StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity

Abstract

Liquid sloshing represents a major challenge for the design and operation of space vehicles. In low-gravity environments, a highly non-linear movement can be produced due to the lack of stabilizing forces. This gives rise to significant disturbances that impact on the propulsion and attitude control systems of the spacecraft. The employment of magnetically susceptible fluids may open an interesting avenue to address this problem, but their dynamics in low gravity remain practically unexplored. The UNOOSA DropTES StELIUM project aims at filling this gap by studying the lateral sloshing of a ferrofluid solution subjected to an inhomogeneous magnetic field in microgravity. This paper describes the design process, challenges and preliminary results of the experiment, which was successfully launched at ZARM's drop tower in November 2019. The outcomes will be employed to validate the quasi-analytical models developed by the authors and set the path for the design of magnetic propellant positioning devices in space.

Full text

StELIUM: A student experiment to investigate the sloshing of magnetic
liquids in microgravity
Á. Romero-Calvoa,b,∗,A. J. García-Salcedob,F. Garroneb,I. Rivoalenb,G. Cano-Gómezc,
E. Castro-Hernándezd,M. Á. Herrada Gutiérrezdand F. Maggib
aDepartment of Aerospace Engineering Sciences, University of Colorado Boulder, CO, United States
bSpace Propulsion Laboratory, Department of Aerospace Science and Technology, Politecnico di Milano, Via Giuseppe La Masa, 34, 20156, Milan, Italy
cDepartamento de Física Aplicada III, Universidad de Sevilla, Avenida de los Descubrimientos s/n, 41092, Sevilla, Spain
dDepartamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avenida de los Descubrimientos s/n, 41092, Sevilla, Spain
A R T I C L E I N F O
Keywords:
Magnetic liquid sloshing
Microgravity
Ferrofluids
Experiment design
ZARM’s drop tower
A B S T R A C T
Liquid sloshing represents a major challenge for the design and operation of space vehicles. In low-
gravity environments, a highly non-linear movement can be produced due to the lack of stabilizing
forces. This gives rise to significant disturbances that impact on the propulsion and attitude control
systems of the spacecraft. The employment of magnetically susceptible fluids may open an interest-
ing avenue to address this problem, but their dynamics in low gravity remain practically unexplored.
The UNOOSA DropTES StELIUM project aims at filling this gap by studying the lateral sloshing
of a ferrofluid solution subjected to an inhomogeneous magnetic field in microgravity. This paper
describes the design process, challenges and preliminary results of the experiment, which was suc-
cessfully launched at ZARM’s drop tower in November 2019. The outcomes will be employed to
validate the quasi-analytical models developed by the authors and set the path for the design of mag-
netic propellant positioning devices in space.
1. Introduction
The forced movement of liquids in partially filled tanks,
commonly named sloshing, has been an active field of re-
search for centuries. The first dynamic theory of tidal waves
is attributed to Laplace as early as in 1775 (1), and the non-
linear wave problem was solved by Stokes in 1847 (2). By
1895, when the classical Hydrodynamics by Lamb was first
published (3), there was already a solid heritage on the topic.
The fundamental aspects of normal-gravity sloshing can be
then considered to be well-established by the beginning of
the Space Era, in 1957.
Propellant sloshing represents a major concern for space
engineers (4). In extreme cases, like the Jupiter IRBM AM-
1B (1957), the test vehicle F1 (1964) or the SpaceX Falcon
1 Demo Flight 2 (2007) (5), it may lead to a partial or to-
tal mission failure. Low-gravity sloshing is characterized by
its highly stochastic and unpredictable dynamics, which re-
sult in a complicated propellant management system design
and a complex impact on the attitude control system of the
spacecraft. Moreover, propellant management devices in-
crease the inert mass of the vehicle and present long-term
reliability issues with cryogens (6;7).
The sloshing of liquids in low-gravity is driven by sur-
face tension and residual accelerations, that generate a curved
equilibrium free surface (or meniscus) and a non-trivial in-
teraction with the walls of the vessel (8). In the context of the
Space Race, considerable efforts were devoted to the theo-
retical and experimental study of low-gravity sloshing (8;9;
10;11;12;13). These early works generally assume small,
linear displacements around the equilibrium state. In most
∗alvaro.romerocalvo@colorado.edu
ORCID(s): 0000-0003-3369-8460 (Á. Romero-Calvo)
situations of interest for space applications, however, these
assumptions do not hold, and complex Computational Fluid
Dynamics (CFD) simulations become necessary (14;15). In
addition to their computational cost, numerical simulations
rely on a good estimation of the initial conditions and accu-
rate inertial measurements.
Different passive and active mitigation strategies have
been traditionally employed to minimize low-gravity slosh-
ing disturbances (6). An interesting alternative would be re-
producing the restoring force of gravity by means of elec-
tromagnetic fields if the liquid can answer to such stimulus.
That would transform a complex nonlinear sloshing prob-
lem into a linear, and hence easy to model, system. The use
of dielectrophoresis, a phenomenon on which a force is ex-
erted on dielectric materials in the presence of non-uniform
electric fields, was explored by the US Air Force with suit-
able propellants in 1963 (16). The study unveiled a high risk
of arcing inside the tanks and highlighted the need for large,
heavy and noisy power sources. The inherent magnetic prop-
erties of paramagnetic and diamagnetic liquids may also be
exploited in what is known as Magnetic Positive Positioning
(MP2) (17). Numerical simulations and microgravity exper-
iments have been presented to validate this concept (18;19).
