thickness was coated on top of the first
layer. Subsequently, horizontal and vertical copper electrodes
where installed between the fins of the heat exchangers via ex-

Figure 5 Image of initiation of droplet purge using electrowetting using vertical electrodes, for different elapsed times. The environmental conditions are
THX = 0.2◦ C, relative humidity = 80% and exposed time duration of 60 mins.
The location of the droplet is indicated using arrows. Note the contrast between
fins with and without electrowetting.

heat transfer engineering

105

ternal acrylic frame. Then the heat exchangers were connected
to a refrigeration unit and were operated under 80% humidity
condition for 60 min. The heat exchanger surface temperature
TH X was measured to be 0.2◦ C. When condensation began to
form, electric potential of 600 V was applied. The experiment
was photographed using a DSLR camera with a 1:1 macrolens.
The figure shows that there exists clear contrast between the
fins which have been subjected to electrowetting forces and
the ones which were not. The droplets which were formed under heat exchanger operations have either been purged or on
the verge of purge for the fins which have electrodes, whereas
significant droplet retention is observed on the fins which do

not have electrodes. Figure 6 shows the drainage rate (mass of
water drained per unit time) normalized with respect to base
(no coat) heat exchanger of different passive and active surface
treatments. The data show approximately 150% improvement
in drainage rate compared to heat exchanger with no coat. Also,
for manual target excitation (where electrodes were manually
brought in proximity to the droplets), there was approximately
290% increase in the drainage rate showing significantly improved drainage potential when optimization is achieved. In
light of previously shown potential-improvement of drainage
rate in heat exchangers, we present a ideal conceptual design in
which the electrowetting assisted drainage can be implemented
in a full scale heat exchanger. Figure 7 shows one of the optimized implementations of electrowetting technique in heat
exchangers. The heat exchanger is coated with a hydrophobic
dielectric coating and the electrodes are suspended between the
fins via external frame. The electrodes are vertically oriented
to minimize the blockage of liquid droplets. Although there

Figure 6 Drainage rate for prototype heat exchangers with different passive
and active droplet-retention prevention methods. The drainage rates have been
normalized with respect to base (no coat) heat exchanger.

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106

J. KIM AND M. KAVIANY

pose an electrode-heat exchanger design which will enhance the
current performance of the evaporator. By using the new electrowetting implemented heat exchanger design and overcoming

the following challenges: need for enhanced electrical insulation, high performance dielectric coating and polished find tip,
it is expected that the evaporator performance will increase by
many folds.

NOMENCLATURE
A
Bo
D
E
Fif
fs
g
k
n
p
R
r1
T
THX
V

area, m2
bond number
diameter, m
electric field strength, V/m
total force, N
friction force, N
gravitational acceleration, m.s−2
retention force constant
unit vector

pressure drop, Pa
droplet radius, m
minuscule radius, m
Maxwell stress tensor, Pa
Temperature, ◦ C
Volume, m3

Greek Symbols

Figure 7 Conceptual rendering of one of the optimized electrode designs
which utilizes electrowetting as an active means of purging of droplets.

still exist many challenges in electric isolation and current lack
of high performance coating, in the future, we expect that these
kinds of electrowetting assisted drainage in heat exchangers will
significantly reduce the water retention rate thereby improving
the heat exchanger performance by many folds.

Kronecker delta
azimuthal angle, ◦
contact angle, ◦
Lagrange multiplier
mass density, kg/m3
liquid charge density, C/m3
surface charge density, C/m3
i − j interfacial tension, N/m

δik
ζ
θc

λ
ρ
ρf
ρs
σij

Subscripts
CONCLUSION
Electrowetting purged surface condensate in evaporators has
been investigated using physics of the force balance at the threephase contact line. Using a prototype heat exchanger, the theory
was applied to investigate the improvement of drainage under electrowetting conditions. Significant improvements—up to
290% increase in the drainage rate—were observed paving the
way to a full scale implementation of physics using elecrowetting as the means of condensate purge. Based on the theoretical
insight and the preliminary experimental investigation, we proheat transfer engineering

c,a
c,e
c,o
c,r
g
HX
if
l
max
min
s

advancing contact angle
electrowetted contact angle
equilibrium contact angle

receding contact angle
gas
heat exchanger
interface
liquid
maximum
minimum
static or solid

vol. 31 no. 2 2010


J. KIM AND M. KAVIANY

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[21] Peykov, V., Quinn, A., and Ralston, J., Electrowetting: A Model
for Contact-Angle Saturation, Colloid and Polymer Science, vol.
278, pp. 789–793, 2000.
[22] Kang, K. H., How Electrostatic Fields Change Contact Angle in Electrowetting, Langmuir, vol. 18, pp. 10318–10322,
2002.

Jedo Kim is a Ph.D. student at the Heat Transfer
Physics lab, Department of Mechanical Engineering, University of Michigan, Ann Arbor. He received
his M.S. from University of Michigan and his B.S.
from University of Toronto (2004). Currently, he is
working in atomic-level heat regeneration using antiStokes luminescence.

Massoud Kaviany is Professor of Mechanical Engineering and Applied Physics at University of Michigan, since 1986. His Ph.D. is from University of
California-Berkeley. His education-research field is
heat transfer physics.

vol. 31 no. 2 2010

Heat Transfer Engineering, 31(2):108–118, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903285369

The Effect of the
Electrohydrodynamic on the
Two-Phase Flow Pressure Drop
of R-134a during Evaporation inside
Horizontal Smooth and Micro-Fin
Tubes
SURIYAN LAOHALERTDECHA,1 JATUPORN KAEW-ON,1,2
and SOMCHAI WONGWISES2
1

Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Laboratory (FUTURE), Department of Mechanical
Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand
2
Department of Physics, Faculty of Science, Thaksin University, Papayom, Phattalung, Thailand

This article concerns the pressure drop caused by using the electrohydrodynamic (EHD) technique during evaporation of
pure R-134a inside smooth and micro-fin tubes. The test section is a counter-flow concentric tube-in-tube heat exchanger
where R-134a flows inside the inner tube and hot water flows in the annulus. A smooth tube and micro-fin tube having an
inner diameter of 8.12 mm and 8.92 mm, respectively, are used as an inner tube. The length of the inner tube is 2.50 m. The
outer tube is a smooth copper tube having an inner diameter of 21.2 mm. The electrode, which is a cylindrical stainless steel
wire having diameter of 1.47 mm, is placed in the center of the inner tube. The electrical field is established by connecting
a DC high voltage power supply of 2.5 kV to the electrode while the inner tube is grounded. Experiments are conducted
at saturation temperatures of 10–20◦ C, mass fluxes of 200–600 kg/m2 s, and heat fluxes of 10–20 kW/m2 . The experimental
results indicate that the application of EHD introduces a small pressure drop penalty. New correlations for the pressure drop
are proposed for practical applications.

