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CAPILLARY AND ELECTROMAGNETIC SMALLSAT
, E. Glenn Lightsey†
Low gravity ﬂuid management is key to a variety of spaceﬂight applications from life support
systems aboard the international space station to propellant management in satellite tanks.
Various methodologies have been developed to drive ﬂuids to their desired positions in a
microgravity environment, but these traditional strategies are not particularly well suited to
the needs of modern CubeSat propulsion systems, in part due to their conformal tank ge-
ometries and two-phase propellants. This is made clear in the high power and volumetrically
inefﬁcient propellant management devices that are relied upon in many cold gas propulsion
systems of a CubeSat form factor. In order to meet the stringent requirements of future small
satellite missions, a new generation of propellant management devices must be developed.
This paper focuses on the application of capillary and electromagnetic ﬂuid management
devices to the case of a small satellite propellant tank. Magnetic positive positioning, di-
electrophoretic, and capillary propellant management systems are considered alone and in
combination with an applied thermal gradient. Each concept is evaluated based on its per-
formance in reorienting the propellant and maintaining propellant position during operation,
as well as its size, weight, and power. Ultimately, the systems deemed to be best suited to
this use case are dielectrophoretic devices and combined magnetic positive positioning and
thermal architectures. These new systems could offer a novel and robust solution to small
satellite propellant management, a key enabling technology for the future of maneuverable
CubeSats are increasingly popular due to their low cost and growing capability, with their numbers grow-
ing from a dozen satellites launched in 2011 to nearly 300 in 2017 alone.1These small satellites utilize a
standardized form factor developed by California Polytechnic State University in the late 1990s. They consist
of 10 cm cubes (1U) and commonly appear in 1, 3, and 6U conﬁgurations. Due to their small size, CubeSats
have traditionally been relegated to simple educational missions; however, this has begun to change. In recent
years, there has been increased interest in formation ﬂight missions utilizing multiple small satellites.2, 3 This
enables the execution of complex tasks, but it also requires a more sophisticated satellite. Each spacecraft
is required to have an onboard propulsion system in order to maintain the formation. CubeSat propulsion
systems are a relatively recent technology, and as such, they still face a variety of challenges, not the least of
which is propellant management.
In the absence of gravity-induced buoyancy forces, the management of a ﬂuid becomes a primary technical
challenge. Deliberate methods must be used to ensure that this liquid-gas separation is properly achieved. A
common solution employed in traditional axisymmetric propellant tanks is to use surface-tension-based pro-
pellant management devices (PMDs), which are able to passively position the propellant within the tank.4–6
These devices are well-suited to traditional spherical and cylindrical tank geometries. However, due to the
*Graduate Research Assistant, Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, 620 Cherry Street
NW, Atlanta, GA 30332-0150, United States of America. Contact: email@example.com
†David Lewis Professor of Space Systems Technology, Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of
Technology, 620 Cherry Street NW, Atlanta, GA 30332-0150, United States of America. Contact: firstname.lastname@example.org
‡Assistant Professor, Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, 620 Cherry Street NW,
Atlanta, GA 30332-0150, United States of America. Contact: email@example.com
small form factor of CubeSats and other small satellites, a traditional axisymmetric tank geometry is not
always possible. In many cases, propellant tanks must be designed to conform to the available geometries
within a small satellite. This often results in unusually shaped propellant tanks that produce complex capillary
A further complication to cold gas CubeSat propulsion systems in particular is that these systems often use
a two-phase propellant stored as a saturated mixture.7, 10–13 When these propellants are drawn from their tank,
the remaining liquid begins to vaporize until the equilibrium pressure is reached. This vaporization occurs
throughout the propellant tank and further complicates the separation of the two phases by generating multiple
small-diameter gas bubbles. Capillary PMDs are generally designed to position a single vapor bubble, and
driving multiple small-diameter bubbles imposes signiﬁcant design challenges.4Capillary devices operate on
the principle of capillary forces, and these forces are only realized at an interface between the vapor bubble,
the liquid, and the device. In order for this device to drive the position of small-diameter bubbles, it must be
designed to leave no space larger than the diameter of the bubble in any section of the tank intended to be
occupied by liquid propellant. This results in a large and massive propellant management system.
In light of the challenges associated with the use of surface-tension-based PMDs, alternate methods are
employed in current cold gas propulsion systems using two-phase propellants.7,9, 11, 12 These devices rely
on a two-tank system to separate the liquid and vapor phases of the working ﬂuid. A main tank is used to
store the majority of the propellant as a saturated liquid-vapor mixture, while a plenum is used to store a
smaller volume of gas. Vapor is drawn from the plenum for thruster actuation. As the pressure in the plenum
decreases, it must be replenished from the main tank. The exact mechanism that allows the plenum to be
replenished varies between manufacturers. Some use just a solenoid valve, while others use a ﬂow control
valve along with a heat exchanger to ensure liquid propellant is vaporized en route to the plenum.7, 10–12 The
latter system is able to reﬁll the plenum more quickly and can allow for continuous operation at the expense
of increased power usage and complexity. The former requires the propulsion system to cease ﬁring when
reﬁlling the plenum to ensure that all liquid propellant in the plenum is vaporized prior to resuming thruster
actuation.14 Regardless of the plenum reﬁll mechanism, the two-tank system is inherently volumetrically
inefﬁcient. The propellant can be efﬁciently stored as a liquid, and any volume devoted to the storage of a gas
reduces the overall propellant mass that can be contained within a given volume. In addition, these propellant
management systems have been known to fail, allowing liquid to exist within the plenum and leading to
unpredictable performance.15 The high volume and power requirements of these devices coupled with their
lack of reliability drive the search for an improved propellant management architecture.