The MP2concept must deal with the rapid decay of mag-
netic fields with distance, which limits its applicability to
relatively small regions. This difficulty may be faced by em-
ploying highly susceptible magnetic fluids. Ferrofluids, de-
fined as colloidal suspensions of magnetic nanoparticles in
a carrier liquid, belong to this category and were indeed in-
vented to enhance the susceptibility of rocket propellants in
1963 (20). However, contributions addressing their appli-
cation to the control of liquid sloshing are scarce. Normal-
gravity works have explored the natural frequency shifts due
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
Nomenclature
CCS Capsule Control System
CFD Computational Fluid Dynamics
DLR German Aerospace Center
DropTES Drop Tower Experiment Series
ELGRA European Low-Gravity Research Association
ESA European Space Agency
FEA Finite Element Analysis
FFT Fast Fourier Transform
GDS General Detection Subsystem
HL High Level
IAC International Astronautical Congress
ISS International Space Station
LED Light-Emitting Diode
MAPO Magnetically Actuated Propellant Orientation
MP2Magnetic Positive Positioning
NASA National Aeronautics and Space Administration
PDU Power Distribution Unit
PLA Polylactic Acid
SD Storage Device
SDS Sloshing Detection Subsystem
SPLab Space Propulsion Laboratory
StELIUM Sloshing of magnEtic LIqUids in Microgravity
ToF Time Of Flight
UNOOSA United Nations Office for Outer Space Affairs
ZARM Center of Applied Space Technology and Micro-
gravity
to the magnetic interaction (21), two-layer sloshing (22), ax-
isymmetric sloshing (23;24), the swirling phenomenon (25)
or the development of tuned magnetic liquid dampers (26;
27). The sloshing of ferrofluids in low-gravity was indirectly
studied in 1972 with a focus on gravity compensation (28).
In the mid 1990s, a series of parabolic flight experiments
with ferrofluids were performed to validate the magnetic po-
sitioning of liquid oxygen in the framework of the NASA
Magnetically Actuated Propellant Orientation (MAPO) ex-
periment (17). Subsequent publications present refined nu-
merical models for diamagnetic propellants (29;30;31). More
recently, the ESA Drop Your Thesis! 2017 experimental
campaign measured the axisymmetric sloshing of ferroflu-
ids when subjected to an inhomogeneous magnetic field in
microgravity (32;33;34). Quasi-analytical magnetic slosh-
ing models (35) and feasibility analyses (36) have also been
presented.
Based on the existing bibliography on the topic, the lat-
eral sloshing of magnetic liquids in microgravity can be re-
garded as an almost unexplored phenomenon with potential
applications in space. Those include passive MP2, active
MP2for center of mass positioning, and propellant sloshing
damping, among others (36). Defining characteristics, such
as the magnetic deformation of the meniscus or the shift of
natural sloshing frequencies and damping ratios, have to be
explored in relevant environments in order to improve our
physics understanding and modeling capabilities.
With the goal of addressing the previous questions, in
April 2019 the Sloshing of magnEtic LIqUids in Micrograv-
ity (StELIUM) experiment was selected by the United Na-
tions Office for Outer Space Affairs (UNOOSA) Drop Tower
Experiment Series (DropTES) programme to study the lat-
eral sloshing of magnetic liquids in microgravity. This paper
describes the project objectives (Sec. 2), selected micrograv-
ity facility (Sec. 3), experiment setup (Sec. 4), and prelim-
inary results of the campaign at the drop tower of the Cen-
ter of Applied Space Technology and Microgravity (ZARM)
(Sec. 5). The main conclusions and future work are described
in Sec. 6.
2. Experiment objectives
Experimental works on linear liquid sloshing have his-
torically focused on the measurement of oscillation frequen-
cies and modal shapes for different tank geometries and grav-
ity levels (4;6;8). As previously stated, the sloshing of
magnetic liquids in microgravity can be studied by assuming
small oscillations through modal analysis (35). The design
of StELIUM is consequently based on this methodology and
has the following objectives:
1. Obtain high-quality free surface measurements of the
lateral sloshing of a ferrofluid solution in microgravity
when subjected to an inhomogeneous magnetic field.
2. Measure natural frequencies, damping ratios, modal
shapes and meniscus profiles as a function of the ex-
ternal magnetic field.
3. Validate the inviscid quasi-analytical model developed
by the authors (35) and share results with the scientific
community.
4. Analyze the feasibility of magnetic sloshing damping
techniques for space applications and other scenarios
of interest in reduced-gravity environments.
The High-Level (HL) requirements of the experiment
arise from the previous and are listed in Tab. 1.
3. Microgravity facility
3.1. On-ground microgravity platforms
The term microgravity refers to the residual relative ac-
celeration between an observer and a target that fall simulta-
neously. In addition to on-orbit laboratories, such as the In-
ternational Space Station (ISS), various on-ground facilities
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
Table 1
High-level requirements of StELIUM
ID Requirement
HL-1 The lateral sloshing waves shall be excited in mi-
crogravity.
HL-2 The ferrofluid solution shall be subjected to a
static, controllable and inhomogeneous magnetic
field.
HL-3 The fundamental lateral sloshing frequency and
damping ratio shall be measured.
HL-4 The second lateral sloshing frequency and damping
ratio should be measured.
HL-5 The ferrofluid free surface shape shall be recon-
structed.