INTRODUCTION
Normally, heat transfer enhancement techniques can be divided into two groups: namely passive techniques and active
techniques. The passive techniques require special surface geometries, such as rough surface or extended surface. The active
techniques require external forces, such as fluid vibration, surface vibration, and an electrical field. An electrohydrodynamic
(EHD) technique is one of the types of active techniques, which
The present study was supported financially by the Joint Graduate School
of Energy and Environment (JGSEE) and the Thailand Research Fund (TRF)
whose guidance and assistance are gratefully acknowledged.
Address correspondence to Professor Somchai Wongwises, King Mongkut’s
University of Technology Thonburi, 126 Pracha-utid Road, Bangmod,
Toongkru, Bangkok 10140, Thailand. E-mail:

can be achieved by the interaction between the electrical field
and the flow of dielectric fluid medium. This interaction creates
additional fluid motion which leads to a higher heat transfer
coefficient. The electrical body force density acting on the fluid
element of dielectric fluid in the presence of an electrical field
can be expressed as:
1
1
∂ε
fe = qE − E 2 ∇ε + ∇ E 2 ρ
2
2
∂ρ

(1)
T

The three terms on the right side of Eq. (1) represent the
electrophoretic, dielectrophoretic, and electrostrictive components of the force, respectively. The first term represents the
force acting on the free charges in the presence of an electrical
field, called Coulomb force. The second term is a consequence
of inhomogeneous or spatial change in the permittivity of the
dielectric fluid due to non-uniform electrical fields, temperature

108


S. LAOHALERTDECHA ET AL.

109

Table 1 Refrigerants, electrode and tube configurations studied by various researchers

Source

Refrigerant

Test section

Singh et al. [1]

R-123

Smooth stainless steel tube
ID = 9.4 mm
Length = 1220 mm

Cylindrical stainless steel
electrode having
diameter of 3 mm

Singh et al. [2]

R-134a

Smooth stainless steel tube
ID = 9.4 mm
Length = 1220 mm

Cylindrical stainless steel
electrode having
diameter of 3 mm

Salehi et al. [3]

R-404A

Micro-fin copper tube
ID = 11.78 mm
OD = 12.7 mm
Length = 304.8 mm

Salehi et al. [4]

R-134a

Bryan and Seyed-Yagoobi [5]

R-134a

Cotton et al. [6]

R-134a

1. Smooth copper tube
ID = 9.5 mm
OD = 11.56 mm
Length = 114.3 mm
2. Corrugated copper tube
with helical angle of 18
with height of ridge of
0.25 mm
Smooth copper tube
ID = 14.1 mm
OD = 15.9 mm
Length = 100, 200, 300,
500 mm (connecting in
series)
Smooth stainless steel tube
ID = 10.92 mm
OD = 12.7 mm
Length = 1800 mm

Cylindrical stainless steel
wire having diameter of
0.46 mm
Helical electrode

ID = 8.92 mm, OD = 9.84
mm
Cylindrical rod

gradients, and phase differences. The third term is caused by
inhomogeneous electrical field strength and the variation in dielectric constant with temperature and density.
Heat transfer enhancement during evaporation using EHD
has been published in the literature. Some of the works were
performed by Singh et al. ([1, 2]), Salehi et al. [3, 4], Bryan and
Seyed-Yagoobi [5] and Cotton et al. [6] as shown in Table 1.
It can be noted that the mass fluxes of the reported test tubes
are almost all below 300 kg/s.m2 . As a consequence, the objective of this study is to study the pressure drop penalty from
the use of electrohydrodynamic technique during evaporation of
R-134a flowing in a horizontal smooth tube and micro-fin tube
at high mass flux conditions.

EXPERIMENTAL APPARATUS
The experimental apparatus can be divided into two parts: the
refrigeration test unit and the direct current (DC) high voltage
power supply unit. A schematic diagram of the test apparatus is
heat transfer engineering

Electrode geometry

Experimental
condition

Supplied energy to
the test section

Tsat = 27.52◦ C
EHD = 0, 10 kV
q = 5, 10, 20 kW/m2
G = 50–400 kg/m2 s
Inlet quality = 0–0.5
Tsat = 20.15◦ C
EHD = 0, 10 kV
q = 5, 10, 20 kW/m2
G = 50–400 kg/m2 s
Inlet quality = 0–0.5
Tsat = 20.15◦ C
EHD = 0–3 kV
q = 5, 10 kW/m2
G = 50–200 kg/m2 s
Average quality = 0–0.8

Hot water

Re =500, 1000
EHD = 0–3 kV
q = 25 kW/m2
Inlet quality = 0–0.6

Electric heater

Cylindrical brass rod
electrode having
diameter of 1.6 mm

Tsat = 4.9–25.1◦ C

EHD = 0, 5, 15 kV
G = 99.9–300.7 kg/m2 s
Inlet quality = 0–0.8

Hot water

Cylindrical stainless steel
electrode having
diameter of 3.175 mm

Tsat = 24◦ C
EHD = 0–8 kV
q = 10, 20 kW/m2
G = 100–500 kg/m2 s
Inlet quality = 0–0.6

Hot water

Hot water

Electric heater

shown in Figure 1. This experimental apparatus was designed to
measure the heat transfer coefficient and pressure drop of pure
R-134a over the length of the test tube.
The test loop consists of a test section, refrigerant loop, heating water flow loops, sub-cooling loop, and the relevant instrumentation. For the refrigerant circulation loop, liquid refrigerant
is pumped by a magnetic gear pump which is regulated by an
inverter. The refrigerant flows in series through a filter/dryer, a
sight glass tube, and enters the test section. The inlet quality before entering the test section is controlled by the pre-heater. The
pre-heater is a spiral counter flow heat exchanger that supplies

energy to control inlet quality of the refrigerant. The refrigerant leaving the test section is then condensed and sub-cooled
by the chilling loop that removes heat load receiving from the
pre-heater and, returns from the two-phase refrigerant to a subcooled state and later collects in a receiver and eventually returns
to the refrigerant pump to complete the cycle.
The test section as shown in Figure 2 is a horizontal
counter-flow double tube heat exchanger. The length of the
heat exchanger is 2.5 m. Refrigerant temperature and the tube
vol. 31 no. 2 2010


110

S. LAOHALERTDECHA ET AL.

Figure 1 Schematic diagram of experimental apparatus.

