Microgravity Transport Processes in Fluid, Thermal, Biological, and Materials Sciences. Annals of the New York Academy of Sciences Volume 974

626 Pages·2002·109.93 MB·English

by  S. S.

Preface
With several Space-Shuttle experiments that have been conducted during the past
two decades, significant new insights have been gained into various physical phe-
nomena under microgravity conditions. There is at present a need to provide direc-
tion for microgravity research in which fluid flow and other transport processes form
a common basis for many investigations. For example, in biomedical engineering
and materials processing, fluid, thermal, and mass-transport aspects have gained pri-
macy among various researchers, and the sharing and complementing of expertise
have become a necessity for technical progress. In addition, with long-term manned
space missions in the near future, technical problems encompassing several of these
disciplines have been envisioned. The Banff conference provided a forum for the
free flow of ideas under this common theme of transport phenomena and focused on
interdisciplinary aspects.
One of the main objectives of the conference was to promote the exchange of
technical information and ideas among the various scientists and engineers working
in microgravity fluid, thermal, biological, and materials sciences. These areas have
become of importance to various disciplines within the broader realm of micrograv-
ity research. The conference, therefore, addressed the cross-cutting aspects of micro-
gravity science and technology and provided a forum for the synthesis of knowledge
that has been acquired during the past several years. It was intended to effectively
cover the growing interdisciplinary aspects of microgravity science and technology.
As a result, many of the participants were able to gain considerable knowledge and
insight into new areas, and it is expected that such sharing of expertise will create
new frontiers in the emerging science.
We were indeed fortunate to have scientific diversity among the participants, and
the high level of interdisciplinary activity that emanated from interaction among the
participants. By crossing traditional boundaries of scientific expertise, it is our hope
that new grounds for collaborative research will continue to emerge, and healthy
research programs will develop. The scientific community has indeed recognized
that transport phenomena as a science has reached a point whereupon it has a very
significant role in many different areas.
The conference organizing committee expresses its sincere gratitude to Professor
Frank Schmidt who, as the United Engineering Foundation’s technical liaison, gave
enormous support. In addition, we appreciate the valuable input from various mem-
bers of the scientific committee in putting the conference together, and we are grate-
ful to all the participants for sharing their technical expertise. Thanks are also due to
NASA and the U.S. National Science Foundation for financial support. On behalf of
all the participants, we thank Barbara Hickernell and the rest of the Foundation’s
staff in New York who, in spite of the catastrophic tragedy of September 11, 2001,
remained resilient in carrying out the final planning for the conference. Finally, we
thank the editorial staff of the New York Academy of Sciences for their role in pub-
lishing these keynote articles and scientific papers in the Annals of the New York
Academy of Sciences in archival form.
SATWINDAR SINGH SADHAL (USA), Chair & Scientific Secretary
VIJAY K. DHIR (USA), Co-Chair
HARUHIKO OHTA (Japan), Co-Chair
REGINALD W. SMITH (Canada), Co-Chair
JOHANNES STRAUB (Germany), Co-Chair
Ann. N.Y. Acad. Sci. 974: xi–xii (2002). ©2002 New York Academy of Sciences.

Use of an Electric Field in an
Electrostatic Liquid Film Radiator
S.G. BANKOFF,a E.M. GRIFFING,a AND R.A. SCHLUTERb
aChemical Engineering Department, Northwestern University, Evanston Illinois, USA
bPhysics and Astronomy Department, Northwestern University, Evanston Illinois, USA
ABSTRACT: Experimental and numerical work was performed to further the
understanding of an electrostatic liquid film radiator (ELFR) that was origi-
nally proposed by Kim et al.1 The ELFR design utilizes an electric field that
exerts a normal force on the interface of a flowing film. The field lowers the
pressure under the film in a space radiator and, thereby, prevents leakage
through a puncture in the radiator wall. The flowing film is subject to the Tay-
lor cone instability, whereby a cone of fluid forms underneath an electrode and
sharpens until a jet of fluid is pulled toward the electrode and disintegrates
into droplets. The critical potential for the instability is shown to be as much
as an order of magnitude higher than that used in previous designs.2 Further-
more, leak stoppage experiments indicate that the critical field is adequate to
stop leaks in a working radiator.