HL-6 The equilibrium surface shape (or meniscus) shall
be reconstructed.
HL-7 The experiment setup shall be monitored during
the drop.
HL-8 The experiment setup shall withstand at least four
catapult drops.
HL-9 The stability of the capsule shall be guaranteed.
HL-10 The experiment shall be integrated into the drop
tower capsule
can replicate this condition. Each of them provides different
gravity residuals 𝑔𝑟𝑒𝑠 and flight durations 𝑡𝜇𝑔, as summarized
in Tab. 2.
Low gravity sloshing has been studied by making use
of drop towers (37), parabolic flights (17), sounding rockets
(38), on-orbit facilities (15) or simulated low-gravity (9;28).
The excessive gravity residual discourages the employment
of parabolic flights, while on-orbit facilities are discarded
due to their high cost and limited access. Sounding rockets
offer several minutes of microgravity, but at a higher risk,
as there is only one opportunity to perform the experiment.
Thus, in order to obtain high-quality and repetitive measure-
ments, ZARM’s drop tower is selected to carry out the ex-
periment.
3.2. ZARM’s drop tower
With a 120 m high vacuum chamber, ZARM’s drop tower
is one of the largest on-ground microgravity facilities of its
class in the world. The tower can operate with drop and cata-
pult modes. In the first case, the capsule is released from the
top giving 4.74 s of microgravity conditions and experienc-
ing a deceleration of approximately 50 𝑔0at the end of the
flight. The catapult mode, available since 2007, launches the
capsule vertically from the bottom of the tower extending the
Table 2
Characteristics of most relevant microgravity facilities
Drop
tower
Parabolic
flight
Sounding
rocket
ISS
𝑡𝜇𝑔 4.5-9.3 s 20-25 s Minutes Months
𝑔𝑟𝑒𝑠 10−6 10−2 10−6 10−6
Frequency 2-4
drops/day
20-25
par/flight
1
exp/flight
-
Interaction No Yes No Yes
Cost Low Medium Medium High
x axis
y axis
z axis
Acceleration [g]
−5
0
5
10
15
20
25
30
35
40
45
50
t [s]
0 2.5 5 7.5 10
Figure 1: Acceleration profile of a catapult drop measured at
ZARM’s drop tower during the experiment campaign
flight duration to 9.3 seconds. The capsule and its enclosed
experiment experience an acceleration of up to 50 𝑔0before
the experiment begins, as shown in Fig. 1. Both modes are
characterized by highest-quality conditions of weightless-
ness of approximately 10−6𝑔0.
The catapult capsule allows a maximum payload weight
of 165 kg and a cylindrical payload volume with 600 mm di-
ameter and 953 mm height. The system is monitored by the
Capsule Control System (CCS), which is connected to the
external control room through radio telemetry and telecom-
mand to satisfy the HL-7 requirement. To ease integration,
the experimental setup is mounted on a standardized plat-
form. The capsule is carefully balanced before launch to
avoid undesired perturbations. A constant environmental
pressure level is kept during flight. Further specifications
can be found at ZARM’s Drop Tower User Manual (39).
Due to its extended low-gravity period, the catapult mode
is selected for StELIUM. The design of the experiment must
then consider an additional launch acceleration that induces
an initial axisymmetric oscillation in the ferrofluid surface
and imposes further restrictions to the structure.
4. Experiment setup
4.1. Historical review
Several drop tower experiments addressing low-gravity
liquid sloshing have been carried out in the past. A non-
extensive list may include the pioneering works by Satterlee
and Reynolds (8) or the later contributions by Salzman and
coworkers (37;40). In spite of its age, the layout of Salz-
man’s experiment setup is conceptually similar to StELIUM
and hence of particular relevance for this project. His ex-
periment used a DC engine to excite a test cylinder in mi-
crogravity (actuation system) illuminated by a diffuse back-
light while a high-speed camera recorded the evolution of the
surface (detection system). The experiment was mounted
on a series of platforms that supported and protected each
element (structure). In addition, this setup implemented a
thruster to produce a range of gravity levels. Since StELIUM
studies a prescribed range of magnetic field intensities, the
functionality of the thrust system is here undertaken by a set
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
Figure 2: experiment setup of the ESA Drop Your Thesis!
2017 experiment The Ferros. Fixed and mobile parts are re-
spectively labeled in blue and red. Adapted from (33).
of coils (magnetic system).
A second setup of reference, this time designed for a
parabolic flight, was used in the NASA MAPO experiment
(17). The purpose of the project was to address the feasi-
bility of magnetic propellant orientation devices and vali-
date a custom CFD model in microgravity. The authors de-
cided to employ a magnet whose magnetic field was mapped
before running the experiment. Various oil-based ferrofluid
solutions with different concentrations were then tested, but
tended to coat the walls of the Plexiglas containers hamper-
ing visualization. In contrast, StELIUM employs a single
ferrofluid solution under the action of a controllable mag-
netic field generated by a pair of coils. This choice reduces
the overall cost of the experiment and avoids the irregular-
ities in the magnetization field of most commercial magnets.
To mitigate the aforementioned coating problems, water-based
ferrofluids are employed together with an hydrophobic sur-
face treatment on the walls of the containers (Aquapel).