Figure 2 Schematic diagram of test section.

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vol. 31 no. 2 2010


S. LAOHALERTDECHA ET AL.
Table 2 Smooth tube and micro-fin tube dimensions
Parameter

Smooth tube

Outside diameter, Do (mm)

Bottom thickness, t (mm)
Wwetted perimeter (mm)
Maximum inner diameter, Di (mm)
Hydraulic diameter, Dh (mm)
Cross sectional area, Ac (mm2 )
Number of fins, n
Spiral angle, β (degrees)
Fin height, ef (mm)
Fin pitch, p (mm)
Bottom width (mm)
Apex angle, γ (degrees)
Fin tip diameter, Dt (mm)

9.52
0.7
25.5
8.12
8.12
51.78
—
—
—
—
—
—
—

111

Table 3 Experimental uncertainty

Micro-fin tube
9.52
0.3
43.2
8.92
5.43
61.31
60
18
0.2
0.47
0.27
52.45
8.52

wall temperatures in the test section are measured by T-type
thermocouples. A total of eighteen thermocouples are soldered
at the top, bottom and side at six points along the tube. All
the temperature measuring devices are well calibrated in a
controlled temperature bath using standard precision mercury
glass thermometers. The uncertainty of the temperature measurements after considering the data acquisition system is ±
0.1◦ C. All static pressure taps are mounted in the tube wall. The
refrigerant flow meter is a variable area type. The flow meter is
specially calibrated in the range of 0–8.3 × 10−3 m3 /min for R134a by the manufacturer. The differential pressure transducer
and pressure gauges are calibrated against a primary standard,
the dead weight tester. A stainless steel cylindrical electrode,
1.47 mm in diameter, is used in all experiments. The cylindrical
electrode is supported in the center of the test section by electrically insulating spacers (Teflon type material) at intervals of 250
mm. The electrode is attached to the spacers by using a special
epoxy-resin. Since the electric field is applied to the test section

by a DC high voltage power supply, the electrode attached to a
modified automotive spark plug serves as the charged electrode
and the heat transfer surface as the receiving electrode.
The dimensions of the smooth and micro-fin tubes are shown
in Table 2. The cross-section of micro-fin tube is shown in

Parameter

Uncertainty
(◦ C)

±0.1◦ C
±0.075 kPa
±2% Full scale
±5% Full scale
±11%
±8%
±12%
±8%

Temperature, T
Pressure drop, P (kPa)
˙ ref
Mass flow rate of refrigerant, m
˙w
Mass flow rate of water, m
˙ TS
Heat transfer rate at test section, Q
˙ ph
Heat transfer rate at pre-heater, Q

Heat transfer coefficient, havg
Inlet quality, xin

Figure 3. The inlet water temperature is controlled by a thermostat. A differential pressure transducer and thermocouples
are installed at the test section to measure the pressure drop
and temperature across the test section respectively. The length
between the pressure taps is 3 m.
It is necessary to realize that the maximum voltage before
starting the electrical breakdown in the test section must be
known and should not be exceeded during any steady-state
condition. Before the two-phase experiment was performed,
the heat balance between refrigerant-side and water-side of the
single-phase experiment was conducted. The uncertainties of
the heat balance were within 8% and 5% for the pre-heater and
the test section, respectively. The uncertainties of the measured
quantities and calculated parameters are shown in Table 3.

DATA REDUCTION
The data reduction of the measured results can be summarized as follows:
The inlet vapor quality of the test section (xT S,in )
xT S,in =

iT S,in − if @TT S,in
ifg@TT S,in

(2)

where if is the enthalpy of the saturated liquid based on the
temperature of the test section inlet, ifg is the enthalpy of vaporization based on the temperature of the test section inlet, iT S,in
is the refrigerant enthalpy at the test section inlet and is given

by:
iT S,in = iph,in +

Q˙ ph
˙ ref
m

(3)

where iph,in is the inlet enthalpy of the liquid refrigerant be˙ ref is the mass flow rate of the
fore entering the pre-heater, m
refrigerant and Q˙ ph is the heat transfer rate in the pre-heater:
˙ w,ph cp,w (Tw,in − Tw,out )ph
Q˙ ph = m

(4)

˙ w,ph is the mass flow rate of water entering the prewhere m
heater.
The outlet vapor quality of the test section (xT S,out )
Figure 3 The cross-section of micro-fin tube.

heat transfer engineering

xT S,out =
vol. 31 no. 2 2010

iTS,out − if @TTS,out
ifg@TTS,out

(5)


112

S. LAOHALERTDECHA ET AL.

where iT S,out is the refrigerant enthalpy at the test section outlet,
if is the enthalpy of the saturated liquid based on the temperature
of the test section outlet, and ifg is the enthalpy of vaporization.
As a consequence, the outlet enthalpy of the refrigerant flow is
calculated as:
Q˙ T S
iT S,out = iT S,in +
(6)
˙ ref
m
where the heat transfer rate in the test section is obtained from:
˙ w,T S cp,w (Tw,in − Tw,out )T S
Q˙ T S = m

(7)

˙ w,T S is the mass flow rate of the water entering the test
where m
section.
The average heat transfer coefficient (havg )
havg =

Q˙ T S

Ainside (Tavg,wall − Tavg,sat )

(8)

where havg is the average heat transfer coefficient, Q˙ T S is the
heat transfer rate in the test section, Tavg,wall is the average
temperature of the wall, Tavg,sat is the average temperature of
the refrigerant at the test section inlet, and outlet.
Tin,sat + Tout,sat
2
is the inside surface area of the test section:
Tavg,sat =

Ainside

Ainside = πDf L

(9)

(10)

where Df is the inside diameter of the test tube. L is the length
of the test tube. The inside diameter of the micro-fin tube is
defined as the outer diameter of the micro-fin tube minus twice
the minimum wall thickness.