A propellant management concept recently proposed for application to CubeSats is the use of electro-
magnetic forces to position ﬂuids in microgravity.16 This methodology has already seen use in a variety of
contexts including electrolysis and phase separation.17,18 This concept does not depend upon gas bubbles
being large and continuous because it relies upon a volume force rather than surface tension. Additionally, it
may be better suited to nontraditional tank geometries which can constrain the use of surface-tension-based
devices. There are two primary ﬂuid management strategies of interest that employ electromagnetic forces,
magnetic positive positioning (MPP) and dielectrophoresis (DEP), both of which will be explored in this
MPP uses magnetic ﬁelds to attract or repel diamagnetic, paramagnetic, and ferromagnetic ﬂuids. The
force applied to the liquid and gas phases of the ﬂuid is not identical, and therefore a magnetic buoyancy
force is imparted, which results in phase separation.18 MPP devices have existed as a concept since at least
1963, but they have not seen signiﬁcant use.19 This is partially due to the fact that they are difﬁcult to employ
in large propellant tanks because magnetic ﬁeld strength drops rapidly as distance from the source increases.
However, interest in the use of these systems has renewed with the availability of high-density neodymium
magnets and the increase in popularity of small-scale propulsion systems.16, 20
Dielectrophoresis is the phenomenon of dielectric ﬂuids being attracted to areas of high electric ﬁeld in-
tensity.21 The force exerted on the ﬂuid is proportional to its permittivity. The permittivities of the gas and
liquid phases of a ﬂuid are different, and therefore the dielectrophoretic forces are dissimilar. This results in a
dielectric bouyancy effect.22 DEP can be thought of as analogous to MPP, with the equations for their driving
Table 1. System-level properties.
Spacecraft Mass, Msc (kg) 12
Propellant Tank Volume (cm3) 3000
Operating Temperature Range (◦C) 0 - 50
Thrust, T(mN) 15 - 90
Speciﬁc Impulse, Isp (s) 42.9 - 46.7
Table 2. Propellant properties.
Saturation Pressure (kPa) 107 580
Liquid Saturation Density, ρl(kg/m3) 1442 1269
Gas Saturation Density, ρg(kg/m3) 7.54 39.0
Liquid Dynamic Viscosity, µ(Pa·s) 3.971e-4 2.102e-4
Surface Tension, σ(N/m) 0.0127 0.0067
Molar Mass (g/mol) 152
forces sharing nearly identical forms. The use of DEP in propellant management has been studied since the
1960s, but it has not become commonplace due to a number of factors related to safety and scalability.21, 23
In particular, the use of DEP systems in large volumes requires high voltage to increase the range of the DEP
force. The introduction of these high voltages poses a risk of electrical arcing which may damage the tank.
Because of their small size, CubeSat propellant tanks require a lower voltage to generatelarge electric ﬁeld
gradients and may be better suited to a DEP system.
This paper outlines the analytical and numerical analysis of capillary, dielectrophoretic, thermal, and mag-
netic positive positioning PMDs in a case study of a 3U propellant tank. First, the natural behavior of the
propellant in the absence of a PMD is discussed, followed by analyses of each of the previously mentioned
propellant management devices. Finally, a comparative assessment of these technologies is conducted. Each
technology is compared on the basis of size, weight, power, maturity, scalability, and manufacturability as
well as their expected performance in the initial reorientation of the propellant and the maintenance of the
propellant position during operation.
This paper will explore the application of a variety of propellant management methods to the speciﬁc
case of a 3U propellant tank containing R-236fa, a two-phase refrigerant stored as a saturated mixture. The
propellant tank is composed of three 1U cubes in an L-shaped conﬁguration, as shown in Fig. 1. This study is
conducted under the assumption that the thruster performance will be comparable to that of the BioSentinel
CubeSat propulsion system, which used R-236fa as a propellant and was previously developed by the Georgia
Tech Space Systems Design Lab (SSDL).9The propulsion system is assumed to operate between 0◦C and
50◦C, with performance dependent on the operating temperature. Additionally, it is assumed that the thruster
will have a single nozzle. The propulsion system is assumed to operate onboard a 6U CubeSat with a mass
of 12 kg. The relevant characteristics of the spacecraft and the propellant are summarized in Tables 1 and 2,
NATURAL LIQUID BEHAVIOR
In a microgravity environment and without the presence of any other perturbing forces, the ﬂuid geometry
within a propellant tank is governed by wettability. Analytical methods for determining the equilibrium,
stability, and dynamic response of liquid interfaces exist for axisymmetric tank geometries.24 However,
CubeSat propulsion systems do not generally have geometrically simple propellant tanks. In these cases, the
propellant position can only be determined experimentally or computationally.
Figure 1. Propellant tank geometry with nozzle positioned on the bottom of the tank
and propellant tank outlet located at top of tank.
(a) 10% Fill Fraction (b) 30% Fill Fraction (c) 50% Fill Fraction (d) 70% Fill Fraction
Figure 2. Simulated vapor bubble geometry in microgravity without propellant management.
The Surface Evolver - Fluid Interface Tool (SE-FIT) allows for the minimum energy ﬂuid surface to be
computed.25 This tool is freely available and builds upon the Surface Evolver program pioneered by Professor
Ken Brakke.26 Using this software package, the minimum energy ﬂuid geometry is computed for a variety
of ﬂuid ﬁll fractions assuming a perfectly wetting propellant with a zero-degree contact angle. All other
propellant properties are those of R-236fa and are documented in Table 2. This simulation operates by
minimizing the energy of the ﬂuid surface, and any perturbing forces are ignored. SE-FIT includes a built-in
convergence algorithm primarily relying upon the conjugate gradient method, which reﬁnes and grooms the
mesh until a user-deﬁned improvement tolerance is met. Additional, minor perturbations are applied to the
surface to ensure that a stable solution has been reached. The results of these simulations are shown in Fig.