The experiment setup of StELIUM is an evolution of the
one employed at the ESA Drop Your Thesis! 2017 campaign
(33), represented in Fig. 2. The setup made use of two coils
in a quasi-Helmholtz configuration to generate the desired
magnetic field. The actuation was carried out by a stepper
engine controlled by an Arduino board. A pattern fringe re-
flectometry detection system was developed to measure the
sloshing frequencies. However, the free surface shape could
not be reconstructed due to the presence of strong light re-
flections (32). This experience has been considered for the
design of StELIUM.
4.2. Overall description
From the systems engineering viewpoint, the experiment
setup is subdivided into actuation, sloshing detection, mag-
netic, and structure subsystems. The actuation subsystem
imposes a single lateral oscillation with prescribed ampli-
Line laser
GoPro camera
ToF sensor
Laser pointer
Detection head
Ferrofluid container
Coil
Stepper engine
Brake
Linear slider
Platform
Support
Figure 3: Experiment setup of StELIUM. The labels are
grouped under the Sloshing Detection Subsystem (red), the
Magnetic Subsystem (green), the structure (yellow), and the
Actuation Subsystem (blue).
tude (𝐴) and frequency (𝜔) to a ferrofluid solution that par-
tially fills a cylindrical container. The response of the liq-
uid is measured by the Sloshing Detection Subsystem (SDS)
to extract relevant kinematic parameters. During this pro-
cess, the magnetic subsystem imposes a static, inhomoge-
neous magnetic field to the ferrofluid. Only the magnetic
field intensity and actuation frequency vary between drops
and, as described in Ref. (35), the sloshing frequencies vary
accordingly. The structural configuration of the system is
maintained throughout this process.
As shown in Fig. 3, the experiment setup is distributed
between two capsule platforms that hold identical assem-
blies. Each of them is composed of a Plexiglas container
surrounded by a magnetic coil which is fed by a constant
current power source. The container has a diameter of 11
cm, a height of 20 cm and is filled up to 5 cm with a 1:5
volume solution of the Ferrotec EMG-700 water-based fer-
rofluid. Both assemblies are simultaneously actuated by a
sliding mechanism that produces an oscillatory movement
with a prescribed amplitude and frequency. The SDSs are
located over each container and return a three dimensional
liquid surface profile from which relevant parameters are ex-
tracted. Arduino based electronics powered by on-board bat-
teries guarantee the autonomy of the system. The integrated
setup is shown in Fig. 4.
The total mass of the experiment, including the addi-
tional platform, is approximately 60 Kg. The experiment
setup fits into the available payload area with an overall vol-
ume of 930x530x295 mm3, satisfying the requirement HL-
10.
4.3. Drop tower plan
The experimental campaign at ZARM’s drop tower is
split into integration and experimentation weeks. The pur-
pose of the first is to install and extensively test each subsys-
tem to minimize the risk of failure during flight, given the
limited number of drop opportunities. The second week is
dedicated to performing the drops and running the experi-
ment itself.
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
Figure 4: Drop tower capsule of StELIUM after integration at
ZARM’s drop tower
Four catapult drops were scheduled for StELIUM, with
a rate of one per day. As explained in Sec. 4, the response of
the liquid is analyzed as a function of the magnetic field in-
tensity (or, equivalently, the coils current intensity 𝐼), which
changes between drops. The first of them has the purpose of
testing the performance of every subsystem and validating
the amplitude of the actuation, which must induce an observ-
able oscillation without reaching the non-linear regime. The
following configurations, including the non-magnetic case,
are shown in Tab. 3. During each flight, a single oscillation
is induced 3 seconds after launch, when the surface reaches
its equilibrium position. The frequency of such actuation is
set between the first and second modes, so both are excited
and measured by the SDSs.
4.4. Structure
The acceleration profile shown in Fig. 1represents a tech-
nical challenge from the structural viewpoint. Finite Ele-
Table 3
StELIUM test matrix
Drop 𝜔(rad/s) I(A)
1 6.5 20
2 3.3 10
3 3.3 0
4 5 15
ment Analyses (FEA) of critical structural parts become then
mandatory to satisfy the requirement HL-8. Although the
use of expendable components is extended in low-gravity re-
search, this option was not considered appropriate for StELIUM.
The most critical structural parts are (i) the vessels con-
taining the ferrofluid solution, and (ii) the sliding unions be-
tween the linear modules and the carriages that support the
experiment setup. In the case of the vessels, a structural fail-
ure would release the ferrofluid content and potentially harm
the electronics of the drop capsule. If the sliding unions
were harmed, the oscillation produced by the actuation sys-
tem would be much noisier.
A dynamic-implicit, two-dimensional, axisymmetric FEA
is carried out in ABAQUS to analyze the stress and deforma-
tion of the Plexiglas vessel when subjected to a time-varying
gravity load, as shown in Fig. 5. The mesh employs 2364
quadrilateral CAX4R elements with 1 mm edge length and
2683 nodes. A maximum Von Misses stress of 20 MPa is
predicted during the drop sequence, but the tensile strength
of Plexiglas is approximately 70 MPa. For safety reasons,
lateral rods are added to hold the upper structure and dis-
tribute the loads.