KEYWORDS: electric field; electrostatic liquid film radiator
INTRODUCTION
Various possible applications have spurred a general interest in electrohydrody-
namics. Examples include separation enhancement, electrostatic spraying to pro-
duce fine droplets or powders, ink-jet printers, spray painting, electrohydrodynamic
pumps, and a variety of MEMS devices. Electrostatic fields produce tensile stresses
at fluid interfaces. Typically, these forces are smaller than gravitational forces on
Earth. However, in a microgravity environment, electrostatic fields can be quite
important. The principal subject of this review is the application of strong electro-
static fields to flowing thin liquid films (usually liquid metal), including the stability
of the free surface. This is in connection with a very lightweight enclosed radiator
concept by the author, termed the electrostatic liquid film radiator (ELFR). An exten-
sive review of free-surface, thin-liquid-film dynamics and long-wave instability has
been given by Oron, Davis, and Bankoff.3 Comprehensive treatments of electrohy-
drodynamics were provided by Melcher4 and by Woodson and Melcher.5 A more
recent review of the literature, including details of the leaky dielectric model, is giv-
en by Saville.6
Lightweight radiator concepts include droplet,7–10 controlled free-stream,11,12
and falling film.13–19 Generally, however, losses over time, in an unenclosed radiator
of hot coolant, by evaporation into free space and/or droplet collision have not been
Address for correspondence: S.G. Bankoff, Chemical Engineering Department, Northwest-
ern University, Evanston, IL 60208, USA.
[email protected]
Ann. N.Y. Acad. Sci. 974: 1–9 (2002). ©2002 New York Academy of Sciences.
2 ANNALS NEW YORK ACADEMY OF SCIENCES
quantified. Two experimentally observed modes of droplet breakup are (1) the for-
mation of conical points (Taylor cones) that eject a fine spray of liquid droplets along
field lines, and (2) the separation of one drop into two drops that are temporarily con-
nected by a thin thread of fluid. Miksis,20 Sherwood,21 and others calculate a critical
value of the dielectric constant that separates the two modes of breakup. When the
dielectric constant is greater than the critical value, the charge accumulates on the
fluid, and tangential stresses induce circulatory flow. Both authors predict the forma-
tion of conical interfaces, but the methods break down due to a singularity when the
cone tip is too sharp. More recently several authors have used finite element methods
to more accurately calculate droplet break-up and Taylor cone dynamics. Notz and
Basaran,22 measured droplet formation from a capillary tube in the presence of an
electric field and used a finite element method to calculate droplet breakup.
Far less work has been done involving the deformation of a planar fluid interface.
An important difference between these problems is the disparity in length scale that
is often encountered in planar interface problems. For instance, typical length scales
are 15cm, whereas the Taylor cones often form over less than 1cm. This presents an
added difficulty in obtaining numerical solutions. Taylor and McEwan23 observed
Taylor cones on flat non-moving fluids. They showed that linear stability theory
could accurately determine the threshold potential for cones. Mayberry and
Donohoe24 measured the wavelength of the instability of liquid gallium, and found
it to be consistent with linear stability predictions. Melcher and Smith25 investigated
the effect of surface charge on the stability of non-conducting fluids by turning on a
dc field, both slowly and quickly. The dc fields had similar effects regardless of how
quickly they were administered.
ELECTROSTATIC LIQUID FILM RADIATOR DESIGN
The EFLR design is a pumped-loop, double-membrane radiator in which a thin
coolant film runs along the inside of an outer membrane that radiates heat into space.