RESULTS AND DISCUSSION
In general, the EHD technique can provide enhancement of
heat transfer. However, the heat transfer enhancement should be
considered together with pressure drop penalty. In the present

study, the effects of electrode, supporter, mass fluxes, saturation
temperatures, heat fluxes, and applied voltage of 2.5 kV on
the pressure drop during evaporation of R-134a inside smooth
and micro-fin tubes are experimentally investigated. The test
conditions were selected to cover as much as possible of the
range of inlet quality. The pressure drop is the sum of a frictional
pressure drop and a momentum pressure drop. The pressure drop
per unit length is obtained by dividing the measured pressure
drop by the length between pressure taps. In our apparatus, the
length between pressure taps is 3 m, while the length of the heat
exchanger is 2.5 m.
There are two phenomena that are usually encountered inside EHD-enhanced smooth and micro-fin tubes [7]. The first is
the liquid-extraction phenomenon. When a coaxial cylindrical
electrode is used with a smooth tube, the highest electrical field
is at the electrode surface due to its small radius of curvature
heat transfer engineering

Figure 4 Liquid-extraction phenomenon [7].

since the liquid surface extends into the gas toward the electrode
as shown in Figure 4. The second is the electro-convection phenomenon. When a coaxial cylindrical electrode is used with a
micro-fin tube, the highest electrical field is at the tip of the fin
due to its small radius of curvature (sharp) since the liquid interface is pulled toward the tip of the fin, as shown in Figure 5. Both
liquid-extraction and electro-convection phenomena generate a
secondary fluid motion inside the tube leading to increase in
heat transfer and pressure drop.
Figures 6 and 7 show the comparisons of the measured pressure drop inside smooth and micro-fin tubes for the absence of
an electrode, the presence of an uncharged electrode (0 kV),
and the presence of a charged electrode (2.5 kV). The test conditions are performed at the saturation temperature (Tsat ) of
20◦ C, heat flux (q”) of 10 kW/m2 , and mass flux (G) of 400

kg/m2 s. The measured pressure drop in the absence of an electrode is obtained by Wongsa-ngam et al. [8]. These figures also
show that the pressure drops obtained from both tubes increase
with increasing inlet quality. At the same quality, the pressure
drop obtained with the presence of an uncharged electrode (0
kV) is higher than that with the absence of an electrode up to

Figure 5 Electro-convection phenomenon [7].

vol. 31 no. 2 2010


S. LAOHALERTDECHA ET AL.

113

Figure 6 Pressure drop versus inlet quality for smooth tube at Tsat = 20◦ C,
G = 400 kg/m2 s and q = 10 kW/m2 .

Figure 8 The effect of mass flux on the pressure drop for smooth tube at
Tsat = 20◦ C and q = 20 kW/m2 .

100% for smooth tube and 80% for micro-fin tube. This is because the supporter and electrode obstruct the fluid flow. The
pressure drop obtained with the presence of a charged electrode
is slightly higher than that with the presence of an uncharged
electrode at the same inlet quality because of the instabilities
at the liquid-vapor interface resulting from the molecules of
refrigerant disturbed by the EHD force.
Figures 8 and 9 show the variation of the measured pressure
drop with inlet quality of pure R-134a during evaporation in the
smooth and micro-fin tubes for the presence of an uncharged

electrode (0 kV) and for the presence of a charged electrode
(2.5 kV) at a saturation temperature of 20◦ C and heat flux of 20
kW/m2 for different mass fluxes of 200, 400, and 600 kg/m2 s.
These figures show that the measured pressure drops obtained
from the presence of an uncharged electrode (0 kV) and the
presence of a charged electrode (2.5 kV) increase with increas-

ing inlet quality. As expected, at the same quality the pressure
drops for the presence of an uncharged electrode (0 kV) and the
presence of a charged electrode (2.5 kV) obtained from higher
mass flux are always higher than at lower mass fluxes across the
range of the inlet quality. However, the effect of the mass flux
on the pressure drop can be clearly seen at higher inlet quality,
i.e., the pressure drop is much higher for a higher mass flux
than that for a lower mass flux. The application of EHD seems
to be negligible for almost all pressure drops obtained from the
broadest range of inlet quality.
Figures 10 and 11 show the variation of the measured evaporation pressure drop with inlet quality in the smooth and microfin tubes for the presence of an uncharged electrode (0 kV) and
the presence of a charged electrode (2.5 kV) at a mass flux of 400
kg/m2 s and saturation temperature of 20◦ C for different heat
fluxes of 10, 15 and 20 kW/m2 . These figures also show that

Figure 7 Pressure drop versus inlet quality for micro-fin tube at Tsat = 20◦ C,
G = 400 kg/m2 s and q = 10 kW/m2 .

Figure 9 The effect of mass flux on the pressure drop for micro-fin tube at
Tsat = 20◦ C and q = 20 kW/m2 .

heat transfer engineering

vol. 31 no. 2 2010


114

S. LAOHALERTDECHA ET AL.

Figure 10 The effect of heat flux on the pressure drop for smoth tube at
Tsat = 20◦ C and G = 400 kg/m2 s.

the pressure drops for both smooth and micro-fin tubes with
the presence of an uncharged electrode (0 kV) and the presence of a charged electrode (2.5 kV) increase with increasing
inlet quality. It can be seen that pressure drop increases with
increasing heat flux. This is because more vapor bubbles are
created at higher heat flux. This phenomenon promotes more
agitation in the fluid flow, leading to the increase in pressure
drop. Application of EHD voltage of 2.5 kV also has a slight
effect on the pressure drop in a wide range of inlet qualities.
Figures 12 and 13 show the variation of the measured evaporation pressure drop with inlet quality in the smooth and microfin tubes for the presence of an uncharged electrode (0 kV) and
the presence of a charged electrode (2.5 kV) at a mass flux of
400 kg/m2 s, heat flux of 20 kW/m2 and different saturation temperatures of 10, 15 and 20◦ C. These figures also show that the
pressure drops increase slightly with increasing inlet quality. As

