10.26 Final Report

i
Oil Sorption Kinetics of Electrospun Nanofiber Membranes
Jennifer Subler, Francesca Majluf, and Anna Neuman
10.26
Professor Gregory Rutledge
Teaching Assistant Yi-Min Lin
Final Report
Second Draft
May 17, 2017

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Dear Professor Rutledge,
We chose to follow nearly all of your suggestions. The largest change in this work is the
incorporation of the tensiometer method and preliminary results from it, which you will find
impacts nearly every section. Additionally, we restructured some parts of the paper, making the
introduction much more high-level, moving details into the methods section, and moving
derivations into the appendix when appropriate. A large amount of data collected after the
submission of our final draft was added to the work and many new conclusions and hypotheses
are touched upon in the discussion. Particularly, we formulated stronger ideas for future
recommendations supported by our methods and models and have included those in the
discussion.
We have also made several grammar and style changes based on Juergen’s comments.
We believe that these will make the paper significantly more clear. The most significant change
we made was attempting to point out the important numbers and details in tables and figures
within the text of the work to make the large amount of data we have easier to process.
Additionally, we added some details in explaining technical terms, parameters, and experimental
setups that we had left out because it had become obvious to us by the end of the term, but would
not be obvious to any reader.
We believe that this paper clearly states our progress and conclusions from the term. We
hope it can stand as a foundation for the next 10.26 team that continues our work.
Best,
Anna, Francesca, and Jennifer

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Contents
Abstract........................................................................................................................................... 1
1. Introduction................................................................................................................................. 1
1.1 Motivation, Background, and Objective............................................................................... 1
1.2 Theoretical Kinetics Models................................................................................................. 4
1.3 Approach............................................................................................................................... 5
1.3.1 Choosing a Polymer Solution and Oil ........................................................................... 6
1.3.2 Collecting and Fitting Kinetics Data.............................................................................. 6
1.3.3 Varying Oils................................................................................................................... 7
2. Methods....................................................................................................................................... 8
2.1 Materials Specifications........................................................................................................ 8
2.2 Electrospinning Membranes ................................................................................................. 9
2.2.1 Original Membranes ...................................................................................................... 9
2.2.2 Thick Membranes ........................................................................................................ 10
2.2.3 Long Membranes ......................................................................................................... 10
2.3 Characterizing the Membrane and Oil................................................................................ 11
2.4 Timed Capacity................................................................................................................... 12
2.5 Filmed Distance .................................................................................................................. 13
2.6 Tensiometer......................................................................................................................... 14
3. Results....................................................................................................................................... 14
3.1 Characterization of Material and Oils................................................................................. 15
3.2 Timed Capacity Experiment ............................................................................................... 18
3.2.1 Timed Capacity for Soybean Oil ................................................................................. 18
3.2.2 Capacity ....................................................................................................................... 21
3.3 Filmed Distance Experiment............................................................................................... 22
3.3.1 Fits to Gravitational and Non-Gravitational Model for Soybean Oil .......................... 22
3.3.2 Comparison of Fitted and Calculated Parameters for Soybean Oil ............................. 24
3.3.3 Fits to Gravitational and Non-Gravitational Model for 5 cSt Silicone Oil.................. 25
3.3.4 Comparison of Fitted and Calculated Parameters for 5 cSt Silicone Oil..................... 25
3.3.5 Fits to Gravitational and Non-Gravitational Model for 20 cSt Silicone Oil................ 26
3.3.6 Comparison of Fitted and Calculated Parameters for 20 cSt Silicone Oil................... 26
3.3.7 Estimated Equilibrium Height and Time for Both Oils............................................... 27

