ABSTRACT

Title of Thesis: Expansion of Polyurethane Foam in Low Pressure

Environment for Space Debris Removal Applications

Team JUNK: Edward Cai, Ethan Green, Aravind

Kavuturu, Finnegan O’Neill, Joseph Shedleski, John

Yang, Robert J. Young, & Muhamad Zakaria

Thesis Directed By: Dr. Raymond Sedwick

Department of Aerospace Engineering

As the privatization of space flight has led to an increased number of rocket launches and

a new era of space exploration, the issue of space debris is becoming a well-researched

phenomenon. With more emphasis on future extraterrestrial missions, such as NASA’s Artemis

and SpaceX’s Mars missions, there is a growing concern surrounding the unsustainable practices

that create space debris. Although there is a plethora of papers discussing the sources of space

debris, as well as its negative impacts on the future of space flight, there are comparatively fewer

papers discussing active debris removal methods. This study focuses on one such method -

namely, using spray foam to remediate space debris. Spray foam has the advantage of being

low-cost and multi-use, which differs from most other active removal methods. To determine the

viability of spray foam in space debris removal, this study tests the expansion of polyurethane

foam in vacuum, a poorly documented characteristic in current literature. From a sample of 20

tests, a maximum volumetric expansion ratio of 53 was found. The resulting discussion focuses

on spray foam’s efficacy as an active debris removal method from these observations.

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Expansion of Polyurethane Foam in Low Pressure

Environment for Space Debris Removal Applications

Team JUNK

Edward Cai, Ethan Green, Aravind Kavuturu, Finnegan O’Neill,

Joseph Shedleski, John Yang, Robert J. Young, and Muhamad Zakaria

Thesis submitted in partial fulfillment of the requirements of the

Gemstone Honors Program, University of Maryland, 2023

Advisory Committee:

Dr. Raymond Sedwick, Advisor

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Acknowledgements

The team would like to firstly thank Dr. Raymond Sedwick for his mentorship and lab provisions

throughout the research and experimentation process. The team would also like to thank Ms. Jodi

Coalter for her librarian assistance. For their time and insight at the Gemstone Thesis

Conference, the team thanks discussants Dr. John Crassidis, Dr. Steve Mork, Dr. Gordon Roesler,

and Dr. Jarred Young. Finally, the team thanks Dr. David Lovell and Dr. Allison Lansverk for

their planning and organization of the Gemstone research program and the Thesis Conference,

and making this research opportunity possible.

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TABLE OF CONTENTS

1 INTRODUCTION 5
2 LITERATURE REVIEW 8

2.1 Introduction to Foam-Based Removal Methods 8
2.2 Proposed Deployment Techniques 8
2.3 Foam Static Mixing Nozzle Design 11
2.5 Foam Expansion Properties 15
2.6 Review Conclusion 17

3 METHODOLOGY 18
3.1 Final System Design 18
3.2 Vacuum Chamber Design 19
3.3 System Validation / Iteration 20
3.4 Experimental Procedure and Data Collection 21
3.5 Additional Testing 21

4 RESULTS 22
4.1 Raw Data 22
4.2 Analytical Results 23

5 DISCUSSION 27
5.1 Findings from Data Analysis 27
5.2 Sources of Error 28

6 CONCLUSION 29
7 APPENDICES 31

7.1 Appendix A: Equity — Impact Analysis 31
7.2 Appendix B: Project Timeline 32
7.3 Appendix C: Budget 34

REFERENCES 35

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1 INTRODUCTION

By the end of the century, space debris could be the greatest hazard for space exploration. An

increasingly privatized space industry has led to more interest in rocket launches in recent

decades, and the result is an ever-growing number of objects in Earth’s orbit. To that end, there

has been an increased focus on space debris in recent literature - the causes, sizes, and impacts of

space debris are well documented. Although there is a greater awareness for this emerging threat,

there has been comparatively little done to remove space debris. The currently proposed

technologies are slow to be adopted, and though the field of active debris removal has many

options, there have been no major efforts on the part of space agencies or governments to employ

one of these methods to clean up space debris.

Space debris is defined as any man-made object currently in orbit around Earth that no longer

serves a purpose. The various forms of space debris include, but are not limited to,

decommissioned spacecraft and payloads, spent rocket stages, collisional debris, and debris from

unidentified sources. From a European Space Agency (ESA) estimate for 2022, there are

approximately 30,000 pieces of space debris currently being tracked, ranging in size and altitude,

in Earth’s atmosphere today [4]. The number of objects from each source is shown in Figure 1

below.

Figure 1: Graph of orbital debris from 1960 to 2020, separated by source.

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UI - unidentified, RM - rocket mission related object, RD - rocket debris, RF - rocket

fragmentation debris, RB - rocket body, PM - payload mission related object, PD - payload

debris, PF - payload fragmentation debris, PL - payload.

From the graph, the most common form of debris is in the form of unidentified debris, with

rocket-related debris and payload-related debris following. Although there are about 30,000

pieces being tracked, the total number of objects is estimated to be over 100 million, with the

bulk ranging from 1mm to 10cm [4].

The time-sensitive nature of the space debris problem comes from collisional cascading, a

positive feedback loop where the presence of space debris increases the likelihood of collisions

and fragmentation, which increases the amount of space debris. The positive feedback loop of

collisional cascading is known as the Kessler Syndrome, which was first formally named after

Donald J. Kessler [2]. In this paper, Kessler presented a mathematical model for predicting when

collisional cascading would reach critical mass - at this point, even if no more space objects were

introduced into orbit, the amount of space debris would continue to grow indefinitely. The

original prediction for the “critical mass date” was approximately 2010-2020.

In considering methods of handling space debris, there are active and passive methods. Active

debris removal methods are primarily focused on removing larger, trackable debris due to the

inability to efficiently remove smaller debris [16]. Thus, active debris methods are more widely

studied, as there are more efficient options to deorbit large debris. There have been many

proposed methods of active debris removal, with only a few discussed here. Net capture involves

the use of a net to drag debris down to deorbit with a leading satellite, tether or harpoon removal

involves directly penetrating the debris with a satellite in order to deorbit, and laser-based

ablation ionizes the surface of debris to cause a slight thrust down towards Earth, deorbiting. All

three methods listed here have been studied extensively, but the focus of this study is on a less

popular method: spray foam.