Figure 11 The effect of heat flux on the pressure drop for micro-fin tube at
Tsat = 20◦ C and G = 400 kg/m2 s.

heat transfer engineering

Figure 12 The effect saturation temperature on the pressure drop for smooth
tube at Tsat = 20◦ C and G = 400 kg/m2 s.

expected, the pressure drop at lower saturation temperatures is
higher than those at higher saturation temperatures at an equivalent inlet quality. The effect of the saturation temperature on the
pressure drop is clear at higher inlet quality. The pressure drop is
higher for a lower saturation temperature than that for a higher
saturation temperature, and this is caused by the decrease in the
mixture viscosity. The application of an EHD voltage of 2.5 kV
for smooth and micro-fin tubes slightly increases the pressure
drop at all saturation temperatures.
Figures 14 and 15 show the comparisons of the average measured evaporation heat transfer coefficient obtained from the
smooth tube with that obtained from the micro-fin tube at a
mass flux of 400 kg/m2 s, a heat flux of 20 kW/m2 , and saturation temperatures of 20◦ C for the presence of an uncharged
electrode and a charged electrode, respectively. It can be clearly
seen that the heat transfer coefficient increases with increasing
inlet quality. Both in the presence of uncharged electrode and
charged electrode, the heat transfer coefficient obtained from

Figure 13 The effect saturation temperature on the pressure drop for microfin tube at Tsat = 20◦ C and G = 400 kg/m2 s.

vol. 31 no. 2 2010


S. LAOHALERTDECHA ET AL.

115

Figure 14 Heat transfer coefficient versus inlet quality for the presence of an
uncharged electrode at Tsat = 20◦ C, G = 400 kg/m2 s, and q = 20 kW/m2 .

Figure 16 The heat transfer ratio and the pressure drop ratio versus inlet

quality for smooth tube at Tsat = 20◦ C, G = 400 kg/m2 s, and q = 20 kW/m2 .

the microfin tube are higher than that obtained from the smooth
tube at the same inlet quality.
In the case of a smooth tube, with the presence of charged
electrode, due to liquid extraction phenomenon, the liquid-vapor
interface becomes unstable. This causes the average heat transfer
coefficient to be higher than in the case of uncharged electrode.
In the case of micro-fin tube, due to electro-convection phenomenon, the liquid interface was pulled toward the tip of the
fin causing the increase of heat transfer coefficient.
Figures 16 and 17 show the heat transfer coefficient ratio
(hratio ), pressure drop ratio ( P/L)ratio and enhancement factor
((hratio )/( P/L)ratio ) with inlet quality at a saturation temperature of 20◦ C, heat flux of 20 kW/m2 and mass flux of 400 kg/m2
s in smooth and micro-fin tubes, respectively. The heat transfer coefficient ratio (hratio ) is defined by havg,e /havg,o , where
havg,e is the heat transfer coefficient with the presence of a
charged electrode (2.5 kV) and havg,o is the heat transfer coefficient with the presence of an uncharged electrode (base

case, 0 kV). The pressure drop ratio (( P/L)ratio ) is defined
by [( P/L)e /( P/L)o ], where ( P/L)e is the pressure drop with
the presence of a charged electrode (2.5 kV) and ( P/L)o is
the pressure drop with the presence of an uncharged electrode
(base case, 0 kV). From these figures it can be seen that heat
transfer coefficient ratio and pressure drop ratio are decreased
with an increase in inlet quality. The heat transfer coefficient
ratios are all higher than the pressure drop ratio. The enhancement ratios (hratio /( P/L)ratio ) are almost always higher than 1
in the whole range of the tested inlet quality. It can be explained
that the slight pressure drop penalty is compensated by the heat
transfer augmentation.

Figure 15 Heat transfer coefficient versus inlet quality for the presence of a

charged electrode at Tsat = 20◦ C, G = 400 kg/m2 s, and q = 20 kW/m2 .

Figure 17 The heat transfer ratio and the pressure drop ratio versus inlet
quality for micro-fin tube Tsat = 20◦ C, G = 400 kg/m2 s, and q = 20 kW/m2 .

heat transfer engineering

Correlation for Predicting Pressure Drop
The two-phase friction pressure gradient (dpF /dz) of smooth
and micro-fin tubes may be expressed in term of two-phase

vol. 31 no. 2 2010


116

S. LAOHALERTDECHA ET AL.

multiplier φ2l defined as follow:
dpF
dz

φ2l =

/

dpF
dz

(11)

l

Martinelli parameter (X) is given by:
X=

(dpF /dz)l
(dpF /dz) v

(12)

where (dpF /dz)l and (dpF /dz)v are the single-phase liquid and
vapor pressure gradients (kPa/m) calculated by using the actual
phase flow as follows:
(dpF /dz)l =

2fl G2 (1 − x)2
Dρl

(13)

and

Figure 19 Predicted pressure drop versus the measured pressure drop.

(dpF /dz)v =

2 2

2fv G x
Dρv

(14)

where fl is the single phase liquid friction factor calculated
from:
4fl = 1.325 ln

5.74
e/D
+ 0.9
3.7
Rel

−2

(15)

And
Rel =

GD(1 − x)
µl

(16)

where fv is the single phase vapor friction factor calculated
from:
e/D
5.74
+ 0.9

4fv = 1.325 ln
3.7
Rev
GDx
µv

e/D = 0.18(ef /Dt )/(0.1 + cos β)

(17)

(18)

(19)

where ef is the fin height. Dt is the fin tip diameter. β is the
spiral angle.
For smooth tube, empirical correlation shown in Eq. (20) is
developed based on the presence of a charged electrode. It is
created by fitting the Martinelli parameter (X) against a twophase multiplier.
The presence of a charged electrode the two-phase multiplier
is:
φ2l = 1 +

−2

And
Rev =

For micro-fin tube the relative roughness (e/D) in Eqs. (15)
and (17) are replaced by the equation: Cavalini and Zecchin [9]:

22.473
X1.237

(20)

The correlation is also plotted in Figure 18. It can be explained that the present correlation can predict the pressure drop
within a deviation of ±25%.
For micro-fin tube, the empirical correlation shown in Eq.
(21) is developed based on the presence of a charged electrode.
It is created by fitting the Martinelli parameter (X) against a
two-phase multiplier.
The presence of a charged electrode the two-phase multiplier
is:
φ2l = 1 +

50.848
X0.995

(21)

The correlation is also plotted in Figure 19. It can be explained that the present correlation can predict the pressure drop
within a deviation of ±30%.