In the absence of any external forces, the gas bubble positions itself in the center of the tank so long as
there is an energy gradient to drive it there. This is expected given the nature of the tank geometry. The
center of the tank allows the bubble to reach the nearest approximation to a sphere for the majority of ﬁll
ratios, and a sphere having the minimum surface area for a given bubble volume results in it providing the
minimum energy solution.24 When the gas bubble is sufﬁciently small such that it can potentially form a
(a) 10% Fill Fraction (b) 30% Fill Fraction (c) 50% Fill Fraction (d) 70% Fill Fraction
Figure 3. Simulated vapor bubble geometry during actuation without propellant management.
sphere in multiple positions in the propellant tank, any one of those solutions is equally likely. This is the
case when the gas bubble occupies a volume of less than 523 cm3. While this holds when there are no
perturbing accelerations, it ceases to apply during thruster actuation.
In order to simulate the position of the gas bubble when the propulsion system is actuated, it is assumed
that a thrust of 15 mN is imparted, which is comparable to the performance expected from the 3D-printed cold
gas propulsion systems designed by the SSDL.27 In this case, SE-FIT is used to minimize the total energy
of the system accounting for both surface tension and the acceleration of the spacecraft. The results of these
simulation are shown in Fig. 3. Under these conditions, with a Bond number of 1.7, the bubble position is
no longer determined purely by wettability. Instead, the bubble position is now largely governed by the 1.25
mm/s2acceleration of the spacecraft, a=msc/T , and it will reside near the top of the tank. The gas bubble
will not reach the middle of the tank where it previously resided until the liquid propellant ﬁll ratio decreases
to less than 60%.
This presents a problem. In order for the propulsion system to properly function, it must draw a single-
phase gas from the propellant tank, but the position of the gas varies depending on whether the propulsion
system is currently ﬁring. Additionally, it will take a ﬁnite time for the gas bubble to reach equilibrium as it
transitions between these two states. A method of actively positioning the bubble over the propellant outlet
will be required for this system to operate nominally. The logical positions for the outlet to be placed are near
the center of the tank, where the propellant bubble naturally exists in the absence of perturbations, or near
the top of the tank, where the bubble naturally resides during thruster actuation. The top of the tank is chosen
to avoid competition between the propellant management device and the forces experienced during thruster
actuation. The methods used to maintain the vapor bubble over this chosen position are described throughout
the remainder of this paper.
Ullage Volume Analysis
In order to ensure that a single-phase gas can be reliably extracted from the propellant tank, the gas bubble
must be actively positioned near the exit. Before a propellant management device can be designed to perform
this function, the minimum required tank ullage must ﬁrst be calculated. As gas is extracted from the ullage
bubble, liquid propellant will begin to vaporize since the propellant is stored as a saturated mixture. Small
bubbles will nucleate on the walls and grow until they reach a critical diameter, at which they will detach and
begin to rise toward the top of the tank. The formation and rise of the bubbles will take a ﬁnite amount of
time, during which the liquid level in the tank will rise as the bubbles displace the liquid. When the bubbles
begin reaching the top of the tank, a pseudo-equilibrium liquid level will be reached. It is critical that this
liquid level be low enough so that no liquid will be extracted from the tank. This is ensured by establishing a
minimum required amount of ullage volume.
To calculate the required ullage in the tank, the rate at which gas is extracted is ﬁrst determined by calcu-
lating the mass ﬂow rate of propellant out of the thruster nozzle
where speciﬁc impulse, Isp, and thrust, T, are analytically determined. With the mass ﬂow rate known, the
volumetric ﬂow rate of gas from the tank is then
with ρgbeing the saturation density of the gas in the propellant tank. Gas is produced through vaporization
to compensate for the outﬂow of propellant gas from the tank. Additionally, as the mass of propellant in the
tank decreases, the volume of liquid in the tank decreases, and inversely, the total volume of vapor in the tank
increases. The rate at which gas is generated in the propellant tank to account for these combined effects
when ﬁring can then be shown to be
where ρlis the liquid saturation density. In order to determine the amount of ullage needed, the rate at which
bubbles rise to the surface of the tank must be calculated. To perform this calculation, the bubble detachment
diameter can, in ﬁrst-order approximation, be estimated based on Fritz’s equation28
with θbeing the contact angle, σbeing surface tension, and a=T /msc being the acceleration of the
spacecraft. The contact angle is arbitrarily assumed to be 20◦for these calculations as measured values are
not readily available.
The terminal velocity of the bubble can be found using a balance of forces between drag, buoyancy, and
where utis the terminal (or steady-state) bubble velocity, and the drag coefﬁcient, Cd, is calculated as29
log Cd= 1.6435 −1.1242 log Re+ 0.1558(log Re)2,(6)
with µlbeing the dynamic viscosity of the liquid. This calculation assumes that the bubbles will act as
rigid spheres and the Reynolds number, Re, will remain in the range of 260 to 1500, which it will under the
previously mentioned assumptions. These assumptions hold in the presence of impurities in the propellant.30
The necessary ullage volume in the tank can be determined by
where hrepresents the height of the tank. This calculation assumes a worst-case scenario where all bubbles
are generated at the bottom of the tank and move vertically upward to the top of the tank unaffected by any
forces aside from drag and buoyancy.
In order to ensure proper operation, a margin of 50% is applied to the calculated minimum ullage vol-
ume. This calculation is repeated across the expected operating temperature range of the propulsion system.
0 10 20 30 40 50
(a) Maximum stored propellant mass
Minimum required ullage
0 10 20 30 40 50
(b) Ullage volume where the calculated ullage is the volume of
vapor that will exist in a tank containing 3677 grams of propellant
Figure 4. Analysis of ullage bubble volume and propellant storage potential.31
Because the propellant is stored as a saturated mixture, the pressure in the tank varies signiﬁcantly with
temperature. The maximum mass of propellant that can be stored in the propellant tank is determined by
with Vtbeing the propellant tank volume. Maximum propellant storage mass and minimum required ullage
volume are shown in Fig. 4. As shown in Fig. 4(a), the propulsion system can only contain 3677 grams of
propellant at the worst-case operating temperature. This is the maximum mass that can be loaded into the
propellant tank before ﬂight to ensure that the minimum required ullage volume is maintained. When this
mass of propellant is loaded into the propellant tank, the system will have a minimum ullage volume of 106
cm3at 50 ◦C. At any temperature below 50 ◦C, the ullage volume will be larger than this and will always
exceed the minimum required ullage volume, as illustrated in Fig. 4(b), where calculated ullage volume is
determined by solving for Vuin Eq. 9, with mpbeing 3677 grams.