In using spray foam, the leading satellite can carry a large volume of liquid reagents that can

combine to form foam on the debris. By increasing the mass-to-area ratio, the foam allows the

debris to deorbit itself, without the need for physical contact. By using foams with high

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expansion ratios, the deployment satellite can be highly reusable and could feasibly deorbit many

hundreds of debris objects before becoming non-operational. However, this method requires the

satellite to deploy foam directly onto the surface of debris, requiring high precision for either

aiming foam reagents from a distance or manipulating an exterior arm for direct deployment. In

either case, the deployment system for spray foam is a topic for further study and refinement. In

this study, the basic expansion characteristics of foam are tested in order to determine if spray

foam can conceivably deorbit space debris.

The use of spray foam is a relatively novel field of research. Studies into dynamic simulations of

deorbiting debris with spray foam are widespread, along with the characteristics of different

foams. However, there is little practical research into the expansion characteristics of foam in

vacuum conditions. Some studies have modeled the expansion theoretically, but very few

experimental studies are available to verify these results.

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2 LITERATURE REVIEW

2.1 Introduction to Foam-Based Removal Methods
Foam-based removal methods involve a spacecraft that deploys expandable foam on the surface

of orbital debris, which when activated, significantly increases the debris’ surface area, inducing

more atmospheric drag and eventually causing the target to deorbit. Most of the research into this

method stems from a singular source  — a lengthy report presented to the ESA in 2011 detailing

the chemistry, effectiveness, and feasibility of a foam removal method [10]. The report proposed

the foam to be sprayed from a gun or a nozzle from a single spacecraft or a potential satellite

swarm. Specific types of foam, from glass to polymer-based, were researched, and computer

simulations modeled the expansion behavior of polymer-based foams.

While the idea is novel and untested, the study found numerous potential advantages. First, this

method could be tailored to remove various sizes and masses of LEO debris based on the

quantity of foam deployed. Second, there would be no necessity to control the target debris after

deployment — the debris would simply make an uncontrolled reentry and disintegrate in the

Earth’s atmosphere.

There are certainly disadvantages to this method as well - since the method relies on

aerodynamic drag, it is most effective for LEO debris. Large debris located in higher orbits

would take significantly longer to deorbit or be unable to be deorbited at all. The relative lack of

research into this method compared to other proposed methods indicates a low technology

readiness level, implying that such a method would have significant development hurdles to

overcome in testing and validation to be spaceworthy.

2.2 Proposed Deployment Techniques
An essential element in the foam debris removal process is the method of deploying the foam.

Optimally, foam will be deployed in such a manner that it will surround the debris as shown in

Fig. 4.

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a. b. c.

Figure 4: (a) The rendezvous with debris, (b) the beginning of foam deployment, (c)

separation and de-orbiting of debris [10].

Based on previous work on the subject, four main methodologies for the deployment of foam

onto orbital debris were identified [10]:

Chameleon Tongue

The spacecraft approaches a piece of debris. A retractable-wire extends from the spacecraft, with

the reservoirs storing the foam components and the mixing chamber that catalyzes the reaction

attached to the extended end. Once the wire reaches the debris, the foam chamber is placed on

the debris and the wire retracts back to the spacecraft. The mixing chamber then catalyzes the

reaction, enveloping the debris in the created foam.

One of the main concerns with this method is its lack of development. Retractable tether, active

reaction deployment device, and foam catalyzing chamber technologies all exist independently,

with no collective design of the system. Furthermore, the foam chamber must also adhere to the

debris while foaming. This could pose a problem if the foam chamber detaches from the debris

during the reaction process. Smaller debris introduce complications, as generally, they have

higher velocities and are more prone to rotation which would make it more difficult to place the

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chamber on the debris. Finally, this method has the same drawbacks as many tether technologies

—it requires precise data on the debris’ position, velocity, and rotation.

Foam Ejection Nozzle

This method consists of a nozzle attached to a robotic arm, which ejects foam onto the debris

face. The length of this arm depends on the radius of the ball of foam surrounding the debris. If

the spacecraft is too close to the debris, there is a chance that the foam might attach to the

spacecraft, so a robotic arm with a length of 15 m is a conservative estimate for a foamed debris

with a maximum radius of 12 m, as seen in Fig. 4 [10].

Figure 5: A diagram with the foam reservoir attached to a robotic arm and nozzle,

illustrating the deployment method listed above [10].

One of the main issues with this method is the foam buildup in the nozzle after each use. This

could affect the rate of foam flow, and could eventually lead to total blockage. A possible

remedy to this problem is to increase the foam ejection velocity; however, too high of a velocity

could generate a thrust on the debris that propels it away from the spacecraft. Another solution

that seems more viable is to ventilate the ducts using an inert gas to clear any foam deposits left

in the nozzle. Additionally, as with the chameleon tongue, the robotic arm requires precise data

on the debris’ position and velocity. The arm also has limited maneuverability in comparison to

other methods, such as a satellite swarm or a foam gum dispenser.

Satellite Swarm

The satellite swarm method utilizes a constellation of satellites that are each equipped with a

foam ejection nozzle. The constellation, or one of its subgroups, surrounds a large piece of debris

and sprays it with foam from many points. This greatly increases the chance of total coverage of

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the debris. In addition, each satellite would be capable of spraying small debris by itself.

The main drawback to this method is that the proposed satellites have a low storage capacity for

the components of the foam. Consequently, this system can only deorbit a small amount of debris

mass unless a method for refilling is developed. Furthermore, the satellite swarm is the most

expensive method as it necessitates the production of multiple separate complex bodies, unlike

other methods. Finally, an area for development exists in coordination of the satellite swarm

towards the goal of deorbiting debris.

Foam Gums

A reservoir, called a gum, is filled with foam components and shot onto the surface of the debris.

Once on the debris, the foam components mix to create the foam which the gum then releases

onto the surface. The chambers are estimated to have a volume of 10 cm3, with 1000 L

(expanded volume) of foam.