A similar analysis is used to verify the resistance of the
carriages with the simplified two-dimensional model depicted
in Fig. 6. The combined weight of the ferrofluid vessel,
magnetic coil, detection system, and platform is distributed
among eight cylindrical unions that interface the assembly
with the rails. Each union is composed of an inner plas-
tic bearing located inside an aluminum holder. The proper-
ties of the plastic ring are assumed to be similar to the Igus
Iglide J1, whose maximum recommended surface pressure
is 35 MPa. An encastre boundary condition is applied to the
upper face of the plastic ring to simulate the presence of the
rail. Quadrilateral (1542) and triangular (34) elements are
employed in the mesh. The maximum compression stress
suffered by the plastic ring is 8 MPa, while the aluminum
1https://www.igus.com/product/66. Consulted on: 30/01/2020
Figure 5: FEA model of the ferrofluid vessel. a) Geometry
(units in cm), b) Loads and boundary conditions, c) Mesh.
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
Figure 6: FEA model of the structural union. a) Geometry
(units in mm), b) Loads and boundary conditions, c) Mesh.
box is subjected to a maximum stress of 1.1 MPa. Those
values are far below the elastic limits of the materials. A
sufficiently large safety margin is then present for both el-
ements. However, important simplifying assumptions are
taken in this analysis (e.g. 2D modeling of a 3D structure,
that neglects 3D structural dynamics), and hence supports
are added to the platforms to distribute the impact load.
During the drop campaign, the structure withstood four
consecutive drops without apparent damages in either the
Plexiglas vessels or the structural unions.
4.5. Magnetic subsystem
The magnetic setup produces a steady inhomogeneous
magnetic field in the region where the ferrofluid is located,
fulfilling the requirement HL-2. Such field generates a restor-
ing force that keeps the liquid at the bottom of the container.
This contribution can be decomposed as the sum of a mag-
netic body-force density
𝐟𝑉=𝜇0𝑀∇𝐻, (1)
with 𝐇being the magnetic field and 𝐌the magnetization
field, and a surface-force density, also known as magnetic
normal traction,
𝐟𝑆=𝜇0
2𝑀2
𝑛𝐧,(2)
where 𝑀𝑛is the normal magnetization component at the
interface of the ferrofluid (34;41). It is important to note
that the volume component appears only when an inhomo-
geneous field 𝐇is considered, since it depends on the gra-
dient of 𝐻. Solutions with higher magnetic susceptibilities
exhibit a stronger response.
As shown in Fig. 3, the magnetic field is generated by
two circular coils located at the base of the vessels in a quasi-
Helmholtz configuration. The coils have a diameter of 94.25
mm, a width of 25 mm and are built with 200 windings
of a 1.8 mm copper wire. Their resistance increases dur-
ing operation due to the rapid increase in temperature. In
order to produce a static magnetic field, constant voltage
power sources or batteries should then be discarded. A JT-
DPM8600 constant current power source is employed in-
stead, achieving an excellent performance.
Table 4
Properties of the Ferrotec EMG-700 solution and the 1:5 vol
concentration solution at 25°C.
Property Ferrotec
EMG-700
1:5 Solution
Carrier liquid Water Water
Nature of surfactant Anionic Anionic
Nominal particle diameter (nm) 10 10
Saturation magnetization (kA/m) 25.86 4.16
Initial magnetic susceptibility 𝜒12.57 0.39
Viscosity (mPa.s) <5 1.448
Density (kg/m3) 1290 1058
Surface tension (mN/m) N/A 45.7
Concentration of particles (%) 5.8 1.16
The magnetic liquid is provided by Ferrotec Corporation
and consists on a 1:5 volume solution of the Ferrotec EMG-
7002water-based ferrofluid. As explained in Sec. 4.1, low-
viscosity water-based solutions are preferred over oil-based
to avoid the severe coating effects reported in previous exper-
iments (17). The properties of the original ferrofluid and the
1:5 volume solution are given in Tab. 4. The magnetization
curve depicted in Fig. 7was measured with a MicroSense
EZ-9 Vibrating Sample Magnetometer at the Physics De-
partment of Politecnico di Milano.
4.6. Actuation subsystem
The actuation subsystem induces an oscillatory liquid
motion by imposing a sinusoidal displacement to the fer-
rofluid tank, hence addressing the requirement HL-1. The
displacement is limited to 12 mm of amplitude for safety rea-
sons, and the movement is configured to have an intermedi-
ate frequency between the first and second sloshing modes.
This aims to excite the corresponding waves and unveil rel-
evant kinematic parameters, like the actual modal frequen-
cies.
The movement is transmitted as sketched in Fig. 8. Both
containers are bolted to identical platforms that rest over two
Igus ZLW-1040 linear modules. The sliding mechanisms are
2https://ferrofluid.ferrotec.com/products/ferrofluid-emg/water/
emg-700- sp/. Consulted on: 30/01/2020
M [A/m]
0
1000
2000
3000
4000
H [106 A/m]
0 0.2 0.4 0.6 0.8 1
χini=0.39
M [A/m]
0
500
1000
1500
2000
2500
3000
3500
H [104 A/m]
0 0.5 1 1.5 2
Figure 7: Experimental magnetization curve at 25°C of the 1:5
vol Ferrotec EMG-700 water-based ferrofluid solution
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
Detection head
Ferrofluid container
Coil
Stepper engine
Linear slider
Platform
Rod
Capsule CoM
x
z
Support
Figure 8: Operation of the Actuation Subsystem
actuated by highly resistant toothed belts connected to a ver-
tical shaft. A Drylin NEMA-23 XL stepper engine located at
the lower end of the shaft actuates the system. This configu-
ration minimizes the number of moving parts and maintains
the relative position between coils, hence avoiding undesired
disturbances of the magnetic field. A single oscillation is im-
posed for each drop 3 seconds after launch, once the menis-
cus is stabilized after the initial acceleration peak.