CAPILLARY PROPELLANT MANAGEMENT DEVICES
Capillary Propellant Management Device Alone
Propellant management devices are designed to maintain the propellant vapor bubble in a constant position
over the outlet of the tank in all operating regimes. The chosen position is located at the top of the tank
as shown in Fig. 1. The outlet from the tank is located such that the acceleration imparted during thruster
ﬁrings will position the vapor bubble over it. The propellant management device is then entirely responsible
for maintaining the position of the vapor bubble between ﬁrings. It is also required to keep the vapor bubble
centered at the top of the propellant tank during thruster actuation.
While most propellant management devices are designed to ensure that a liquid propellant is consistently
positioned over the outlet to a tank, this device will be required to maintain the position of a gas. In many
ways, this can be more challenging, as it is effectively a task of ensuring that every part of the propellant tank
is more attractive to a liquid than the outlet, though this is not an entirely new problem. The Viking orbiter
housed an axisymmetric propellant tank with a capillary PMD intended to position a bubble over the vent
port.32 A conformal tank geometry prevents this design from being applied directly to the use case discussed
in this paper. However, the fundamental concepts employed in this design are an active area of research in
CubeSat propellant management, with devices such as vanes being a primary interest.5,8 Another signiﬁcant
issue is that the system developed for the Viking orbiter was also not designed for a saturated mixture, but
rather a liquid with a separate gaseous pressurant. For these reasons, a capillary PMD similar to the one used
on the Viking orbiter will not be effective in this use case. In fact, it is unlikely that any capillary PMD on
its own will be capable of positioning the propellant. The root causes of this are distributed vapor bubbles
(a) Capillary PMD system concept with heater shown
in red, simpliﬁed capillary PMD in yellow, liquid pro-
pellant in blue, and vapor in gray.
(b) Results of SE-FIT model of simpli-
ﬁed capillary propellant management de-
vice for use with heater and 106 cm3va-
Figure 5. Capillary PMD with heater.
and sharp-edged conformal geometries. Vapor bubble distribution is caused by propellant vaporization along
the walls as the thruster actuates. It is also contributed to by the vaporization and condensation of propellant
on hot and cold walls respectively. Both of these phenomena will result in many small vapor bubbles being
generated throughout the propellant volume. These bubbles are not easily positioned by capillary forces due
to their small diameter.4
The conformal tank geometry poses an issue for the positioning of the vapor bubble because surface tension
drives liquids to position themselves in the corners of the propellant tank.8At high ﬁll fractions, it becomes
challenging to ensure that the liquid phase will not migrate from these corners to the propellant outlet. In
traditional spherical tank geometries, this is not a concern because the walls of the tank are rounded and
therefore unattractive to the liquid propellant. In such cases, a sponge-style device can be designed to collect
the liquid propellant effectively.4Conformal tank geometries are not afforded this luxury.
Capillary Propellant Management Device with Heater
The performance of capillary PMDs can be augmented by imposing a thermal gradient within the pro-
pellant tank. Such a gradient is easily be generated by placing a resistive heater near the exit of the tank.
Because R-236fa is stored as a two-phase ﬂuid, it vaporizes in the higher temperature section near the heater
and condenses in lower temperature regions of the propellant tank. This reorients the propellant within the
tank. It can also localize the majority of vaporization during thruster operation to the area near the heater. A
diagram of this system architecture is shown in Fig. 5(a).
A small thermal gradient alone is not capable of reorienting the propellant at high ﬁll fractions. This is
demonstrated in the NASA Tank Pressure Control Experiment.33 The movement caused by vaporization
disturbs the ﬂuid equilibrium, and capillary forces drive the propellant to coat the walls of the tank. By
implementing a capillary PMD in combination with the thermal gradient, the propellant is driven to condense
in the PMD and is then held there by capillary forces. This device also reduces ﬂuid circulation within
the tank. An additional beneﬁt of this system is that the capillary PMD is not required to drive gas toward
the propellant outlet, it simply has to retain the liquid propellant. Designing a PMD to achieve this task is
signiﬁcantly less challenging.
A simple propellant management device composed of six ﬂat panels is proposed. All panels leave a small
gap at the top of the tank. The two central panels have a curvature in their top face to encourage the propellant
vapor bubble to remain centered in the top of the tank. A simpliﬁed version of this device was modeled in
the SE-FIT software with a 106 cm3vapor bubble, and the results are shown in Fig. 5(b). The vapor bubble
reaches a minimum energy conﬁguration when positioned over the outlet of the tank, as intended. Note that
the capillary PMD is not designed to reorient the vapor bubble, but rather to maintain its position at the
top of the tank. The estimated volume of this device is 86 cm3with a wall thickness of 0.8 mm driven by
additive manufacturing constraints. A light weighting hole pattern is included in the design of this device but
is excluded from the SE-FIT model.
This system requires a power input to establish the thermal gradient and conduct initial positioning of the
propellant. The exact power input will vary based on the ﬁlling ratio of the tank, the conduction path between
the heater and the propellant, internal circulation of the ﬂuid, and other thermal characteristics of the system.
A ﬁrst-order analysis based upon the latent heat of vaporization of the propellant as well as the volume of the
ullage bubble calculated previously indicates that a minimum of 540 J will be required to establish an initial
reorientation of the propellant. Utilizing a 5 W heater, this can be accomplished in no less than 108 seconds.
When the propulsion system begins actuation, the acceleration of the spacecraft will drive the position of the
vapor bubble, and the heater can be deactivated, meaning that the system would not need to draw any power
after the initial reorientation of the propellant.