The inner membrane, which is very thin, has an array of metallized rectangular elec-
trodes, any one of which can be charged to a high voltage if a leak is detected by
means of a conductive layer on the exterior surface. The electric field pulls the liquid
surface away from the puncture and can overcome the combined vapor pressure of
the coolant and the hydrostatic head of the thin coolant layer. The voltage is supplied
by a small van de Graaf generator in the interior of each module.
Because of thin walls (about 100 µm) and a large view factor (0.85–0.95), the
ELFR is extremely light in weight. According to preliminary calculations, the spe-
cific weight for a lithium-cooled radiator, in kg/kW thermal power, for a rotating
disk radiator with inflow temperature of 800K, outflow temperature of 725K, and
inlet Reynolds number of 300, is estimated to be 0.094kg/kW without the circulating
coolant, and 0.141kg/kW including the coolant. Note that all radiator types require
a circulating coolant to remove waste heat from the power cycle. This implies that a
1-MW thermal radiator would weigh only about 150kg, in part because of its excel-
lent view factor. Even this number can be substantially reduced if a thinner niobium
lining to protect against corrosion by the lithium can be used (possibly 25, rather
BANKOFF et al.: ELECTROSTATIC LIQUID FILM RADIATOR 3
than 50 microns). If proven practicable, the ELFR could provide dramatic cost sav-
ings for a variety of missions.
Several ultralight systems, including droplet, conveyor belt, and thin film radia-
tors have been proposed and studied in recent years to accomplish this goal. Tagliafi-
co and Fossa suggest liquid sheet or droplet radiators.18,19 They report design
weights as low as 1kg/kW at 300–400K.
The international space station generates about 75kW of power. More ambitious
designs might require one megawatt of power or more, necessitating the rejection of
two or more megawatts of waste heat. Practical radiators for this amount of radiation
might use temperatures of 700 to 1,000K. We have made two designs to satisfy both
power generation and housekeeping operating conditions. A high temperature radi-
ator would use a liquid metal such as lithium and operate at about 700K, and a low
temperature radiator utilizing either oil, NaK, or gallium would operate at about
300K. Lithium and NaK have both been used in space designs to date. They are very
light (Li, about 0.45g/cm3 and NaK, about 0.85g/cm3) and have good heat transfer
properties. A carbon coating on the exterior of the radiator would be used to decrease
the wettability (and hence the tendency to leak), and at the same time increase the
emissivity of the surface. With oil, a Teflon coating could be used to obtain non-wet-
ting, but in general a liquid metal coolant is preferred because its high surface ten-
sion and conductivity. However, the long-term chemical reactions, and hence
wettability, of the exterior surface of the radiator after leakage is arrested from a par-
ticular puncture are still unknown. Note that with a liquid metal all punctures are ini-
tially non-wetting, and probably remain so, because with a continuous meniscus, the
required driving pressures are many orders of magnitude greater than that available.
Previous work by Kim, Bankoff, and Miksis13–15 showed fluid film profiles for
flow under finite electrodes (see FIGURE 1). They derived lubrication and Kármán-
Pohlhausen models to calculate the height profiles and compared the results to a
numerical solution of the Navier-Stokes equations as calculated with the SOLA
code.26 They solved for the height profile and pressure under the film for conical and
cylindrical radiator geometries. Designs were then optimized based on minimum
specific weight with constraints on fluid depth and maintaining the ability to gener-
ate a negative pressure on the wall at the leak location with an electric field.
In the current work, we consider an electrohydrodynamic instability similar to
Taylor cones, leak dynamics within the hole, and electrical breakdown. Critical
fields for the Taylor cone type instability are obtained experimentally for mercury
and oil films. These fields are representative for the liquid metal and hydrocarbon
type radiators suggested. A large margin is observed for the liquid metal, which is
greatly stabilized by surface tension. However, the critical field for Taylor cones on
oil films is comparable to that used in previous designs.