The stepper engine is controlled by a Leadshine DM542
digital driver and an Arduino Nano board. The board imple-
ments a proportional control that computes the number of
constant-velocity steps required to follow a sine wave. As
a result, approximate wave profiles are obtained. This is
shown in Fig. 9, where the slider displacement of the second
launch is obtained from a VL6180X Time of Flight (ToF)
sensor and compared with the expected sine wave. Since the
1-sigma bounds are 0.9510 mm in idle state and 1.1896 mm
while the movement is produced, the measurements do not
provide a reliable reconstruction of the movement, but con-
firm the sinusoidal profile.
To avoid unexpected displacements of the moving parts
during launch and deceleration, a safety locking mechanism
controlled by the CCS is installed. It is composed of a set
TOF data
Theoretical
xslider [mm]
−8
−6
−4
−2
0
2
4
6
8
t [s]
0 2 4 6 8
Figure 9: Lateral displacement of the sliders during the second
launch
Figure 10: Pneumatic piston used to fix the moving assembly
of four pneumatic cylinders that block the platforms of the
experiment at the beginning and end of the drop. One of
them is shown in Fig. 10.
Liquid sloshing is modeled as the superposition of three
spring-mass linear oscillators with natural frequencies 𝑤𝑛,1=
4.6rad/s, 𝑤𝑛,2= 10.2rad/s and 𝑤𝑛,3= 10.3rad/s oriented
in the direction of the actuation. The parameters of the sys-
tem are obtained from a simplified low-gravity mechanical
sloshing model with an effective gravity acceleration of 1
m/s2(6). This roughly approximates the effect of the mag-
netic force with a current intensity of 20 A. A damping co-
a)
xmax of 1st spring [mm]
0
2.5
5
7.5
10
12.5
A = 10 mm
A = 15 mm
A = 20 mm
A = 25 mm
A = 30 mm
b)
A = 10 mm
A = 15 mm
A = 20 mm
A = 25 mm
A = 30 mm
xmax of 2nd spring [mm]
0
2.5
5
7.5
10
12.5
c)
A = 10 mm
A = 15 mm
A = 20 mm
A = 25 mm
A = 30 mm
xmax of 3rd spring [mm]
0
2.5
5
7.5
10
12.5
ω [rad/s]
2.5 5 7.5 10 12.5 15
Figure 11: Maximum displacement of the a) fundamental
spring-mass system, b) second spring-mass system, and c) third
spring-mass system as a function of the frequency of the single-
period quasi-sinusoidal excitation. The parameter of the plot
represents the excitation amplitude.
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
efficient of 0.15 is assumed after analyzing the results of the
precedent ESA Drop Your Thesis! 2017 - The Ferros exper-
iment.
The maximum displacement of the 𝑖𝑡ℎ spring 𝑥𝑚𝑎𝑥,𝑖 is de-
picted in Fig. 11 as a function of the excitation amplitude and
frequency for a single-period quasi-sinusoidal excitation. It
should be noted how, for excitation frequencies between 𝑤𝑛,1
and 𝑤𝑛,2, the first two modes are excited but the third remains
relatively unperturbed.
4.7. Capsule stability
The lateral excitation displaces the center of mass and
produces a disturbance torque that results in a temporary os-
cillation of the capsule. StELIUM is the very first experi-
ment launched at ZARM’s drop tower that produces this ef-
fect. A detailed analysis including worst-case scenarios be-
comes then mandatory to satisfy the requirement HL-9 and
ensure a safe operation.
Two cases of analysis are here presented. In the regu-
lar scenario, both sliders move simultaneously in the same
direction. Since the center of mass of the capsule is as-
sumed to be placed just between them, only a small torque
is generated by the oscillation of the liquid. In the worst-
case scenario, one of the assemblies is blocked avoiding self-
compensation, and the largest disturbance torque is produced.
The most powerful actuation in Tab. 3, with a frequency ap-
a)
Bottom
Top
xs [mm]
6
3
0
−3
−6
b)
First mode Second mode Third mode
x [mm]
−10
−5
0
5
10
c)
xcg [mm]
−0.4
−0.2
0
0.2
0.4
d)
T [mNm]
0.1
0.05
0
−0.05
−0.1
t [s]
0123456789
Figure 12: Regular scenario with optimum center of mass po-
sition. a) Slider displacement, b) springs displacement, c) cap-
sule center of mass position, d) disturbance torque.
proximately equal to 1 Hz, is assumed.
Figure 12 shows the regular scenario, a sine wave oscil-
lation of 12 mm amplitude. The displacement of the sliders
is represented in subfigure a). Subfigure b) depicts the dis-
placement of the first three spring-mass sloshing analogies,
the first and second being successfully activated. The hor-
izontal position of the center of mass is illustrated in sub-
figure c). Finally, the torque induced by the movement is
shown in subfigure d). Since both assemblies move simulta-
neously, this represents the worst case scenario for the dis-
placement of the center of mass. However, it remains well
within the 1 mm circle around the symmetry axis, as required
by ZARM’s drop tower user manual (39). The vertical posi-
tion of center of mass of the capsule is assumed to be located
just between the two moving assemblies, so the torque gen-
erated by the sliders is self-compensated. Since the center
of mass of the moving fluid does not match that of the as-
sembly, a residual component remains due to liquid sloshing.
Moreover, if the vertical position of the center of mass is not
located exactly between the platforms, a maximum tilting of
1.45⋅10−5 deg/[mm of deviation] is obtained.