Once again, this method exists mostly in theory. There is little research in the deployment of

projectiles to apply foam to orbiting bodies. Additionally, the gum must be fired from a device

on the spacecraft that can track debris of different sizes, velocities, and rotations. Moreover, the

momentum from the gum impacting the debris poses a potential problem. The impact itself could

deorbit the debris or add/remove spin, making the debris more unpredictable overall. Finally, for

very large bodies, multiple gums could be required to successfully deorbit the debris.

These are the few methods of deployment for foam from a single paper. Although there are many

other method possibilities, the field requires more research into possible deployment methods,

which falls outside of the scope of this paper.

2.3 Foam Static Mixing Nozzle Design
In the aforementioned paper, the suggested nozzle is specifically a static mixing nozzle. We will

briefly describe how this nozzle works, as the nozzle is incorporated into many other deployment

methods. In a static mixing nozzle, two liquids are forced through a long nozzle with many

scaffolds obstructing flow inside the nozzle. As seen in Fig. 6 below, these scaffolds force the

liquids to combine through static means, or without the addition of energy or motion. In this way,

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two liquids can be easily mixed by forcing them through the nozzle with high pressure at one

end. Due to the simple nature and implementability in space, static mixing nozzles are the

optimal choice for a nozzle design. The exact shape of the nozzle tip, placement of scaffolds

inside, as well as length of the nozzle, are all quantities that must be considered in nozzle design.

Figure 6: A diagram depicting the mechanisms behind a static mixing nozzle. The two

reservoirs of red and blue fluid are mixed statically without the addition of energy or motion

[11].

2.4 Types of Foams

The possible candidates for the foam can be separated into two categories related to the cell

structure of the foam determined within the paper by Andrenucci et al. in 2011:

Closed-Cell Foams

Types of foam in which an insulating gas is retained within the cells during decomposition. This

makes closed-cell foams great insulators with very low permeability and good water resistance.

Open-Cell Foams

Types of foam in which the cell structure is not closed and an insulating gas is not trapped within

the foam during decomposition. This makes open-cell foams less dense than closed-cell foams.

Open-cell foams however are much more permeable and worse insulators than closed-cell foams.

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These categories are useful for organization of foam types by physical structure; however, each

individual type of foam has unique characteristics that are not described by the two categories

above. Below, additional types of chemistry are listed along with a brief description of their

general chemical properties:

Glass Foams

Glass foams, a type of closed-cell foam, are made from molten glass or sintered — meaning

compaction by heat and pressure until just before liquefaction — glass particles. They are

generally more brittle than other foams. The longevity of the structural properties makes them

suitable for insulation applications. The initial state of the glass used determines the need for a

foaming agent; for instance, sintered glass particles will require a foaming agent in foam

production. When the foam is made, the foaming agent decomposes into a gas that is trapped

within the melted glass material so long as the viscosity of the fluid is sufficient [10]. It is noted

that the temperature of the reaction is critical; if the temperature becomes too high, the gas

bubbles will rise excessively causing a collapse of the overall structure of the material [10]. In a

patent developed by Solomon et al. in 1992, the particle size of the foaming agent will affect the

foam’s cell dimension and thus the density [12]. A lower density results in a lower thermal

conductivity, while a smaller cell dimension results in higher compressive strength [10]. The

associated brittleness of glass foams is unsuitable for application to space debris removal.

Ceramic Foams

Ceramic foams are an incredibly flexible category of foams, including both open and closed-cell

foams, with a wide range of adjustable material properties, such as electrical resistance. Because

of this flexibility, ceramic foams have a large number of applications on Earth including thermal

protection systems and filters. In 2005, Biasetto discussed three techniques for developing

ceramic foams: development by 1) filling the cellular structure of a polymeric foam with a

ceramic suspension and then removing the polymeric foam, 2) preparing a continuous ceramic

matrix and then burning out sections to create the intended porosity, or 3) direct foaming, which

utilizes a blowing agent to generate a ceramic foam mixture [13]. All three of these techniques

would be extremely difficult and expensive to perform in space with current technologies,

making ceramic foams a poor choice for debris removal.

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Metallic Foams:

Metallic foams can be either open cell or closed cell, depending on the manufacturing process

[14]. Metallic foams are essentially a metallic structure with gaseous pores throughout and

primarily retain the physical characteristics of the original metal. In general, the pores lower the

density of the structure, but it varies based on the base metal’s mass and the percent volume of

the pores. The uses of metallic foams can vary depending on the base metal chosen, although

they are most commonly used in structural applications. It should be noted that the production of

metallic foams requires either a metal in its liquid state or powdered metal heated to just below

the melting point to achieve the foaming process. Heating a metal to its melting point requires a

large amount of energy, so applying it to the topic of deorbiting space junk means the satellite

either needs to be very large to carry the premade foam, or have access to a large enough energy

supply to produce the foam in orbit. Both of these are unrealistic, making metallic foam a poor

choice for this application.

Polymeric Foams:

Polymeric foams encompass a wide range of polymers, including polyurethane, polyethylene,

polystyrene, and polyvinyl chloride (PVC). In general, compared to other foam types, polymeric

foams are less expensive and more widely available while still maintaining desirable properties.

Depending on the exact composition of constituent ingredients such as foaming agents,

properties like density, flexibility, and material strength vary widely, even between foams of

similar polymers. Such flexibility of options in polymeric foams enable them to be used in a

variety of purposes, a clear advantage compared to the previously discussed foam chemistries.

Additionally, composite foams expand upon previously discussed foam types by introducing an

additional hollow phase or solid phase to the foam material, allowing for the enhancement of

specific properties such as improved strength/rigidity. For the purpose of this research, the foam

materials are classified to be biphasic (consisting of two phases of matter) and are defined by

some firm structure surrounding hollow regions, or gas bubbles, within the material [10]. Table 1

below summarizes the general physical properties of closed and open cell foams:

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Table 1: Comparison of open-cell and closed-cell foams based on physical characteristics [10].

Based on the summarizations above, open-cell foams are generally lighter in mass than

closed-cell foams which correspond to the lower density associated with open-cell foams.