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3.3.8 Changes in Marmur Parameters over Time ................................................................. 27
3.4 Comparison of Timed Capacity and Filmed Distance Methods......................................... 28
3.5 The Tensiometer Method.................................................................................................... 29
4. Discussion................................................................................................................................. 30
4.1 Timed Capacity................................................................................................................... 30
4.1.1 First vs. Second Order.................................................................................................. 30
4.1.2 Problems with Timed Capacity Experiments .............................................................. 30
4.2 Filmed Distance and the Marmur Model............................................................................ 32
4.2.1 Gravitational vs. Non-Gravitational Model ................................................................. 32
4.2.2 Comparison Between Oils ........................................................................................... 33
4.2.3 Comparison of Fitted Parameters to Calculated Values .............................................. 35
4.2.4 Problems with the Filmed Distance Method................................................................ 36
4.3 The Tensiometer Method.................................................................................................... 37
4.4 Comparison of Methods and Future Recommendations..................................................... 38
5. Conclusion ................................................................................................................................ 40
References..................................................................................................................................... 41
Appendix 1: Image of Filmed Distance Lab Set Up..................................................................... 43
Appendix 2: Different Electrospinning Set-Up ............................................................................ 43
Appendix 3: Permeability Calculations ........................................................................................ 44
Appendix 4: Surface Area Approximation ................................................................................... 44
Appendix 5: Sample Marmur Calculations Calculations.............................................................. 45
Appendix 6: Example of Fingering in the Oil Front..................................................................... 46

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List of Figures
Figure 1: Electrospinning apparatus schematic .............................................................................. 2
Figure 2: Timed capacity method for measuring kinetics. ............................................................. 7
Figure 3:Filmed distance method for measuring kinetics............................................................... 7
Figure 4: Tensiometer method for measuring kinetic..................................................................... 7
Figure 5: A SEM image of a 75:25 PS/PAN membrane. ............................................................. 16
Figure 6: Capacity vs. time data for a membrane of average thickness. ...................................... 18
Figure 7: The first and second order fits for average thickness membrane.................................. 19
Figure 8: Capacity vs. time for a thick membrane........................................................................ 20
Figure 9: The first and second order fits for a thick membrane.................................................... 21
Figure 10: Filmed distance-vs.-time data for three soybean oil trials........................................... 24
Figure 11: The data for the two trials run with 5 cSt grade silicone oil….................................25
Figure 12: The data for the two trials run with 20 cSt grade silicone oil ..................................... 26
Figure 13: Mass and distance data for the tensiometer experiment.............................................. 29
Figure 14: Distance and distance approximated by the mass measurements of the tensiometer
experiment..................................................................................................................................... 29
Figure 15: Equipment to film distance vs. time............................................................................ 43
Figure 16: Image of Setup for spinning thicker and longer membranes....................................... 43
Figure 17: An example of fingering in the oil front...................................................................... 46
List of Tables
Table 1: 25/75 PAN/PS Long Membrane Properties.................................................................... 15
Table 2: Soybean Oil Properties ................................................................................................... 17
Table 3: 5 cSt Silicone Oil Properties........................................................................................... 17

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Table 4: 20 cSt Silicone Oil Properties......................................................................................... 17
Table 5: First and Second Order Parameters for Average Thickness Membrane......................... 19
Table 6: First and Second Order Parameters for Thick Membranes ............................................ 21
Table 7: Maximum Capacity ........................................................................................................ 22
Table 8: Parameters for Soybean Oil Marmur Model .................................................................. 24
Table 9: Marmur Parameters for 5 cSt Silicone Oil ..................................................................... 25
Table 10: Marmur Parameters for 20 cSt Silicone Oil ................................................................. 27
Table 11: Maximum Height and Time.......................................................................................... 27
Table 12: Marmur Parameters over Time..................................................................................... 28

1
Abstract
Oil spills are highly disruptive to marine environments. Sorbents, particularly electrospun
nanofiber membranes, are a promising alternative to current oil remediation methods. However,
there is little in literature about the kinetics of the sorption process, which is vital in developing
useful sorbents. This project aims to find a reliable method to measure kinetics experimentally
and fit the results to theoretical equations based on material and oil properties. In this project,
three different measurement methods, timed capacity, filmed distance, and the tensiometer
method were evaluated by fitting experimental data to three possible theoretical models. Of these
three methods, the filmed distance method produced the most reliable data that fit well to a
theoretical model and that theoretical model was quantitatively related to physical properties. In
contrast, the timed capacity method resulted in only equilibrium data and can only be fitted to a
theoretical model that is not empirically related to properties. The tensiometer method produced
reliable mass data, but was not fully developed. Future work should focus on the development of
a mathematical relationship between mass and distance that can be used to apply the tensiometer
data to a theoretical model related to physical properties.
1. Introduction
1.1 Motivation, Background, and Objective
Throughout the years, oil spills have had disastrous consequences for aquatic ecosystems
and have resulted in financial losses for the oil and gas industries (1) . Methods for oil recovery
include using skimmers and booms, burning the oil, and using sorbents (1). Out of all these
methods, sorbents are preferable because they are not environmentally harmful and can work in
more turbulent water conditions (2).