In an hypothetical critical scenario where the link be-
tween both sliders fails and only the bottom assembly is ex-
cited, a maximum tilting angle of less than 1°is ensured
for excitation amplitudes lower than 25 mm and unfavorable
vertical center of mass deviations below 150 mm.
The integrated capsule had a total mass of approximately
500 kg and a moving mass of less than 15 kg. Since an op-
timal vertical position of the center of mass could not be
guaranteed, the displacement amplitude was limited to 12
mm for safety reasons. However, these values return a neg-
ligible tilting angle. This is verified with inertial data from
the fourth drop, shown in Fig. 13. The upper plot shows the
z axis
y axis
x axis
a)
ω [deg/s]
−1
−0.5
0
0.5
z axis
x axis
y axis
b)
θ [mdeg]
−5
−2.5
0
2.5
5
t [s]
0123456789
Figure 13: Inertial data of the fourth flight. a) Angular veloc-
ity, and b) mean-centered rotation imposed by the actuation.
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
evolution of the angular velocity, while the lower plot illus-
trates the mean-centered tilted angle induced by the excita-
tion. The actuation effects can be observed between seconds
3 and 4.3, resulting in a maximum rotation of approximately
0.006 degrees. The requirement HL-9 is consequently satis-
fied, demonstrating for the first time the safe operation of a
torque-generating experiment at ZARM’s drop tower.
4.8. Detection subsystem
The detection subsystem includes all the components that
measure the evolution of the liquid surface or relevant phys-
ical variables. It is composed of (i) the SDSs, (ii) two lateral
cameras, (iii) two general visualization cameras, and (iv) the
General Detection Subsystem (GDS).
The SDS, represented in Fig. 14, is the main component
of the detection subsystem. Its goal is to reconstruct the liq-
uid surface during flight, satisfying the requirements HL-3
to HL-5. A container cover with 20 laser diodes, a tilted
line laser and a 4K resolution GoPro Hero 5 Session camera
working at 30 fps conform the core of this device. The laser
projections on the opaque ferrofluid surface are recorded by
the camera, which correlates their apparent lateral displace-
ment with the actual three-dimensional position of the sur-
face. From the resulting kinematic evolution of each point,
relevant parameters, such as modal shapes and frequencies,
are computed. Furthermore, the liquid surface can be recon-
structed with a set of suitable fitting functions to fulfill the
requirement HL-4. The ideal accuracy of the system is be-
low 0.4 mm for the laser pointers and 0.25 mm for the line
laser.
The laser-based system is complemented by a VL53L0X
ToF sensor, which offers a rough measurement of the funda-
mental sloshing frequency and enables a fast feedback be-
tween drops. An accelerometer is installed at the top of
the container to complete the set of measurements required
for validating CFD models. The signals from both sensors
are continuously stored in the SD card with a sampling fre-
Figure 14: Bottom view of the Sloshing Detection Subsystem
Figure 15: Image of the Sloshing Detection Subsystem inte-
grated over the cylindrical ferrofluid container
quency of approximately 30 Hz. All the electronic elements
are integrated in a 3D-printed PLA structure, which provides
high structural resistance and geometrical adaptability. The
reader is referred to Ref. (42) for a full description of the
system, shown in Fig. 15.
The line laser, which is tilted a prescribed angle with re-
spect to the axis of symmetry, projects a red line that crosses
the center of the liquid surface. When the system enters mi-
crogravity conditions, the free surface and laser projection
are deformed. The equilibrium surface can be then recon-
structed by comparing both images, satisfying the require-
ment HL-6.
During the experimental campaign, the actuation mech-
anism produced a neat lateral oscillation of the surface. This
allowed using the line laser alone to reconstruct the free liq-
uid surface during the flight. Unlike the laser diodes, the
high inclination of the line laser ensures a reflections-free
observation of the liquid and improves the measurement res-
olution up to approximately 0.25 mm.
The SDSs are complemented with two Photron Fastcam
MC2-10K lateral visualization cameras with SKR KMP-IR
CINEGON 8 mm lenses working at 125 fps and 512×512
px2resolution. Their purpose is to serve as a backup system
in case of total failure of the SDS. Additional general visual-
ization cameras give a live feed of the experiment during the
fight to satisfy the requirement HL-7. The GDS measures all
the variables which are not directly related to the ferrofluid
tanks (e.g. overall temperature, magnetic field intensity at
selected locations, coils current intensity...). The measure-
ments are continuously stored in a dedicated SD card.
4.9. Electronics
Arduino-based electronics are employed to control the
different mechanisms of StELIUM and record relevant vari-
ables during the drop. Four different boards with separate
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
functionalities are powered by the Power Distribution Unit
(PDU). The full electronic diagram of the experiment is shown
in Fig. 19.
The Arduino boards are operated through of a LabView
interface associated to the CCS. The launch sequence is pro-
grammed both in LabView and the Arduino boards. The for-
mer controls the cameras, trigger signals and braking mech-
anism, while the later receive the trigger, a single 5 V line,
from the CCS. A first trigger signal is sent at the start of the
drop sequence to synchronize the cameras with a LED blink
and start the recording of scientific data at the SDSs and
GDS. The detachment of the drop capsule from the catapult
platform, which is produced in a window of 3 to 5 seconds
from the start of the drop sequence, sends a second trigger
to the boards. From this point, time delays are used to com-
mand the lateral excitation and stop data recording at the end
of the drop. This system was proven to be robust and reli-
able.