However, the lower density implies a greater yield for the volume of foam produced for each unit

of mass, which is important in the expansion of the foam around a material. Under the

assumption that the foam is to be deployed in near-vacuum when applied in the removal process,

the comparison of the vapor permeability of each type of foam would only be factored as the

debris enters the atmosphere upon removal, however in near vacuum with miniscule amounts of

vapors present, the comparison may not be needed for these conditions.

Overall, the previous study by Andrenucci et al. chooses to focus on the application of open-cell

foams in the removal process. Our research can investigate the expansion properties of each type

of foam under standard atmospheric conditions as well as near-vacuum conditions similar to

those of objects in orbit around Earth to further focus on what type of foam to baseline in

application.

2.5 Foam Expansion Properties
Based on previous work by Bruchon and Copez, an expansion model was derived from the

Rayleigh-Plesset equation and rearranged to solve for the expansion of bubble radius [16]. The

study done by Andrenucci et al. implements this foam expansion model in a scenario that is

subject to low pressure conditions, to simulate the effect that space will have on the foam

expansion process. The study uses the theoretical model derived, assumptions on the gas created

during expansion, ESPAK 90 polyurethane resin as the polymeric foam, and other physical

atmospheric quantities such as pressure, density, and viscosity to create its simulations.

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Figure 7: Expansion of foam bubble over time [10].

Although the expansion time, reaction time, and final radius of the foam have been accredited in

another study, there has been no testing to date on the expansion of foam in upper-atmospheric

conditions. However, both studies have verified that the foam takes under a minute to expand

fully, with a reaction time around 0.2 s.

One important aspect is the viscosity and how this affects the process time of foam expansion.

According to the original derived expansion model, there are no significant effects on the volume

of the final foam expansion caused by viscosity. However, in low pressure conditions, viscosity

becomes a factor that greatly influences the reaction time of the foam. This is likely because

viscosity influences the ability of the foam to expand under atmospheric pressure and therefore a

greater viscosity leads to a longer process time.

Another significant factor in the foam expansion model is its dependence on ambient pressure,

the pressure of the surrounding medium. As pressure decreases, the final volume and reaction

time increase, and this relation can be examined in Fig. 8.

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Figure 8: Expansion Factor in terms of final volume and pressure [10].

2.6 Review Conclusion
From above, we discussed previous work on foam in debris removal. It has been found that using

foam to increase the surface area of debris is a feasible solution for debris removal. There are

numerous reasonable techniques for foam deployment, including placing a mixing chamber that

releases foam onto debris, and spraying the debris with foam ejected from nozzles. The different

cell structures, and materials for foams were discussed and their benefits were established.

Polymeric foams were found to be the best for the removal of debris due to their density and

expansion properties. This suggests further research into the exact expansion properties of

polymeric foams in the upper atmosphere.

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3 METHODOLOGY
3.1 Final System Design
The design for the testing apparatus is shown in Figure 9 below. The reagents are initially loaded

into the two syringes at the top of the vacuum chamber, which feed through two manual stopcock

valves, through the top plate, and into the static mixer. With two separate lines for Reagents A

and B of the foam, the mixing is delayed until the reagents enter the vacuum chamber. After

passing through the static mixing nozzle, the two reagents are mixed by the partitions located

inside the mixing nozzle itself, eliminating the need for active mixing. The choice of a passive

mixer was made to avoid the complications of including an active mixer in the vacuum chamber.

Once mixed, the liquid foam is ejected into a measuring cup and allowed to fully expand over the

course of ten minutes.

Figure 9: Block diagram of the test apparatus.

In the system described, almost every part of the design is replaceable. After extensive testing of

various cleaning methods, including the use of acetone through reagent feeds, it was determined

that the diameter of the flow path was too small to allow for effective cleaning. After only a few

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tests, the valves, tubes, or static mixer would become clogged with excess reagent or foam. To

avoid these issues, every part in the foam feed is able to be replaced without impacting the

consistency of testing and data collection. During testing, the entire feed system is evaluated for

blockages after each run, and replaced following two to three runs to avoid accumulation.

The system design is kept simple to avoid sources of error. As discussed below, the iterative

process for data collection is lengthy, and initial complex system designs had many points of air

leaks, inconsistent flow speeds, and other prohibitive issues. The decision to keep the design

simple was made through an extensive iterative process, as discussed below.

3.2 Vacuum Chamber Design
Federico et. al. designed an apparatus to test foam mixing in a microgravity and low pressure

environment. The system was integrated into the Rexus 12 sounding rocket, but unfortunately

the rocket malfunctioned and never reached orbit. In order to increase the repeatability of tests

and to reduce risk, a custom vacuum chamber was designed instead. The system cannot replicate

a microgravity environment, but it can replicate to a degree the low pressure environments of

LEO. The final design of the chamber consisted of a custom acrylic cylinder and baseplate, and

was designed to match the vertical top-down deployment method. The custom baseplate had two

holes drilled into it, which allowed for the valves to be mounted on top of the cylinder. This

minimized the distance between the syringes and the static mixing nozzle. This minimal distance

helped to minimize the issue of the difference in viscosity of the reagents.

The baseplate and cylinder both needed to be able to withstand the stress of the vacuum. Let b be

the radius of the cylinder, t be the thickness, q is the external pressure acting on the cylinder, and

the tensile yield strength of the material. Figure 10 shows the relationship between the ratio ofσ
0

b/t and q/ , where if the value of (b/t, q/ ) falls above the curve, the cylinder will failσ
0

σ
0

(Dell’Aqua and Luzzi, 2005). The tensile yield stress of acrylic at room temperature is 69 MPa

[17]. The external pressure is one atmosphere, or 101 kPa. In order to provide enough room for

the test apparatus, the diameter of the cylinder of our vacuum chamber is 12 inches, or 0.304

meters. In order to maintain a safety factor of 2, a thickness of 0.25 inches was chosen.

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Figure 10: Limit External Pressure of a Cylindrical Vacuum Chamber.

The electronic valves’ interior bore size limited reagent flow and caused clogging, so manual

stopcock valves were used as a replacement. After extensive iteration, the system reached a

“successful” state and data collection could proceed. The next section explains in detail the

iterative process the design of the system went through.