CONCLUSIONS

Figure 18 Predicted pressure drop versus the measured pressure drop.

heat transfer engineering

The present article reports the pressure drop penalty from
the application of EHD force on evaporation heat transfer enhancement of R-134a in horizontal smooth and micro-fin tubes.
The pressure drop obtained from the presence of an uncharged
vol. 31 no. 2 2010


S. LAOHALERTDECHA ET AL.

electrode (0 kV) is higher than that from the absence of an electrode, up to 100% for smooth tube and 80% for micro-fin tube.
Pressure drop results from both smooth and micro-fin tubes indicate that the application of an EHD voltage of 2.5 kV slightly
increases the pressure drop across the range of tested conditions. The enhancement ratio is almost always higher than 1.
The present correlation can predict the pressure drop within a
deviation of ±25% for smooth tube and ±30% for micro-fin
tube, respectively.

NOMENCLATURE
Ainside
Ac
cp
Dh
Do
Df
ef
E
fe
G
h
i
L
˙

m
n
p
P
˙
Q
q
q
T
u
x
X
φ2l

inside surface area of test section (m2 )
cross section area (m2 )
specific heat at constant pressure (J/kg-K)
hydraulic diameter (m)
outside tube diameter (m)
inside tube diameter (m)
fin height (m)
electric field strength (V/m)
EHD force density (N/m3 )
mass flux (kg/m2 s)
heat transfer coefficient (W/m2 K)
enthalpy (J/kg)
tube length (m)
mass flow rate (kg/s)
number of fin
fin pitch (m)

pressure (Pa)
heat transfer rate (W)
heat flux (W/m2 )
electric charge density (C/m3 )
temperature (◦ C)
velocity (m/s)
quality
Martinelli parameter
two-phase multiplier

Greek Symbols
β
γ
ε
εo
ρ

spiral angle (degree)
apex angle (degree)
electric permittivity (F/m)
electric permittivity of free space (8.854 × 10−12 )
(F/m)
density (kg/m3 )

Subscripts
avg
e

average
presence of an uncharged electrode

heat transfer engineering

exp
f
fg
in
l
o
out
ph
pre
ref
sat
TS
V
w
wall

117

experiment
saturated liquid
difference in property between saturated liquid and vapor
inlet
liquid
presence of a charged electrode
outlet
pre-heater
prediction
refrigerant

saturation
test section
vapor
water
wall

REFERENCES
[1] Singh, A., Dessiatoun, S., Ohadi, M. M., Salehi, M., and Chu, W.,
In-tube Boiling Heat Transfer Enhancement of R-123 using the
EHD technique. ASHRAE Transactions: Symposia, pp. 818–825,
1994.
[2] Singh, A., Dessiatoun, S., Ohadi, M. M., Salehi, M., and Chu W.,
In-tube Boiling Enhancement of R-134a Utilizing the Electric Field
Effect, ASME/JSME Thermal Engineering Conference, vol. 2, pp.
215–223, 1995.
[3] Salehi, M., Ohadi, M. M., and Dessiatoun, S., The Applicability of
the EHD Technique for Convective Boiling of Refrigerant Blends—
Experiments with R-404A, ASHRAE Transactions: Symposia, pp.
839–844, 1996.
[4] Salehi, M., Ohadi, M. M., and Dessiatoun, S., EHD Enhanced
Convective Boiling of R-134a in Grooved Channels—Application
to Subcompact Heat Exchangers, Journal of Heat Transfer, vol.
119, pp. 805–809, 1997.
[5] Bryan, J. E., and Seyed-Yagoobi, J., Elecrohydrodynamically Enhanced Convective Boiling: Relationship between Electrohydrodynamic Pressure and Momentum Flux Rate, Transaction of the
ASME, vol. 122, pp. 266–277, 2000.
[6] Cotton, J., Robinson, A. J., Shoukri, M., and Chang, J. S., A TwoPhase Flow Pattern Map for Annular Channels under a DC Applied
Voltage and the Application to Electrohydrodynamic Convective
Boiling Analysis, International Journal of Heat and Mass Transfer,
vol. 48, pp. 5563–5579, 2005.
[7] Singh, A., Ohadi, M. M., and Dessiatoun, S., EHD Enhancement

of In-tube Condensation Heat Transfer of Alternate Refrigerant
R-134a in Smooth and Microfin Tubes, ASHRAE Transactions:
Symposia, pp. 813–823, 1997.
[8] Wongsa-ngam, J., Nualboonrueng, T., and Wongwises, S., Performance of Smooth and Micro-fin Tubes in High mass Flux Region
of R-134a during Evaporation, Heat and Mass Transfer, vol. 40,
pp. 425–435, 2004.
[9] Cavallini, A., and Zecchin, R., A Dimensionless Correlation for
Heat Transfer Coefficient in Forced Convection Condensation, International Journal of Heat and Mass Transfer conference, pp.
193–200, 1974.

vol. 31 no. 2 2010


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S. LAOHALERTDECHA ET AL.
Suriyan Laohalertdecha is currently a Ph.D. student
at the Joint Graduate School of Energy and Environment, King Mongkut’s University of Technology
Thonburi, Bangmod, Thailand. He received his Master’s degree in energy technology from the same department in 2005. He also received his B.Eng. degree
from the Department of Mechanical Engineering at
the same university in 2002. Currently, his research
works concern heat transfer enhancement.

Somchai Wongwises is a Professor of Mechanical
Engineering at King Mongkut’s University of Technology Thonburi, Bangmod, Thailand. He received
his Doktor-Ingenieur (Dr.-Ing.) in mechanical engineering from the University of Hannover, Germany,
in 1994. His research interests include two-phase
flow, heat transfer enhancement, and thermal system design. Professor Wongwises is the head of the
Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab.