In some systems, it may be beneﬁcial to actively cool the end of the propellant tank opposite the outlet.
This can be done in combination with actively heating the area near the outlet if necessary. The thermal
gradient can also be imposed through clever positioning of the propellant tank relative to other components
within the spacecraft. If the propellant tank outlet is positioned near high power draw components or near the
sun-facing side of the spacecraft, this could prove to offer sufﬁcient heating.
Capillary propellant management devices are generally composed of thin metal structures within the pro-
pellant tank. These structures are designed to be as light and low volume as possible while still achieving
their intended purpose. However, these devices work by virtue of contacting the propellant, and increasing
their surface area will inherently increase their mass and volume. The capillary PMD designed for this use
case occupies a volume of 86 cm3and if composed of aluminum has a mass of approximately 232 grams.
The mass and volume of this device could be optimized further, but the design shown here is representative
of a traditional capillary PMD.
The capillary PMD does have the advantage of signiﬁcant design heritage, but despite this, it is not expected
to perform well in the initial reorientation or operational maintenance of the propellant vapor bubble. This is
due partially to the conformal shape of the propellant tank. The larger issue though is that this propellant is
stored as a saturated mixture. This means that even a mild thermal gradient in the propellant tank could cause
the propellant to vaporize in warm sections and condense in cool sections of the tank, thereby redistributing
the vapor bubble and likely resulting in the formation of many small bubbles. These small bubbles are not
easily positioned by a capillary device. A further complication to the design of a capillary device is the
requirement to extract a vapor from the tank, rather than a liquid. As a whole, a capillary PMD on its own is
not likely to perform well in this use case.
A system utilizing a resistive heater in combination with a capillary PMD will not see a signiﬁcant increase
in mass or volume, though it will require a power input. The addition of a heater will allow for a thermal
gradient to be applied within the propellant tank, and this can be designed to vaporize propellant near the
outlet of the tank while condensing propellant in the PMD. Signiﬁcant improvements are expected in both
initial reorientation of the propellant as well as maintenance of the vapor bubble position during operation as
a result of the applied thermal gradient.
(a) Without heater (b) With heater
Figure 6. MPP PMD concepts with magnet shown in black, heater in red, liquid
propellant in blue, and vapor in gray.
MAGNETIC PROPELLANT MANAGEMENT DEVICES
Magnetic Propellant Management Device Alone
The use of magnetic propellant management devices has existed as a concept for some time. Investigation
into their use dates back to at least 1963 when a patent was ﬁled for the use of suspended magnetic particles
in a propellant to allow it to be manipulated by magnetic ﬁelds.19 Further experiments on the topic were
conducted by NASA in parabolic ﬂights in the early 2000s.20 In recent years, magnetic positive positioning
(MPP) has seen a renewed interest.16,34 MPP relies on a magnetically induced buoyancy force to separate
liquid and gas phases of a ﬂuid.30 This buoyancy effect is the result of the liquid and gaseous phases of
the propellant having different magnetic susceptibilities and therefore experiencing differing forces. The
magnetic body force on a polarizable medium can be expressed as35
under the conditions that no electric current is passed through the medium and for low-susceptibility pro-
pellants, magnetic surface force terms can be neglected.36 From this expression, the total force on a small
spherical bubble can then be shown to be18
where Rbis bubble radius, ∆χvol =χvol
mis the difference in volume magnetic susceptibilities between
the bubble and the surrounding media, and H0is the applied magnetic ﬁeld. This force has been shown to be
capable of altering ﬂuid position in microgravity environments.30 For a diamagnetic propellant, a permanent
magnet of sufﬁcient strength placed near the outlet of the tank could prevent liquid from exiting the tank. A
diagram of this system concept is shown in Fig. 6(a).
An analysis was performed in COMSOL Multiphysics 6.0 to visualize the acceleration of liquid propellant
away from a permanent magnet. In an MPP PMD, this magnet would be concentric around the propellant
outlet inside of the tank. The magnet under consideration is composed of N52 neodymium with a diameter
of 25.4 mm, a height of 19.05 mm, and a mass of 72.4 grams. It is identical to the description of one shown
to be sufﬁcient to affect the position of gas bubbles in microgravity.30 Due to the unavailability of data on
the magnetic susceptibility of R-236fa, this simulation is conducted on liquid water. The results are shown in
(a) Magnetic ﬁeld (b) Liquid propellant acceleration ﬁeld
Figure 7. MPP simulation results for liquid water in proximity to an N52 neodymium magnet.
As these results indicate, the magnitude of acceleration decreases rapidly as the distance from the magnet
increases. If a mixture of liquid and vapor exists in close proximity to the magnet, propellant vapor will be
attracted, and the propulsion system will be able to extract vapor from the tank. However, if there exists
only liquid in proximity to the outlet, the range of the force may not be sufﬁcient to collect a vapor bubble.
Further analysis of the COMSOL Multiphysics simulation shown in Fig. 7 indicates that a 53 cm3spherical
air bubble positioned 4 cm directly above the base of the magnet will experience an attraction force of 0.11
mN. This force will be overcome should the system experience an acceleration greater than 2.1 mm/s2, with
this analysis based on the use of liquid water and air. This may be sufﬁcient in the lowest thrust cases for the
propulsion system under investigation, but it will not sufﬁce throughout the full operating range. It should be
noted that this analysis examines only the magnetic force and neglects the tendency of surface tension to pin
the vapor bubble to the magnet and resist disturbing accelerations.
One possible method to improve the operation of an MPP system is to use a ferromagnetic propellant.16
This can be accomplished through the suspension of ferromagnetic particles within the ﬂuid.19 The forces
on such a propellant are signiﬁcantly greater than those imparted on a diamagnetic or paramagnetic ﬂuid.