3.3 System Validation / Iteration
In validating the system design, there were two main criteria that constituted a successful system

and mixing test: (1) the ability for foam to enter the vacuum chamber as a well-mixed fluid, and

(2) the ability for the tests to be repeated with the same procedure. In designing the system

described above, there were many failed designs that were unable to meet either or both of these

criteria. Designs with the reagent feeds below the vacuum chamber led to poorly mixed foam

solutions, and those that used electrically-actuated valves above the chamber were unable to

repeat tests extensively due to clogging and ineffective cleaning. In addressing some of these

issues, the initial vacuum design had to be reworked, as discussed in the above section (3.2). By

limiting the size of the vacuum chamber, as well as mounting the deployment system above the

chamber, the foam reagents were deployed at lower pressures and mixed more easily.

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3.4 Experimental Procedure and Data Collection
To validate previous studies’ models on spray foam in vacuum, 5 mL of each part of a two-part

polyurethane foam manufactured by Composite Envisions, according to the manufacturer-

recommended 1:1 ratio, were loaded into syringes above the two closed stopcock valves. The

system was then pumped down to vacuum. The strength of vacuum was determined by allowing

the vacuum to come to a natural equilibrium, or in cases where the vacuum strength was

abnormally low, until the pressure was under 100 mBar. Once the resting pressure is reached, the

valves are opened and the syringes are pulled by the vacuum to deploy the foam into a clear

beaker with volume demarcations. The foam is allowed to expand for approximately 10 minutes,

or until the foam reaches a peak expansion. The total volume of the foam is recorded, along with

the pressure of the vacuum, and the vacuum is then vented. The valves and tubes above the

baseplate are cleaned with water or replaced if they become clogged, and the static mixer is

replaced with a fresh mixer after every test.

3.5 Additional Testing
After preliminary data collection, the observation was made that at low enough pressures, the

foam would continuously collapse while expanding, causing the final volume to be much lower

than anticipated. Although the cause of this phenomenon is unknown, it was observed that by

varying the mixture ratio of reagents, the collapsing could be avoided. Mixture ratios of 1:2 and

2:1 were tested, and it was found that by using a ratio of 1:2 (2.5 mL of Reagent A and 5 mL of

Reagent B), the collapse was avoided completely. However, due to time constraints, the testing

could not be redone with this new mixture ratio. Further research into this collapse phenomenon

and varying mixture ratios must be done to determine if they significantly affect the viability of

foam-based remediation.

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4 RESULTS
4.1 Raw Data
In total, 21 tests were accumulated for foam mixture in our vacuum system with all

measurements. The measured expansion factors of the foam as pressure was varied lied in a

range of 0 to 60. The 21 tests include a combination of tests deemed successes and failures,

which were determined by either the collapse of the foam, or due to failures in the deployment or

mixing stages. Table 2 below summarizes the results of the combined successes and failures:

Pressure
(millibar)

Reagent A Volume
(mL)

Reagent B Volume
(mL)

Total Expanded Volume
(mL) Expansion Ratio

141.0 ± 0.001 3.5 ± 0.2 3.5 ± 0.2 380.0 ± 29.5 54.3 ± 4.8

300.0 ± 0.001 3.0 ± 0.2 3.0 ± 0.2 100.0 ± 20.0 16.7 ± 3.4

280.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 400.0 ± 30.0 40.0 ± 3.2

170.0 ± 0.001 3.0 ± 0.2 3.0 ± 0.2 20.0 ± 14.5 3.3 ± 2.4

120.0 ± 0.001 3.0 ± 0.2 3.0 ± 0.2 200.0 ± 24.1 33.3 ± 4.2

40.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 50.0 ± 17.1 5.0 ± 1.7

180.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 350.0 ± 28.7 35.0 ± 3.0

100.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 450.0 ± 31.2 45.0 ± 3.4

213.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 375.0 ± 29.4 37.5 ± 3.1

370.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 350.0 ± 28.7 35.0 ± 3.0

70.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 400.0 ± 30.0 40.0 ± 3.2

15.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 20.0 ± 14.5 2.0 ± 1.4

112.5 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 500.0 ± 32.4 50.0 ± 3.5

84.1 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 10.0 ± 13.2 1.0 ± 1.3

40.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 50.0 ± 17.1 5.0 ± 1.7

140.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 400.0 ± 30.0 40.0 ± 3.2

97.4 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 350.0 ± 28.7 35.0 ± 3.0

79.6 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 300.0 ± 27.3 30.0 ± 2.9

70.0 ± 0.001 5.0 ± 0.2 5.0 ± 0.2 250.0 ± 25.8 25.0 ± 2.7

80.0 ± 0.001 5.0 ± 0.2 2.5 ± 0.2 100.0 ± 20.0 13.3 ± 2.7

60.0 ± 0.001 2.5 ± 0.2 5.0 ± 0.2 450.0 ± 31.2 60.0 ± 4.7

Table 2: Foam volume expansion ratios for changing pressure

22



The measured expansion factors for each test listed in Table 2 were calculated by taking the final

expanded volume and dividing it by the total initial reagent volume, which was a sum of the

initial volume of each reagent. In order to conduct analysis on our data and complete a

comparison to the model of polyurethane foam expansion [10], the tests determined to be failures

were removed from the data set analyzed. Additionally, the tests with unequal initial reagent

volume were also removed from the final data set, as the model used assumes a complete

reaction between both components. Table 3 below lists the resulting successful tests, of which 12

remained:

Pressure (millibar) Total Expanded Volume (mL)
Total Initial Volume

(mL) Expansion Ratio

141.0 ± 1.0E-3 380.0 ± 29.5 7.0 ± 0.3 54.3 ± 4.8

280.0 ± 1.0E-3 400.0 ± 30.0 10.0 ± 0.3 40.0 ± 3.2

180.0 ± 1.0E-3 350.0 ± 28.7 10.0 ± 0.3 35.0 ± 3.0

100.0 ± 1.0E-3 450.0 ± 31.2 10.0 ± 0.3 45.0 ± 3.4

213.0 ± 1.0E-3 375.0 ± 29.4 10.0 ± 0.3 37.5 ± 3.1

370.0 ± 1.0E-3 350.0 ± 28.7 10.0 ± 0.3 35.0 ± 3.0

70.0 ± 1.0E-3 400.0 ± 30.0 10.0 ± 0.3 40.0 ± 3.2

112.5 ± 1.0E-3 500.0 ± 32.4 10.0 ± 0.3 50.0 ± 3.5

140.0 ± 1.0E-3 400.0 ± 30.0 10.0 ± 0.3 40.0 ± 3.2

97.4 ± 1.0E-3 350.0 ± 28.7 10.0 ± 0.3 35.0 ± 3.0

79.6 ± 1.0E-3 300.0 ± 27.3 10.0 ± 0.3 30.0 ± 2.9

70.0 ± 1.0E-3 250.0 ± 25.8 10.0 ± 0.3 25.0 ± 2.7

Table 3: Foam volume expansion ratios for changing pressure, successful tests

4.2 Analytical Results
To compare the successful tests collected against the polyurethane foam expansion model [10], a

chi-squared goodness of fit test will be used to quantify how well our expansion factors compare

with the expected factors predicted by the model. The pressure and volume units used by the

model are in Pascals and cubic meters, respectively, thus each measured quantity was converted

as needed for fitting.

23



In order to implement the model, the same assumptions made by Andrenucci et. al. [10] were

made, as well as similar constants used. The gas generated in the foaming reaction by the two

reagents is carbon dioxide ( ) gas, which has a gas constant of .𝐶𝑂
2

𝑅
𝐺

= 188. 9233 𝑚2/𝐾𝑠2

Using this constant, along with the standard atmospheric pressure of 101325 Pa, and an assumed

room-temperature of 293 K, the density of the gas released is about . The𝐶𝑂
2

1. 8 𝑘𝑔/𝑚3

relative densities of reagent A and B are provided to be and ,1. 24 𝑔/𝑚𝐿 1. 12 𝑔/𝑚𝐿

respectively, thus combining to give an overall relative density of for the⍴
𝑟𝑒𝑎𝑔𝑒𝑛𝑡𝑠

= 1. 18 𝑔/𝑚𝐿

combined reagent mixture immediately before foaming. Based on the expansion factor for each

measurement, the amount of initial mass of reagent transformed into gas varies for each test. The

initial volume of gas thus varies based on the varying initial mass of gas present, and can be𝐶𝑂
2

used to get the initial gas bubble radius.𝐶𝑂
2

That initial gas bubble radius is determined by the initial volume of gas generated at the𝐶𝑂
2

𝐶𝑂
2

start of the reaction, and is dependent on how much initial reagent mass is converted into 𝐶𝑂
2

gas. The percentage of reagent mass converted into gas is found by determining the initial𝐶𝑂
2

mass of the reagents and the final mass of the gas as follows:𝐶𝑂
2

(1),𝑚
𝑔𝑎𝑠

= ρ
𝑔𝑎𝑠

𝑉
𝑡𝑜𝑡𝑎𝑙, 𝑓𝑖𝑛𝑎𝑙

(2),𝑚
𝑟𝑒𝑎𝑔𝑒𝑛𝑡𝑠

= ρ
𝑟𝑒𝑎𝑔𝑒𝑛𝑡𝑠

𝑉
𝑡𝑜𝑡𝑎𝑙, 𝑖𝑛𝑖𝑡𝑖𝑎𝑙

After taking a ratio of the resulting mass to the initial reagent mixture mass, the % of𝐶𝑂
2

reagent converted into gas by the reaction is then factored into determining the initial gas𝐶𝑂
2

bubble radius. This ratio is quantified by the “Mass Conversion Factor” in Table 4 below. From

this conversion factor, at the initial point of reaction between the reagents, the estimated initial

volume of gas is found by:𝐶𝑂
2

24



(3),𝑉
𝑖

=
ρ

𝑟𝑒𝑎𝑔𝑒𝑛𝑡𝑠
𝑉

𝑡𝑜𝑡𝑎𝑙, 𝑖𝑛𝑖𝑡𝑖𝑎𝑙

ρ
𝑔𝑎𝑠

 * 𝑀
𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛

with being the initial gas volume. Since there is no gas present prior to reaction𝑉
𝑖

𝐶𝑂
2

𝐶𝑂
2

between the reagents, this initial volume is estimated to be shortly after the chemical reaction

begins.

The change in gas bubble radius is modeled by the following relation:𝐶𝑂
2

(4),𝑅(𝑡) =  𝑅
𝑏𝑢𝑏𝑏𝑙𝑒

[(1 −
𝑃

𝑏𝑢𝑏𝑏𝑙𝑒

𝑃
𝑐ℎ𝑎𝑚𝑏𝑒𝑟

)𝑒
−

3𝑃
𝑐ℎ𝑎𝑚𝑏𝑒𝑟

4µ 𝑡
 +

𝑃
𝑏𝑢𝑏𝑏𝑙𝑒

𝑃
𝑐ℎ𝑎𝑚𝑏𝑒𝑟

]1/3

with being the viscosity of the foam, being the initial gas bubble radius,µ 𝑅
𝑏𝑢𝑏𝑏𝑙𝑒

𝐶𝑂
2

𝑃
𝑏𝑢𝑏𝑏𝑙𝑒

being the initial pressure of the gas at the start of mixing, and being the pressure of𝐶𝑂
2

𝑃
𝑐ℎ𝑎𝑚𝑏𝑒𝑟

the environment surrounding the foam reaction. The maximum change in radius of a singular

gas bubble during expansion can be found by taking the difference between the radial𝐶𝑂
2

expansion for infinite time allowed, , and the initial gas bubble radius at t = 0:𝑅(∞)

(5),∆𝑅 = 𝑅(∞) − 𝑅(0) =  𝑅
𝑏𝑢𝑏𝑏𝑙𝑒

[(
𝑃

𝑏𝑢𝑏𝑏𝑙𝑒

𝑃
𝑐ℎ𝑎𝑚𝑏𝑒𝑟

)1/3 − 1]

The initial pressure of the gas is chosen to be approximately atmospheric pressure, as the𝐶𝑂
2

two reagents begin mixing and reacting within the static mixing chamber while being forced into

the chamber by atmospheric pressure. The initial gas bubble radius is found through the

assumption that each gas bubble is essentially spherical, and thus the change in volume and the

expansion factor can then be found by:

(6).∆𝑉 =  4
3 π(∆𝑅)3 𝑓 =

𝑉
𝑓

𝑉
𝑖

=
𝑉

𝑖
 + ∆𝑉

𝑉
𝑖

One item to note is that the model predicts nearly no expansion in atmospheric pressure

conditions, however the model used the assumption from previous research that polyurethane

25



foams have an expansion factor between 10 - 16 at atmospheric pressure. To account for this

difference, a factor of 14 was added to the final expansion factor. Table 4 and Figure 11 below

summarize the results of applying the model to the polyurethane foam used.