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Sorbents are materials that absorb or adsorb oil. Good sorbent materials have high
selectivity for oil over water in addition to having mechanical stability, high oil sorption capacity
and fast uptake rate (1). Electrospun polymer membranes are promising oil sorbents. The
nanofiber morphology offers a large surface area, which is beneficial for adsorption, and small
pore diameter, which promotes capillary action (3). Additionally, they can be made from
polymer blends to combine desirable polymer properties (4,5).
Electrostatic processing, or
electrospinning, is a well-researched
method to form nanofibrous mats of
synthetic polymers (1). Electrospinning
works by pumping a polymer solution
through a needle subjected to an electric
field, which creates repulsion forces that
drive the polymer stream into a winding
jet. As the jet moves through air, the
solvent evaporates and polymer nanofibers
are collected. This process is shown in Figure 1.
To take advantage of different desirable polymer properties, multiple polymers can be
blended into one membrane using electrospinning. Polystyrene (PS) membranes have been
widely employed as an oil sorbent due to their hydrophobicity and oleophilicity yet these
membranes lack the structural integrity necessary for sorbent materials (6). Because of this,
polystyrene has been blended with polymers such as polyacrylonitrile (PAN), polyurethane (PU)
and polyvinylchloride (PVC) to provide stability in the electrospun mats (4,5,7).
Figure 1: Electrospinning apparatus schematic depicting the
power supply, electrodes, solution, syringe, needle and cone
formed due to the electric field that the polymer is subjected to. As
the solvent evaporates, nanofibers are collected in the form of a
mat. Figure from (1)

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In order to characterize electrospun membranes, researchers have focused on measuring
capacity (how much oil a membrane can hold), selectivity (how likely it is that the membrane
sorbs oil over water), and retention (how well a membrane can contain oil over time), but little
has been done to measure oil sorption kinetics (4,3,7). Fast kinetics are crucial for a successful
sorbent material; it is not feasible to leave materials on the ocean for several days. An ideal
sorbent should sorb large amounts of oil within minutes. Not only is the speed of sorption
lacking in understand, but the mechanism behind this sorption have also not been investigated in
depth. A better understanding of the mechanism of sorption can allow researchers to more
effectively optimize membranes.
Typically, sorption capacity is used as the main comparison factor between sorbents. It is
often related to multiple material and oil properties to explain why certain sorbents outperform
others (5–7). These properties include geometric properties of the membrane, such as surface
area and fiber diameter, which are closely related to the complimentary adsorption and capillary
action parts of the sorption mechanism. Other relevant membrane properties are porosity, which
affects the volume available for oil retention, permeability, which describes how oil flows
through the material, and contact angle, which is a measurement of the affinity between a liquid
and material based on the angle formed between a drop of oil and the surface of the membrane.
In addition, oil properties, such as viscosity, surface tension, and density, can affect oil sorption
capacity. These same properties impact the kinetics of oil sorption. Understanding how the oil
and material properties affect kinetics provides a more intelligent path toward optimization,
particularly if the characteristics with the greatest impact on kinetics are revealed.
This project aimed to obtain a clear and consistent method for measuring oil sorption
kinetics of electrospun nanofiber membranes. A successful method is one that results in