A system architecture based on the use of a ferromagnetic propellant involves placing permanent magnets
within the tank, opposite the outlet. The liquid is then attracted to these magnets, leaving the vapor bubble
positioned over the tank outlet. The feasibility of suspending magnetic particles within the R-236fa propellant
requires further investigation. There are also concerns related to the long-term stability of the ferromagnetic
particles within the propellant in the space environment.16
Another possible augmentation of an MPP system is the addition of a resistive heater. By imposing a ther-
mal gradient, as described in the previous section on capillary PMDs, along with an MPP device, a more ro-
bust propellant management system could be created. The thermal gradient could be capable of repositioning
the propellant through vaporization and condensation. The MPP device is then responsible for maintaining
the vapor bubble over the tank outlet during operations. This solution could mitigate issues associated with
the rapid decrease in magnetic ﬁeld intensity as distance from the source increases. It also reduces the risk of
expelling liquid droplets formed during the vaporization of the propellant. These droplets have been shown
to be common when heat is applied to refrigerants in a microgravity environment.20 Additionally, the magnet
will reduce foaming associated with vaporization of the propellant by encouraging the coalescence of vapor
bubbles.30 A diagram of this combined system is shown in Fig. 6(b).
The magnetic positive positioning system designed for this use case operates on a single N52 neodymium
magnet with a volume of 9.6 cm3and a mass of 72.4 grams. This system requires no power input and
no additional structure aside from mounting hardware for the magnet. Additionally, MPP systems have
Figure 8. DEP PMD concept with positively charged wires shown in red, negatively
charged wires in yellow, liquid propellant in blue, and vapor in gray.
been demonstrated in microgravity conditions.20 An MPP system is expected to perform poorly at initial
reorientation of the propellant due to the limited range of the device. However, once the vapor bubble is
positioned over the tank outlet, the MPP device is expected to perform adequately at the task of maintaining
the bubble position based on the previously described analyses.
An MPP system coupled with a resistive heater is expected to see improved performance in the task of
reorienting the propellant at the cost of an increased power input. In this coupled system, the initial reori-
entation of the propellant vapor bubble would be performed by the applied thermal gradient, and the force
imparted on the ﬂuid by the magnet would ensure that only a pure vapor exited the tank during operations.
This system is expected to outperform the capillary PMD and heater system during operations because the
force exerted on the liquid propellant by the MPP device is intended to reject any liquid droplets or foam.
DIELECTROPHORETIC PROPELLANT MANAGEMENT DEVICES
Dielectrophoretic propellant management devices operate by attracting ﬂuids to areas of higher electric
ﬁeld intensity. The force applied to the different phases of the ﬂuid is related to their permitivities. The
electric body force density acting on a ﬂuid can be expressed as37, 38
e= (P· ∇)E=ρfE−1
where Pis the polarization, Eis the elecric ﬁeld, and ρfis the free charge density. From this fundamental
force, it can be shown that the force on an insulative spherical bubble in an insulative ﬂuid medium can be
where ϵland ϵbare the permittivities of the medium and bubble respectively. This force is parallel to the
gradient of electric ﬁeld magnitude, and the direction is a function of the permittivity of the bubble and the
medium. It can then be shown that a gas bubble in a dielectric liquid will always be repelled from areas of
high electric ﬁeld magnitude by the gradient in electric ﬁeld strength.38
Previous dielectophoretic PMD designs intended for use in axisymmetric tanks have positioned concentric
rings of positively and negatively charge electrodes near propellant outlets in order to ensure liquid expul-
sion.21 However, the propulsion system under investigation will require the expulsion of a gas, not a liquid, so
a different strategy is implemented. One possible design conceived by Blackmon uses a series of wires strung
(a) Electric ﬁeld (b) Liquid propellant acceleration
Figure 9. DEP simulation results for R-236fa with 1 kV potential.
in parallel across the propellant tank, away from the propellant outlet.39 The wires alternately have high and
low potentials. The areas of high electric ﬁeld intensity attract the liquid propellant, and the propellant vapor
is driven to areas of lower ﬁeld intensity. By appropriately positioning the wires, this can be used to drive the
vapor towards the propellant outlet. A possible design for such a system is shown in Fig. 8.
A two-dimensional analysis of the previously described dielectrophoretic PMD design was performed in
COMSOL Multiphysics. The results of this analysis are shown in Fig. 9. In this ﬁgure, the blue dots represent
positively charged wires with a potential of 1 kV, and the green wires are grounded along with the casing.
In order to perform this simulation, the relative dielectric permittivity of the propellant was estimated
to be approximately 8. This approximation was made using the B´
aron and Buep equation along with the
correlations developed for HFC-236ea, a hexaﬂuoropropane similar to R-236fa.40 Liquid in proximity to
the wires in the DEP PMD experiences signiﬁcant accelerations. By positioning wires in the simulated
conﬁguration within a propellant tank, the liquid could be drawn away from the outlet. This methodology
could be used to ensure only vapor escapes from the tank. Additionally, the positioning of the wires as well
as their potentials can be adjusted to generate a variety of electric ﬁeld conﬁgurations. There is also the
possibility of actively changing the potential in individual wires during operation in order to adjust propellant
position. This could be used to actively change the center of mass of the spacecraft and thereby vary the
angular momentum imparted during maneuvers.
The mass and volume of the DEP PMD system are not easily analyzed without a detailed design. This is
due to variations in how the charged wires are afﬁxed within the propellant tank and the unknown mass of
the power management system. In this analysis, only the mass of the wires themselves will be considered.
Assuming that the wires span 2.5U of the 3U propellant tank and 28 gauge AWG wire is used, the volume
and mass of the DEP system are estimated to be no less than 0.3 cm3and 2.4 g respectively. Further analysis
is required to reﬁne the estimates of the true mass and volume of the system.
Despite the high potential difference required to operate this system, the power draw is minimal because
no current ﬂows between the wires. The exact power requirements of the system are dependent on the design
and require further analysis.
This system is expected to perform well at both initial reorientation of the propellant and maintenance of
Table 3. Comparative assessment of PMD concepts.