Our leak stoppage experiments were very encouraging. For a non-wetting sub-
strate, the positive pressure required to start or stop a leak was simply the capillary
pressure, 2 σ/r, for small holes. For holes that were significantly larger than the fluid
depth, an even greater pressure was required to start a leak. The capillary pressure
was very large compared to the hydrostatic head and internal pressure that force
leaks. Therefore, choosing a non-wetting substrate would be a great advantage in an
ELFR. For a wetting substrate, the pressure required underneath the film was nearly
4 ANNALS NEW YORK ACADEMY OF SCIENCES
FIGURE 1. Fluid height profiles for liquid lithium (700K) flowing in the presence of
a fixed normal electric field. The field is taken to be Gaussian centered at 0, and the height
is calculated using the Reynolds lubrication model. Taken from Kim et al.,13 who provide
further details.
zero, implying that leaks could be stopped in an organic, as well as metal, based radi-
ator with wetting problems.
Gas phase breakdown can be avoided by going to lower pressures. On the low
pressure (P < 10−1mTorr) side of the Paschen curve, vacuum breakdown takes over
as the pressure is reduced. Fields on the order of (200kV/cm) can be exerted in this
region, making the Taylor cone threshold (8 to 70kV/cm) the limiting factor on the
electric field. From these experiments, we were able to impose additional constraints
on the previous design work, specify new design parameters, and calculate new esti-
mates of weight/power.
PREVIOUS WORK
Kim et al.13 numerically investigated the effect of a fixed electric field or pressure
profile on a fluid flowing down an inclined plane. Using lubrication and Kármán-
Pohlhausen models, as well as a Navier-Stokes solver, they showed steady-states
with a depression in the fluid interface underneath the leading edge of the electrode
and a peak in the interface underneath the trailing edge. The unsteady solutions
exhibited the formation of a traveling wave that washed away downstream. This
work neglected surface tension, as well as the coupling of the electric field with
the fluid interface, thereby precluding the formation of short wave instabilities.
BANKOFF et al.: ELECTROSTATIC LIQUID FILM RADIATOR 5
When fully developed, these are similar to the well-known Taylor cones that have
been observed on a horizontal plate and droplets. Infinite height values were
observed under the trailing edge of a finite electrode as the field was increased. How-
ever, the fields required for this behavior were significantly greater than that
measured experimentally.
Kim et al.14,15 and Bankoff et al.2 also investigated other geometries that are
more applicable to an ELFR. A spinning conical design, in which the coolant flowed
from the apex of a cone to the wide end, had a fluid height solution that typically
thinned as the fluid moved along the radiator wall. The magnitude of the depth
change depended on the cone angle and the rotation rate. A stationary cylindrical
design, in which the fluid thickened as it moved tangentially along the radiator wall,
was also studied. In both cases, the effect of the field on the interface was qualita-
tively the same as that for flow down an inclined plane.
CURRENT WORK
In the current work, we compared the height and pressure calculations of Kim et
al.13 to coupled solutions of the fluid and electric field equations and experimentally
demonstrated the feasibility of the ELFR by using the electric field to stop a leak. We
used diffusion pump oil to simulate the low temperature design and mercury to sim-
ulate the high temperature design. The oil flowed down an inclined plate, passing in
front of a glass electrode, which allowed the quantified fluorescence imaging
method27 to be used for local film thickness measurements. Pressure and stability
measurements were made with ethanol and diffusion pump oil, and stability mea-
surements were made with flowing mercury films. The low temperature design could
be used for electronics and habitat cooling. The high temperature design for power
generation, which incorporates lithium, appears to be quite robust but may present
handling problems.
Taylor cones pose a potential problem in a radiator. Taylor and McEwan23
showed that the stability of a horizontal layer of fluid under an electrode could be
calculated with linear stability theory. When the potential is increased beyond a crit-
ical value, the fluid forms waves that develop into a cone and emit a jet of fluid. Each
cone shorts the electrode requiring it to be recharged. Fluid would possibly leak dur-
ing the recharge time, which is determined by the power (or weight) of the recharg-
ing device. The energy produced during the short could cause irreversible damage to
the electrode as material evaporates. This was observed in a tin-oxide coated glass
electrode in our laboratory. The liquid film could also ionize, enhancing corrosion
chemistry or carbonization.