Mass
Conversion
Factor (%)

Initial Gas
Volume (m^3)

Initial Bubble
Radius (m)

Change in
Radius (m)

Change in
Volume (m^3)

Theoretical
Expansion Factor

8.4 ± 0.7 3.8E-4 ± 3.7E-5 4.5E-2 ± 1.4E-3 9.2E-2 ± 1.3E-3 3.2E-3 ± 3.4E-5 23.5 ± 9.7E-2

6.2 ± 0.5 4.0E-4 ± 3.4E-5 4.6E-2 ± 1.3E-3 7.4E-2 ± 6.9E-4 1.7E-3 ± 1.8E-5 19.3 ± 8.5E-2

5.4 ± 0.5 3.5E-4 ± 3.2E-5 4.4E-2 ± 1.3E-3 8.2E-2 ± 1.0E-3 2.3E-3 ± 2.5E-5 21.7 ± 9.1E-2

7.0 ± 0.5 4.5E-4 ± 3.6E-5 4.8E-2 ± 1.3E-3 1.1E-1 ± 1.5E-3 5.4E-3 ± 4.2E-5 27.0 ± 8.0E-2

5.8 ± 0.5 3.8E-4 ± 3.3E-5 4.5E-2 ± 1.3E-3 8.0E-2 ± 8.9E-4 2.1E-3 ± 2.2E-5 20.6 ± 8.8E-2

5.4 ± 0.5 3.5E-4 ± 3.2E-5 4.4E-2 ± 1.3E-3 6.5E-2 ± 5.3E-4 1.1E-3 ± 1.3E-5 18.2 ± 9.1E-2

6.2 ± 0.5 4.0E-4 ± 3.4E-5 4.6E-2 ± 1.3E-3 1.2E-1 ± 1.9E-3 6.9E-3 ± 4.9E-5 32.1 ± 8.6E-2

7.8 ± 0.5 5.0E-4 ± 3.8E-5 4.9E-2 ± 1.2E-3 1.1E-1 ± 1.3E-3 5.3E-3 ± 4.1E-5 25.7 ± 7.6E-2

6.2 ± 0.5 4.0E-4 ± 3.4E-5 4.6E-2 ± 1.3E-3 9.4E-2 ± 1.2E-3 3.4E-3 ± 3.2E-5 23.6 ± 8.5E-2

5.4 ± 0.5 3.5E-4 ± 3.2E-5 4.4E-2 ± 1.3E-3 1.0E-1 ± 1.6E-3 4.3E-3 ± 3.8E-5 27.3 ± 9.2E-2

4.7 ± 0.4 3.0E-4 ± 3.0E-5 4.2E-2 ± 1.4E-3 1.0E-1 ± 1.8E-3 4.5E-3 ± 4.0E-5 30.1 ± 1.0E-1

3.9 ± 0.4 2.5E-4 ± 2.8E-5 3.9E-2 ± 1.4E-3 1.0E-1 ± 2.1E-3 4.3E-3 ± 4.0E-5 32.1 ± 1.1E-1

Table 4: Foam expansion model per test conditions, adjusting factor used to determine initial

amount of gas𝐶𝑂
2

26



Figure 11: Plot of foam expansion factor vs. pressure, measured and theoretical values.

To quantify the difference between the measured expansion factors and those predicted by the

model, a total value of 152.1 was found which corresponds to a reduced value of 12.7.χ2 χ2
𝑣

Since the atmospheric pressure level, room-temperature, and relative densities of each reagent do

not affect the expansion factor of the predicted model, for a value of 152.1 with 11 degrees ofχ2

freedom, the resulting p-value is on the order of 2E-26, and would thus result in a rejection of the

null hypothesis which assumes the model is a valid model for foam expansion.

5 DISCUSSION
5.1 Findings from Data Analysis
From the plot in Figure 11, visually there is a clear difference between the expansion factors

predicted by the foam expansion model and our measured values. Only a singular point is in

agreement with the model within uncertainties, and thus this leads to an extremely high reduced

of 12.7. The p-value of 2E-26 resulting from the goodness of fit test suggests significantχ2
𝑣

rejection of the null hypothesis at any level. However, despite the significant difference, the

27



measured expansion factors appear to follow a relatively flat or slightly increasing trend as

pressure decreases. The foam expansion model also predicts this behavior, with the expansion

factor scaling as . For pressures in this range, the model does not predict(𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒)−1

incredibly large increases in expansion factor. Thus, the data behaves similarly to the model,

however that does not resolve the significantly large expansion factors measured.

The model assumes that the percentage of initial reagent mixture mass being converted into 𝐶𝑂
2

gas is consistent, however failure to properly mix the reagents together into this initial mixture

may alter that percentage, thus resulting in less gas produced by the reaction. The result𝐶𝑂
2

would be a decrease in expansion factor, however in this case a lower expansion factor would

further align the model and the measurements, as opposed to causing a deviation away from the

model. The atmospheric pressure level, room temperature, and reagent densities did not affect

expansion factors when changed, thus these factors did not deviate the measurements from the

model.

5.2 Sources of Error
During our data collection, it was apparent that some of our results were subject to sources of

error and uncertainty. In our particular case, our system was not automated, and therefore, while

we were conducting experiments, we introduced variables of human error into the equation. The

most common example was not releasing both of the foams into the static mixing chamber

simultaneously, resulting in inadequate mixing that often led to a lack of expansion. During the

experiments in which our ratio was 1:1, this was not as big of an issue, but we wanted to test

different ratios of our foam reagents to see whether certain factors within the foam (viscosity,

density, etc) would affect its expansion. Therefore, we adjusted our ratios to 1:2 and 2:1 (5 mL of

reagent A vs 2.5 mL of reagent B, for example), which meant that the person deploying the

reagent with more volume had to deploy at a faster rate than the person deploying the reagent

with less volume. This led to scenarios in which the timing of the experiment was not precise,

which is a critical factor for achieving the ideal foam expansion ratio.