The illumination inside the capsule is provided by a LED
spotlight placed over the capsule platforms. This light was
too bright to illuminate the ferrofluid surface without pro-
ducing reflections at the surface, so a white panel was used
instead to generate a diffuse homogeneous backlight, as shown
in Fig. 4. Visualization from lateral cameras was signifi-
cantly improved due to the higher contrast.
5. Preliminary results
Redundant measurements from the SDSs, GDS and lat-
eral cameras were obtained for each drop. This focus on re-
dundancy is key for any microgravity experiment, and was
proven to be particularly useful for StELIUM. The high grav-
ity accelerations induced partial subsystem failures in two of
four drops, but the scientific results were never at risk. Al-
though a detailed analysis of the data is still ongoing, the
qualitative outcomes of the experiment are here presented.
Figure 16: Top view of the ferrofluid surface from the main
camera of the SDS
Figure 17: Lateral view of the ferrofluid surface from the high-
speed camera
Figures 16 and 17 represent the top and lateral views of
the upper container when the fundamental lateral sloshing
wave of the second drop achieves its maximum amplitude.
The deformation of the surface is deduced from the shape of
the laser line. Two laser pointers, approximately located over
the neutral line, are employed to detect undesired perpendic-
ular disturbances. A preliminary analysis of their movement
shows that such disturbances are indeed negligible and, con-
sequently, that the laser line provides enough information to
reconstruct the surface. Both images also reveal small rip-
ples in the free surface contour, produced by the slight irreg-
ularities in the distribution of surface properties. Although
undesired, their impact on the modal analysis is expected to
be negligible.
Figure 18 depicts the Fast Fourier Transform (FFT) of
the vertical displacement of each point of the laser line. As
Figure 18: FFT of the vertical displacement of the laser line
during the second drop. Lateral and axisymmetric modes are
detected.
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
Figure 19: Electronic diagrams of StELIUM
expected, the center is only able to detect the axisymmetric
sloshing wave, induced by the drop tower catapult and devel-
oped until the application of the lateral percussion at 𝑡= 3
s. The sides, on the contrary, reflect the fundamental and
second lateral sloshing waves. It is important to note that
the maximum amplitude is not produced at the contour, but
at an intermediate radial position. Consequently, the edge
follows an intermediate behavior between the free and stuck
edge conditions described in Ref. (35).
6. Conclusions and future work
StELIUM was launched at ZARM’s drop tower in Novem-
ber 2019 to study lateral sloshing of magnetic liquids in mi-
crogravity. This remains to be an almost unexplored phe-
nomenon with potential applications in space. In this paper,
the objectives, motivation, configuration, and preliminary
outcomes of the project have been presented with a focus
on its technical aspects.
The experiment setup has been described according to
actuation, detection, magnetic and structure subsystems. Each
of them contributes to the fulfillment of the high level re-
quirements listed in Tab. 1and, consequently, to the high-
level objectives given in Sec. 2. Special attention has been
payed to the development of the detection subsystem, that
implements several redundant approaches to measure the kine-
matic evolution of the free liquid surface. The focus on re-
dundancy an reliability has been key for the success of the
drop tower campaign, that exposed the experiment setup to a
highly demanding operational environment. StELIUM was
also the very first experiment launched at ZARM’s drop tower
that imposed significant disturbance torques to the drop cap-
sule. A dedicated stability analysis has been carried out to
ensure that only minor oscillations are induced, as it was fi-
nally observed.
The meniscus profile, lateral and axisymmetric sloshing
frequencies and operational variables (e.g. current intensity,
acceleration, magnetic field intensity, etc) were recorded by
different subsystems. The processed database will be em-
ployed to validate the magnetic sloshing model presented in
Ref. (35). The outcomes of this experiment will be instru-
mental for increasing our understanding and modeling capa-
bilities of this physical system, and may eventually pave the
path for the development of new liquid management devices
in space.
Competing Interests
The authors declare no competing interests.
Funding Sources
This work was supported by the United Nations Office
for Outer Space Affairs (UNOOSA), the Center of Applied
Space Technology and Microgravity (ZARM) and the Ger-
man Space Agency (DLR) in the framework of the UNOOSA
DropTES Programme 2019. Further financial and academic
support was obtained from Ferrotec Corporation, Politec-
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StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
nico di Milano, the University of Seville, the European Space
Agency (ESA) and the European Low Gravity Research As-
sociation (ELGRA).
Acknowledgements
The authors acknowledge the financial, technical and aca-
demic support offered by UNOOSA, DLR, ZARM, Ferrotec
Corporation, Politecnico di Milano and the University of
Seville. We also thank ESA and ELGRA for financing the
presentation of this work at the 70th International Astronau-
tical Congress (IAC) and the 26th ELGRA Biennial Sym-
posium and General Assembly. This project is in debt with
ZARM’s drop tower engineers Jan Siemer and Fred Oetken,
ZARM’s point of contact Dr Thorben Könemann and UN-
OOSA’s point of contact Ayami Kojima for their endless
support. We finally thank the technicians Giovanni Colombo,
Alberto Verga and the PhD student Riccardo Bisin from the
Space Propulsion Laboratory (SPLab) of Politecnico di Mi-
lano for their academic and technical assistance, as well as
the rest of members of this research group for contributing
to the creation of an extraordinary professional and human
environment.
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