Taylor cones were investigated on a horizontal non-moving layer and on an
inclined flowing film (see FIGURES 2 and 3). In both cases, we used a finite electrode
to determine edge effects. In the horizontal case and small electrode heights, the
cones preferentially formed under the corner of the electrode. This edge effect was
previously noted by Taylor and McEwan.23 We found that the critical potential for
cone formation was not significantly altered and that the stability results can be pre-
dicted well using the linear analysis. Non-linear stability checks with the lubrication
theory also proved to be effective in predicting cone formation.
6 ANNALS NEW YORK ACADEMY OF SCIENCES
FIGURE 2. Experimental values of the critical field are compared to linear stability
predictions for a finite rectangular electrode held above a horizontal mercury film. H′ is
the height of the electrode above the static film height under the electrode corner.
FIGURE 3. Experimental values of the critical field for a flowing mercury film pass-
ing in front of a charged electrode. The data series are for various electrode lengths in the
direction of flow. The critical field is not strongly dependent on the length above 3cm. The
decrease in critical field with increasing Reynolds number (Re) is thought to be due to sur-
face waves.
BANKOFF et al.: ELECTROSTATIC LIQUID FILM RADIATOR 7
Taylor cones were observed on a vertical oil film when the electric field exceeded
a critical value, E ≈ 13kV/cm. Below this value, the height profile showed less than
1% variation along the direction of fluid flow, which was consistent with lubrication
theory. Liquid metals have much higher surface tension than oils. Lithium, which
was considered in Bankoff et al.,2 has a surface tension of 395dynes/cm at 700K
compared to about 30dynes/cm for oil. This allows for a much higher critical poten-
tial and a more robust design. A dimensional balance of the surface tension pressure
with the electric field pressure shows σ ≈ εε E2/2κ, where σ is the surface tension,
0
E is the electric field, ε is the dielectric constant, ε is the permittivity of free space,
0
and κ is the curvature of the conical interface. Neither theoretical work nor experi-
mental data giving Taylor cone thresholds on flowing films exist in the literature.
Therefore, we measured Taylor cone thresholds for flowing mercury. Stable films
were observed with fields of 55 to 90kV/cm, a factor of two higher than the square
root dependence predicted by the dimensional analysis. This is not surprising con-
sidering that the Reynolds number (Re) changed by a factor of 103, the Taylor cones
observed on the oil film were three-dimensional, and the wave number is likely to
vary. The relative stability of the liquid metal film to Taylor cones allows for a large
margin of error.
The following results support design feasibility.
• Fluid film profiles for flow under an electrode were calculated by Kim et al.
for a variety of design types and parameters.
• Film stability has been demonstrated at sufficient electric fields to stop leaks.
In our experiments, vertical flowing mercury films were stable to electric
fields of E > 50kV/cm, compared to 8kV/cm, used in previous design work.
(Values of the field listed in these works are higher due to an error in units.)
• Leaks have been started and stopped, even with the complication of Earth
gravity, for wetting and non-wetting substrates.
• Electrical breakdown in the vapor phase has been considered and can be
avoided without large increases in weight.
Before such a radiator is considered safe, further work should be done concerning
the nature of the leak holes, long-term chemistry of realistic materials, the effect of
reduced gravity, and electrical breakdown in a realistic design. However, it is thought
that these issues will affect design details rather than present significant problems.
Since liquid lithium is toxic, explosive in contact with water and flammable in
contact with air, the recommended experiments should be done in a properly
equipped facility with experienced operators.
ACKNOWLEDGMENTS
This work was supported by the Microgravity Division at NASA with Allen
Wilkinson as the program manager. Helpful comments were made by Professor M.J.
Miksis.
8 ANNALS NEW YORK ACADEMY OF SCIENCES
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