28



Additionally, precision errors in our equipment affected our physical measurements. The

syringes that we used to measure the initial volume of and deploy the foam reagents were

capable of measuring volume at a resolution of 0.2 mL, and thus leading to errors on the initial

volume on that order. Our measuring cups used to determine final expanded volume also had

precision limitations, being capable of measuring volume at a resolution of 10 mL. As observed

during testing, due to the foam not uniformly filling the volume of the cup as it expanded, a

larger uncertainty would be required for each expanded volume. For that reason, the uncertainty

on expanded volume was adjusted to the resolution summed with the square root of the expanded

volume, as larger expansion would lead to less uniform filling of the cup. The pressure gauge

used to measure pressure in the vacuum system had a resolution on the order of 0.001 millibar,

thus leading to pressure uncertainties on that order. The combination of lack of precision

between the timing and the initial volume of the mixture caused our reactions to fall under

expectations.

Another issue our team ran into that we believe could have contributed to our experiments were

the air bubbles that accumulated when measuring our foam reagents using the syringe. Research

suggests that there is a strong dependance of the foam expansion process from the external

pressure and “as pressure decreases…. the final volume and the reaction time increases”.

However, air bubbles introduce an increase in external pressure while the foam is being deployed

into the static mixing chamber. Experiments from previous papers also showed that introducing

bubbles into the mixture created complexity based on how the bubbles reacted with each other,

causing the bounding surfaces to form abnormal shapes where the increase in surface tension

caused our reactions to collapse and lose a significant portion of the expected expansion ratio.

6 CONCLUSION
Space debris management continues to be a relevant issue of discussion as thousands of satellites

enter low Earth orbit each year. Of various removal systems that have been proposed and being

developed, foam-based removal showed promise for its adaptability to a range of debris sizes

and its relative operational simplicity. From research and testing, a polyurethane foam is likely

29



the simplest and least expensive option to get expansion and adhesion in space – however, its

deployment presents unique challenges with vacuum and microgravity. This paper explored

behavior of the former environmental factor, testing the expansion of a commercially available

polyurethane foam under low-pressure environments to quantify the expansion factor as a

function of air pressure. Testing found that the foam expansion exceeds predictions down to an

air pressure of around 70 millibar, where the foam would tend to structurally collapse under its

own weight. During testing, problems with foam reagent deployment timing, adhesion, as well as

structural integrity upon deployment were encountered and recorded. In particular, reagents

sticking to the sides of the deployment system tubes Full rectification of these problems could

be focuses of further research, which would be incremental towards the verification of foam

deployment viability in vacuum. In addition, a microgravity environment may present different

structural behavior than what was encountered in this testing, where the foam may not collapse

due to its low density when deploying in vacuum. All of these factors will need to be evaluated

to show that foam as a space debris removal method will actually function in its intended

working environment, prior to evaluating its deorbiting performance.

30



7 APPENDICES
7.1 Appendix A: Equity — Impact Analysis
Space debris removal is a specialized field that has not had a lot of research done into how it

could have an equitable impact on the affected populations. For that reason, we did not place a

strong emphasis on that aspect of our research in our literature review. However, there are ways

that this research could apply in that scope.

A lot of the satellites that currently exist in LEO are useful in day to day life, whether they be

weather observing satellites, communication satellites used in phones, or satellites used in radios.

If the continuing space debris problem worsens, it could lead to the disruption of these services

for certain populations; populations that could very much rely on these services, and have limited

access to alternative solutions. As an example, without satellites to monitor weather, people may

find it a lot more difficult to prepare for predictable natural disasters like incoming hurricanes. In

our equity-impact report, we will focus on aspects such as the one described.

It was also our intention to cite sources from a diverse collection of researchers. However, we

ran into a problem with this because of the novelty of foam-based remediation methods. There is

not a lot of existing research in the field of space debris, and even less so that focuses on foam

methods. For this reason we have decided we may not be able to address citation bias as we

originally intended within our paper.

31



7.2 Appendix B: Project Timeline
Sophomore Year (2020–2021)

FALL:

● Complete project proposal.

● Design and present preliminary testing procedures.

● Select and purchase the initial set of foams.

SPRING:

● Test viability of foams for intended testing.

● Begin design of static mixing nozzles.

● Flesh out testing procedures, and test chamber design.

● Decide on final candidates for foam procedures.

Junior Year (2021–2022)

SUMMER:

● Finalize testing designs, and purchase any components not already obtained.

● Create timeline for testing procedures for upcoming year.

FALL:

● Run prepared tests and begin collecting data.

● Create models based on experimental data.

● Prepare for the Do Good Showcase.

32



SPRING:

● Continue to iterate on nozzle design.

● Streamline tests for consistent foaming data.

● Develop the results from the tests.

Senior Year (2022–2023)

SUMMER:

● Continue data collection if needed.

● Wrap up research and continue data analysis.

● Plan schedule for thesis completion.

● Find research conferences to attend.

FALL:

● Work on thesis according to the determined schedule.

● Collect any final data needed for the thesis.

● Plan for research conferences.

SPRING:

● Complete the thesis and present at thesis defense.

33



7.3 Appendix C: Budget

Component Unit Cost Quantity Total

Vacuum Chamber $0.00* 1 $0.00

Solenoid Valves $50.00 4 $200.00

Manual Valves $15.00 10 $150.00

Graduated Cylinder $8.00 1 $8.00

Foam Reagents $20.00 10 $200.00

Printing Filament $0.00** N/A $0.00

Hypodermic Needles $0.70 10 $7.00

Testing Rig Frame Materials $250 Various $250.00

Net Total $815.00

*Use of vacuum chamber is free through the Space Power and Propulsion Lab

** Use of 3D printers is free under private ownership and on-campus resources

34



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