Jatuporn Kaewon is currently a Ph.D. student at the
Joint Graduate School of Energy and Environment,
King Mongkut’s University of Technology Thonburi,
Bangmod, Thailand. He received his Master’s degree
in energy technology from the same department in
2003. He also received his B.Eng. degree from the
Department of Mechanical Engineering at the same
university in 1999. He is also currently a lecturer at
Thaksin University.

heat transfer engineering

vol. 31 no. 2 2010


Heat Transfer Engineering, 31(2):119–126, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903285377

Experimental Characterization of an
Electrohydrodynamic Micropump for
Cryogenic Spot Cooling Applications
PARISA FOROUGHI,1 AMIR SHOOSHTARI,1 SERGUEI DESSIATOUN,1
and MICHAEL M. OHADI2
1

Smart and Small Thermal Systems Laboratory, Department of Mechanical Engineering, University of Maryland, College
Park, Maryland, USA
2

Academic Affairs, The Petroleum Institute, Abu Dhabi, United Arab Emirates

This article presents a study on the characterization of a planar, multistage, electrohydrodynamic (EHD) ion-drag micropump
for pumping of liquid nitrogen. Two designs of the pump, consisting of different emitter configurations (flat and saw-tooth),
similar emitter-collector spacing (50 microns), and similar gaps between successive electrode pairs (100 microns), were
tested at DC voltages ranging from 0 to 2.5 kV. The electric currents they generated and the corresponding static pressure
heads were measured to characterize the pumping performance. Pressure and current onset voltages as well as pressurevoltage (P-V) and pressure-current (P-I) relationships were investigated. The highest pressure head (30 Pa at 1700 V) was
generated with the saw-tooth design. After collecting and processing the data for various prototypes, it was evident that
incorporating saw-tooth electrodes can significantly improve the performance of the micropump.

INTRODUCTION
A new electronic era began with the discovery of hightemperature superconducting (HTSC) materials in 1987. HTSC
components, which operate in temperatures from 20 K up to
138 K, are being incorporated into communication and electronic monitoring devices to increase their signal-to-noise ratio
or their channel capacity. These devices must be maintained at
cryogenic temperatures to prevent the loss of their superconducting properties and to retain their performance superiority.
They are conventionally cooled via direct heat conduction to
the cold fingers of a cryocooler, which limits their spatial configuration and can lead to undesirable temperature differences
among the various components being cooled [1–3].
Compact electrohydrodynamic (EHD) micropumps capable
of pumping liquid nitrogen at 77 K into liquid-cooling circuits
would enable a much more compact and lightweight method of
maintaining a uniform temperature across the cooling circuit.
Besides providing precise flow control, EHD pumps, which
have no moving parts, would not vibrate the electronic devices
Address correspondence to Parisa Foroughi, Smart and Small Thermal Systems Laboratory, University of Maryland, Potomac Building (Bldg#092), Rm
1105, College Park, MD 20742. E-mail:

being cooled and would ultimately help to isolate them from the
typical mechanical vibrations of the cryocooler.

Although a significant amount of research has been conducted on the EHD pumping phenomenon in ambient conditions, cited by Foroughi et al. [4], the authors have found only a
limited number of studies with cryogenic liquids [5, 6]. Therefore, a thorough characterization of EHD micropumps for cryogenic applications could be important for advancing the liquid
cooling technology for devices containing HTSC materials, and
for bioengineering applications in which a small dose of LN2
needs to be delivered to a particular spot.
The work summarized in this article focuses on demonstrating the feasibility of the EHD ion-drag pumping phenomenon in
liquid nitrogen and on studying the effect of electrode geometry
on the performance. A more comprehensive study on geometrical characterization of the micropump can be found in Foroughi
[7].

EHD PUMPING PHENOMENON
The EHD ion-drag pumping phenomenon refers to liquid motion caused by an interaction between electric and hydrodynamic

119


120

P. FOROUGHI ET AL.

fields in a dielectric liquid. In an ion-drag pump, the ioninjection phenomenon is the key process for generating ions.
The pumping effect occurs when a sufficiently high electric potential difference is applied between a pair of electrodes, called
the emitter and collector. The ions are generated mostly at the
emitter/liquid interface and move towards the collector because
of the electric force (i.e., the Coulomb force). Friction between
the moving ions and neutral molecules drags the working fluid
and induces fluid motion. The Coulomb force density F acting on a dielectric fluid with free space-charge density of ρe ,
subjected to an electric field E is given by Melcher [8]:
F = ρe E

Figure 1 Micropump components.

(1)

For successful pressure generation, the abundance of one
ion polarity (i.e., the unipolar condition) is preferred, since the
generation of an equal number of ions of both polarities would
result in no net pumping, as positive and negative ions offset
the dragging action of each other. The charge injection process
highly depends on the electrochemical characteristics of the
working liquid, the electrochemistry of the electrode material,
the strength of the electric field, and the electrode geometry.
The pumping performance relies heavily on the electrical and
mechanical properties of the working fluid such as permittivity
ε, conductivity σ, and viscosity µ. Generally, high permittivity
and low viscosity are required for high pumping performance.
As shown in Eqs. (2) and (3), demonstrated by Crowley [9, 10]
and Crowley et al. [11], velocity of the fluid flow u and pressure
P are expected to show quadratic increase with electric field E
and channel depth h:

u≈

εE 2 h2
12µL

P ≈ εE 2

MICROPUMP DESIGN, FABRICATION
AND PACKAGING

The micropump in this study was composed of an alumina
substrate on which multistage gold electrodes of submicron
thickness were microfabricated, a top-cover with an embedded
channel and integrated inlet and outlet ports, and a bottom plate,
as shown in Figure 1. All the components were bonded together
by a cryogenic-compatible epoxy paste adhesive (Figure 2).
Two micropump designs were selected to study the effect
of electrode geometrical pattern on the performance. These designs had different emitter shapes and similar inter-electrode
spacing, electrode-pair spacing, and channel heights as summarized in Table 1. Figure 3 displays sectional views of a couple
of electrode pairs with different emitter shapes.
The micropumps were tested in a test rig specifically designed to measure static pressure head and electric current generation (caused by the migration of ions from one electrode to
another) in a closed loop at different DC voltages.