Characteristics Performance Efﬁcacy
Volume Mass Power Maturity Scalability Manufacturability Positioning Operation
Capillary High High N/A High High High Low Low
Capillary + Heater High High High Medium Medium High High Medium
MPP Low Medium N/A Medium Low High Low Medium
MPP + Heater Low Medium High Low Medium High High High
DEP Low Low Low Low Medium Low High High
the propellant vapor bubble during operation. This is because the magnitude of the acceleration imparted on
the ﬂuid is large and can be easily controlled with wire spacing and applied voltage. Additionally, the system
will be designed to interact with the entirety of the propellant tank. An additional beneﬁt of this system is
that it can be designed to increase the rate at which vapor bubbles detach and rise to the top of the tank during
thruster operation. This will decrease the required ullage volume for nominal operations. In spite of these
beneﬁts, DEP systems are technologically immature and will require signiﬁcant work to be brought to the
readiness level of systems such as MPP or capillary PMDs.
SUMMARY AND CONCLUSIONS
An ideal propellant management system used in a conformal CubeSat propellant tank containing a satu-
rated mixture of R-236fa would be small, lightweight, and require minimal if any power. It would also be
scalable and easily manufactured. The PMD should be capable of initial reorientation of the propellant such
that pure vapor is positioned over the propellant outlet, and it should be capable of maintaining the position
of the vapor bubble during operation of the thruster. Each of the PMDs described throughout this paper is
evaluated on these criteria, and the results are summarized in Table 3.
Analysis indicates that dielectrophoretic PMDs are a promising solution to the management of this pro-
pellant. A combination of a magnetic positive positioning system with a resistive heater also shows promise.
These systems represent a divergence from traditional capillary PMDs, and they are expected to be better
suited to this use case. As CubeSats continue to be employed on increasingly complex mission, systems such
as these will be necessary to meet their propulsion requirements.
This material is based upon work supported by the National Science Foundation Graduate Research Fel-
lowship under Grant No. DGE-2039655. The authors thank Prof. Steven Collicott for his guidance in the
operation of Surface Evolver.
 T. Villela, C. A. Costa, A. M. Brand˜
ao, F. T. Bueno, and R. Leonardi, “Towards the Thousandth CubeSat:
A Statistical Overview,” International Journal of Aerospace Engineering, Vol. 2019, Jan. 2019, pp. 1–
 R. Agarwal, B. Oh, D. Fitzpatrick, A. Buynovskiy, S. Lowe, C. Lisy, A. Kriezis, B. Lan, Z. Lee,
A. Thomas, B. Wallace, E. Costantino, G. Miner, J. Thayer, S. D’Amico, K. Lemmer, W. Lohmeyer, and
S. Palo, “Coordinating Development of the SWARM-EX CubeSat Swarm Across Multiple Institutions,”
Small Satellite Conference, Logan, UT, Aug. 2021.
 A. Koenig, S. D’Amico, and E. G. Lightsey, “Formation Flying Orbit and Control Concept for the
VISORS Mission,” AIAA Scitech 2021 Forum, Virtual Event, American Institute of Aeronautics and
Astronautics, Jan. 2021, 10.2514/6.2021-0423.
 D. Jaekle Jr., “Propellant management device conceptual design and analysis - Sponges,” 29th Joint
Propulsion Conference and Exhibit, Monterey, CA, June 1993, 10.2514/6.1993-1970.
 D. Jaekle, Jr., “Propellant management device conceptual design and analysis - Vanes,” 27th Joint
Propulsion Conference, Sacramento,CA,U.S.A., June 1991, 10.2514/6.1991-2172.
 D. Jaekle, r, “Propellant management device conceptual design and analysis - Traps and troughs,” 31st
Joint Propulsion Conference and Exhibit, San Diego,CA,U.S.A., July 1995, 10.2514/6.1995-2531.
 S. T. Hart, N. L. Daniel, M. C. Hartigan, and E. G. Lightsey, “Design of the 3-D Printed Cold Gas
Propulsion Systems for the VISORS Mission,” 2022 AAS GNC Conference, Breckenridge, CO, U.S.A.,
 S. H. Collicott, E. A. Beckman, and P. Srikanth, “Conformal Tanks: Small-Sat Propellant Management
Technology,” AIAA Propulsion and Energy 2019 Forum, Aug. 2019, 10.2514/6.2019-3874.
 T. Stevenson, E. Glenn Lightsey, and M. Sorgenfrei, “Development and Testing of a 3-D-Printed Cold
Gas Thruster for an Interplanetary CubeSat,” Proceedings of the IEEE, Vol. 106, Mar. 2018, pp. 379–
 T. Stevenson and G. Lightsey, “Design and Characterization of a 3D-Printed Attitude Control Thruster
for an Interplanetary 6U CubeSat,” Small Satellite Conference, Logan, UT, Aug. 2016.
 VACCO, “JPL MarCO - Micro CubeSat Propulsion System X14102000-01,” https://cubesat-
propulsion.com/wp-content/uploads/2015/11/X14102000-01˙2019update.pdf, Nov. 2022.
 N. Hejmanowski, C. Woodruff, R. Burton, D. Carroll, and A. Palla, “CubeSat High Impulse Propulsion
System (CHIPS) Design and Performance,” 63rd JANNAF Propulsion Meeting, Pheonix, AZ, Dec.
 D. Hinkley, “A Novel Cold Gas Propulsion System for Nanosatellites and Picosatellites,” Small Satellite
Conference, Logan, UT, Aug. 2008.
 S. T. Hart and E. G. Lightsey, “Improvements on Two-Phase Cold Gas Propulsion Systems for Small
Spacecraft,” Breckenridge, CO, Feb. 2023.
 D. Sternberg, J. Essmiller, C. Colley, A. Klesh, and J. Krajewski, “Attitude Control System for the Mars
Cube One Spacecraft,” 2019 IEEE Aerospace Conference, Mar. 2019, pp. 1–10. ISSN: 1095-323X,
 A. Romero-Calvo, F. Maggi, and H. Schaub, “Magnetic Positive Positioning: Toward the application in
space propulsion,” Acta Astronautica, Vol. 187, 2021, pp. 348–361, 10.1016/j.actaastro.2021.06.045.