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repeatable data that fits well to a theoretical model. An ideal model allows for kinetics to be
empirically related to material and oil properties.
1.2 Theoretical Kinetics Models
In this project, experimental data was fitted to multiple kinetics models to find the model
that best describes sorption kinetics and relates it to material and oil properties. Two of these
kinetics models are first and second order kinetics, represented by equations [1] and [2]
respectively (3). Here, the change of capacity over time is modeled. Qt is the capacity of the
membrane at time t, Qe is the equilibrium capacity of the membrane, and k1 and k2 are rate
constants.
𝑑𝑄𝑡
𝑑𝑡
= 𝑘1(𝑄 𝑒 − 𝑄𝑡) [1]
𝑑𝑄𝑡
𝑑𝑡
= 𝑘2(𝑄 𝑒 − 𝑄𝑡)2
[2]
Equations [1] and [2] are integrated and linearized for ease of use in data fitting. The
result is equations [3] and [4], for first and second order respectively. If experimental data fits
either model, the plot for equation [3] or [4] using experimental data is a straight line.
ln(𝑄𝑡) = ln(𝑄 𝑒) + ln(𝑄 𝑒) ∗ 𝑘1 𝑡 [3]
𝑡
𝑄 𝑡
=
1
𝑘2 𝑄 𝑒
2 +
𝑡
𝑄 𝑒
[4]
It is common in literature to use data points past equilibrium. When this is done, the
second order fit is the line “time = constant*time”, thus leading to an artificially good fit between
the second order model and the data (4,3). When analyzing kinetics, only pre-equilibrium data
provide useful information. Yet even if the correct data is utilized, these models’ constants lack
an explicit physical meaning and thus its use in quantifying sorbent materials is abstract and non-
ideal.

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The third theoretical model, developed by Marmur in 2003 (8), models one-directional
capillary penetration of fluids into porous media. Marmur creates an alternative to the Lucas-
Washburn equation for use in porous media. Instead of using the Haigen-Poiseulle equation for
flow through a tube, he uses the Darcy equation for flow through porous media. The pressure
drop in the Darcy equation is then defined by balancing the forces due to capillary action and
gravity. The resulting equation and parameters involved are in equations [5] to [8]. Marmur also
derives a complimentary equation in which gravity is neglected in the force balance. This
equation and its parameter are equations [9] and [10].
𝐴∗
𝑡 = −𝐵∗
𝑥 − ln(1 − 𝐵∗
𝑥) [5]
𝐴∗
=
𝐶𝜀3 𝜌2 𝑔2
𝑆3(1−𝜀)3 𝜇𝜎𝑐𝑜𝑠𝜃
[6]
𝐵∗
=
𝜀𝜌𝑔
𝑆(1−𝜀)𝜎𝑐𝑜𝑠𝜃
[7]
𝑘 = 𝐶
𝜀3
𝑆2(1−𝜀)2 [8]
𝑥2
= 𝐷𝑡 [9]
𝐷 =
2𝐶𝜀𝜎𝑐𝑜𝑠𝜃
𝑆(1−𝜀)𝜇
[10]
where A, B, C, and D are constants defined by equations [6], [7], [8], and [10] respectively, t is
time, x is the distance traveled by the oil, 𝜀 is the porosity of the membrane, 𝜌 is the density of
the oil, g is the gravitational constant, k is the permeability, S is the specific surface area (area
per volume) of the membrane, 𝜎 is the surface tension of the oil,  is the viscosity of the oil, and
𝜃 is the contact angle between the oil and polymer membrane.
1.3 Approach
The project was divided into three main phases. The first phase involved choosing a
polymer composition and oil with which to test and validate our kinetics experiments. The

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second and most complex phase involved collecting all the data and properties necessary to
compare kinetics data to theoretical models. The third phase involved verifying the best
measurement method and matching model with oils of varying characteristics.
1.3.1 Choosing a Polymer Solution and Oil
The optimal polymer blend, 15% (w/w) 75:25 PS/PAN, was determined by the 10.26
group in 2015. This blend is easily spun, has relatively high oil capacity, and sorbs oil at an
easily observable rate. Soybean oil was used to preliminary testing due to ease of access and use.
1.3.2 Collecting and Fitting Kinetics Data
Three different methods were used to collect kinetic data relevant to the theoretical
models. The first method repeated what has been done in previous literature: manually measure
capacity vs. time (4,3), see Figure 2. These data were used with the first and second order
models. The second method was to film the advancement of an oil front up the membrane and to
use image analysis software to obtain distance-vs.-time measurements, as shown in Figure 3.
These measurements were used with the Marmur model. The third and final method involved
using a tensiometer to measure changes in mass in the membrane over time. These mass points
were converted to distance using equation 11 in order to fit the data to the Marmur model.
𝑑 = 𝑚 𝑜𝑖𝑙 ∗
1
𝜌 𝑜𝑖𝑙
∗
1
𝐴 𝑐𝑟𝑜𝑠𝑠∗𝜀
[11]