(2)
EXPERIMENTAL APPARATUS
(3)

More studies on theoretical aspects of EHD pumping mechanism can be found in Stuetzer [12, 13], Pickard [14, 15], Melcher
[8], and Seyed-Yagoobi et al. [16].
For a given liquid and electrode material, geometrical considerations are the most important factors in the design. The shape
of the electrode and the distance between them can strongly
influence the magnitude and direction of the electric field and
therefore impact the rate of electric charge generation at the
electrode/liquid interface. One example is the saw-tooth shaped
electrodes, which can substantially enhance the ion generation
due to the creation of a very high electric field [17], sometimes on the order of a few megavolts per meter at the electrode
tips.
In this study, the electrode design is restricted to flat and sawtooth shapes for a clear comparison of the effect of electrode
geometry on the onset voltage value and pressure generation.
heat transfer engineering

The experimental test rig shown in Figure 4 consisted of a
liquid nitrogen Dewar flask, an external nitrogen gas tank (not

Figure 2 Picture of a packaged micropump with expected flow direction.

vol. 31 no. 2 2010


P. FOROUGHI ET AL.

121

Table 1 Summary of micropump design parameters
Design
(50,100,f)
(50,100,s)

Del (µm)

Dpel (µm)

Lel (µm)

Lst (µm)

α (deg)

Emitter shape

Number of stages

50
50

100, 2Del
100, 2 Del

50
20

——
50

——
53

f
s

79
74

Note.
-f & s: electrode shapes (flat & saw-tooth)
-Del : emitter-collector inter-electrode spacing
-Dpel : electrode-pair (stage) spacing
-Lel : electrode base width
-Lst : saw-tooth width
-α : tooth angle

-Hch : channel height (260 µm).

shown in the figure), the micropump, a differential pressure
transducer (Validyne DP-15, range: 0–866 Pa, accuracy: ± 0.1
Pa), a liquid nitrogen reservoir, and stainless steel tubing with
an outer diameter of 3.17 mm and a wall thickness of 0.25 mm.
The Dewar flask with an inner diameter of 150 mm enclosed
the test loop properly. A few temperature sensors were installed
inside the Dewar flask to monitor the temperatures at different
locations. A foam lid isolated the interior space of the Dewar
flask from the outside environment.
To prepare the test rig for the experiments, the system initially underwent a high vacuum (about 40 millitorr) and was
then completely submerged in liquid nitrogen at 77 K. All the

components in the Dewar flask were submerged except the pressure transducer, which was positioned at a higher elevation outside the flask. The external nitrogen gas tank was then used to
feed ultra-pure (99.998%) nitrogen gas into the test section. The
liquid nitrogen reservoir acted as a nitrogen-gas container for
liquefaction purposes. The liquid nitrogen then flowed from the
reservoir into the test section and filled it.
After the system was fully charged with liquid nitrogen, helium gas at a gauge pressure of about 120 kPa was added to
keep the LN2 subcooled during tests and to prevent the formation of micro-bubbles (the boiling temperature of helium at a
gauge pressure of 120 kPa is 5.2 K). During the experiment,
the electric power consumption in the pump usually created
a local temperature increase in the system, which could lead
to micro-bubble formation and partial discharge (PD). According to Krahenbuhl et al. [18], pressurizing the system greatly
reduces the PD intensity and raises the inception stress. The
oxygen boiling point at a gauge pressure of 120 kPa is 98.3 K,
much higher than that of LN2 (i.e., 84.5 K at 120 kPa gauge
pressure), making it easily condensable into LN2 . In addition,
oxygen is a highly reactive substance and can lead to significantly inaccurate measurements. Since our experiments were

run in a closed, well-vacuumed system, however, the possibility
of oxygen solubility in LN2 was greatly reduced.

Figure 3 Different micropump electrode designs.

Figure 4 Schematic diagram of the test section.

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P. FOROUGHI ET AL.

Figure 5 Experimental results of a (50,100,s) design. Positive voltage polarity (0–1600 V) was applied to the emitter while the collector was grounded.

After the test rig was stabilized, the bypass valve was closed
and tests were performed by applying DC voltages ranging from
0 to 2.5 kV with positive polarity (unless otherwise stated) at
different increments to the micropump. The pressure head of the
micropump was measured directly by the differential pressure
cell, and the generated electric current was measured by an
external electric resistant circuit and a data acquisition system
(DAS).

EXPERIMENTAL RESULTS AND ANALYSIS
Figure 5 shows an example of data taken with a (50,100,s)
design with a 260 µm channel height (Hch ). The (50,100,s) notation corresponds to a Del = 50 µm, and Dpel = 100 µm, sawtooth shaped emitter and flat collectors. The static pressure head

and generated electric current (caused by the migration of ions
from one electrode to another) are plotted versus time. The positive voltage polarity was applied to the emitter electrodes, and
the collector electrodes were grounded. The voltage increased
slowly from 0 until the pumping onset occurred at around 1000
V. From then on, the voltage was increased in increments of 100
V until it reached 1600 V. To avoid the possibility of an electrical breakdown, the voltage was not increased further. After
a few minutes, the voltage was incrementally decreased until it
reached zero.
The data set shown above was reduced by taking the time
average of pressure and current data points at each voltage increment and plotting them versus the applied voltage, as shown
in Figure 6. According to the graph, the onset voltage of pressure
head and current for this design was around 1000 V.

Figure 6 P-V and I-V relationship for a micropump with saw-tooth electrodes. Positive voltage polarity was applied to the emitter while the collector
was grounded.

devices. Therefore, it is necessary to have a clear estimation of
onset voltages for each micropump design and prototype.
Onset voltage could not easily be calculated theoretically
due to the complexity of the EHD phenomenon; therefore, a
mathematical approach was used to estimate its value from the
experimental data for every single design. To do this, the equation of the line connecting the first 2 data points in P-V and P-I
curves for every test was determined, and then the line intersection with the voltage axis was calculated and defined as the
onset.
The onset voltages of pressure and current were calculated
separately for many tests run with both designs and compared
against each other, as shown in Figures 7 and 8. Overall, the
mean values of pressure and current onset voltages were expected to be identical, which was confirmed by the results.
However, the uncertainty involved with the current was less than
that of the pressure. This could be mainly due to measurement

errors. The measurement error of the current was within ±1 nA,
and the measurement error of the pressure was within ±0.5 Pa.

Onset Voltage
One of the determining factors in selecting the proper micropump design is the onset voltage. As with most microelectromechanical devices, the trend is to lower their electric power
consumption to make them compatible with microelectronic
heat transfer engineering

Figure 7 Onset voltage of pressure for different designs.

vol. 31 no. 2 2010