 E. Scarl and J. Houston, “Two-phase magnetic ﬂuid manipulation in microgravity environments,”
Proceedings of the 37th Aerospace Sciences Meeting and Exhibit, 1999, pp. 1–5, 10.2514/6.1999-844.
 A. Romero-Calvo, G. Cano-G ´
omez, and H. Schaub, “Diamagnetically Enhanced Electrolysis and
Phase Separation in Low Gravity,” AIAA Journal of Spacecraft and Rockets, 2021, pp. 1–13,
 S. Papell, “Low viscosity magnetic ﬂuid obtained by the colloidal suspension of magnetic particles,”
1963. US Patent 3215572.
 J. Martin and J. Holt, “Magnetically Actuated Propellant Orientation Experiment, Controlling ﬂuid
Motion With Magnetic Fields in a Low-Gravity Environment,” Tech. Rep. TM-2000-210129, NASA,
 D. Chipchark, “Development of expulsion and orientation systems for advanced liquid rocket propulsion
systems,” Tech. Rep. RTD-TDR-63-1048, Contract AF04 (611)-8200, USAF, 1963.
 M. R. Pearson and J. Seyed-Yagoobi, “Numerical sturdy of dielectric ﬂuid bubble behavior within di-
verging external electric ﬁelds,” Journal of Heat Transfer, Vol. 130, 2008, 10.1115/1.2804937.
 J. R. Melcher, M. Hurwitz, and R. G. Fax, “Dielectrophoretic liquid expulsion,” Journal of Spacecraft
and Rockets, Vol. 6, 1969, pp. 961–967, 10.2514/3.29740.
 A. Myshkis and R. Wadhwa, Low-gravity ﬂuid mechanics: mathematical theory of capillary
phenomena. Springer, 1987.
 Y. Chen, B. Schaffer, M. Weislogel, and G. Zimmerli, “Introducing SE-FIT: Surface Evolver - Fluid
Interface Tool for Studying Capillary Surfaces,” 49th AIAA Aerospace Sciences Meeting including
the New Horizons Forum and Aerospace Exposition, Aerospace Sciences Meetings, Jan. 2011,
 K. A. Brakke, “The surface evolver,” Experimental Mathematics, Vol. 1, Jan. 1992, pp. 141–165.
 T. Stevenson, Development of Multi-Functional Structures for Small Satellites. PhD thesis, Georgia
Institute of Technology, Dec. 2018.
 K. Stephan, Physical Fundamentals of Vapor Bubble Formation, pp. 126–139. 1992, 10.1007/978-3-
 R. Clift, J. Grace, and M. Weber, Bubbles, Drops, and Particles. Dover Civil and Mechanical Engineer-
ing Series, Dover Publications, 2005.
A. Romero-Calvo, ¨
O. Akay, H. Schaub, and K. Brinkert, “Magnetic phase separation in microgravity,”
npj Microgravity 2022, Vol. 8, No. 1, 2022, 10.1038/s41526-022-00212-9.
 I. H. Bell, J. Wronski, S. Quoilin, and V. Lemort, “Pure and Pseudo-pure Fluid Thermophysical Property
Evaluation and the Open-Source Thermophysical Property Library CoolProp,” Industrial & Engineering
Chemistry Research, Vol. 53, Jan 2014, pp. 2498–2508, 10.1021/ie4033999.
 M. W. Dowdy and S. C. Debrock, “Selection of a Surface-Tension Propellant Management System
for the Viking 75 Orbiter,” Journal of Spacecraft and Rockets, Vol. 10, Sept. 1973, pp. 549–558,
 M. M. Hasan, C. S. Lin, R. H. Knoll, and M. D. Bentz, “Tank Pressure Control Experiment: Thermal
Phenomena in Microgravity,” Mar. 1996. NTRS Author Afﬁliations: NASA Lewis Research Center,
Analex Corp., Boeing Defense and Space Group NTRS Report/Patent Number: NAS 1.60:3564 NTRS
Document ID: 19960017263 NTRS Research Center: Legacy CDMS (CDMS).
 Romero-Calvo, V. Urbansky, V. Yudintsev, H. Schaub, and V. Trushlyakov, “Novel propellant set-
tling strategies for liquid rocket engine restart in microgravity,” Acta Astronautica, Vol. 202, Jan 2023,
pp. 214–228, 10.1016/j.actaastro.2022.10.012.
 A. Romero-Calvo, G. Cano-G´
omez, E. Castro-Hern´
andez, M. A. Herrada-Guti´
errez, and F. Maggi,
“Magnetic Sloshing Damping in Microgravity,” 8th Interplanetary CubeSat Workshop, Milan, Italy,
 A. Romero-Calvo, G. Cano-G ´
omez, T. H. Hermans, L. Parrilla Ben´
ıtez, M. Herrada, and E. Castro-
andez, “Total magnetic force on a ferroﬂuid droplet in microgravity,” Experimental Thermal and
Fluid Science, Vol. 117, 2020, p. 110124, 10.1016/j.expthermﬂusci.2020.110124.
 J. Melcher, Continuum Electromechanics. MIT Press, 1981.
 T. B. Jones and G. W. Bliss, “Bubble dielectrophoresis,” Journal of Applied Physics, Vol. 48, 1977,
pp. 1412–1417, 10.1063/1.323806.
 J. B. Blackmon, “Collection of liquid propellants in zero gravity with electric ﬁelds,” Journal of
Spacecraft and Rockets, Vol. 2, 1965, pp. 391–398, 10.2514/3.28190.
 A. P. Ribeiro and C. A. N. D. Castro, “Dielectric properties of liquid refrigerants: Facts and trends,”
International Journal of Refrigeration, Vol. 34, Mar 2011, pp. 393–401, 10.1016/j.ijrefrig.2010.11.007.