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Figure 2: Timed capacity method for measuring
kinetics. Here, timed mass measurements are taken for
the membrane submerged in oil and used to obtain
capacity-vs.-time measurements. The oil flows into the
membrane from either of its faces.
Figure 3:Filmed distance method for measuring kinetics. The
camera films from this angle, and image analysis software uses
the ruler to output accurate distance-vs- time data points.
Figure 4: Tensiometer method for measuring kinetics. The tensiometer measures the change in mass in the
membrane over time. The tensiometer has the ability to measure very small time points.
1.3.3 Varying Oils
The last stage of this project consisted of verifying that the best method for kinetics
measurement can be applied to different types of oils. Ideally, the method provides repeatable
measurements with small standard deviations between trials and data that fits well to a
theoretical model. One purpose of varying oils is to verify that the process is widely applicable.
A second purpose is to ensure that changes in properties result in predicted changes in kinetics,
for example a more viscous oil should sorb more slowly.

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Silicone oil was chosen as the next oil for testing. The densities of soybean oil and
silicone oil are similar. Therefore, the experiment focused on changing two characteristics,
viscosity and surface tension. Two silicone oils of varying viscosities (5 cSt and 20 cSt) were
used to test a full range of viscosities. Each of these oils had a surface tension that was
approximately half that of the soybean oil surface tension. The changing properties were used to
determine if experimental values would follow the trends defined by the Marmur model,
particularly as defined in Equations [6] and [7].
2. Methods
The project consisted of electrospinning three types of membranes and measuring their
kinetics through measuring two different methods: timed capacity and filmed distance. Soybean
oil was used to evaluate both methods for measuring kinetics and silicone oil was later on used to
verify that the superior method still applied to an oil with a different viscosity.
2.1 Materials Specifications
All chemicals were obtained from Sigma-Aldrich. Soybean oil as a dietary source of
long-chain triglycerides and other lipids was acquired for preliminary experiments. Silicon oils
with viscosity of 20 cSt and 5 cSt were used for testing our method for measuring. N, N-
Dimethylformamide (DMF) was acquired as the solvent for all polymer solutions used for
electrospinning. Polyacrylonitrile (PAN) with average Mw 150,000 and polystyrene (PS) of
analytical standard, for GPC, 3000, were obtained as the polymers for the solution used to
electrospin. Oil red O (oil dye), certified by the Biological Stain Commission, was used to dye
the soybean oil when conducting the filmed distance experiments.

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2.2 Electrospinning Membranes
A solution of 15% (w/w) 75:25 PS/PAN in DMF was prepared and stirred overnight. A
batch of 50 ml was prepared each time, and thus 5.63 g of PS and 1.87 g of PAN were added to
42.5 ml of DMF. An unused 10 ml syringe was used to collect around 6 ml of this solution and it
was connected to a tube with a needle point that had been previously washed with DMF. The
syringe was then placed on a Harvard Apparatus 11 Syringe Pump and the needle was inserted
into an insulated acrylic box and secured pointing downwards to a stand inside. A power supply
was hooked to the needle and a collecting platform was placed 28 cm under the tip of the needle
and grounded. One can refer back to Figure 1 for a rough schematic of the placement of the
needle, power supply and collecting plate. Three different kinds of membranes were spun. All
preliminary electrospinning studies and membrane characterizations in this project were done
using the original membrane. To measure capacity vs. time, thicker membranes were spun. To
measure distance vs. time, longer membranes were spun. Depending on the kind of membrane
desired, the remaining parameters varied.
2.2.1 Original Membranes
In order to begin electrospinning membranes, 20 cm by 20 cm stationary steel stand was
used as a collecting platform. Standard Reynolds Aluminum Foil covered the platform at first to
start spinning and fine tune the voltage. Once a stable fiber was observed, a sheet of Non-Stick
Reynolds Aluminum Foil was placed on the collecting platform to accumulate the membrane.
The power and pump were run at constant voltage of 24 kV and flow rate of 0.04 ml/min
respectively for 20 minutes. At the end of this period of time, the power supply was shut off and
the plate was grounded. The foil was then recovered and a circular membrane with a diameter of

10
20 cm was obtained. These membranes were what will be referred to as the “original”
membranes, and what were used for all preliminary characterization and kinetics experiments.
2.2.2 Thick Membranes
In order to spin membranes thicker than our initial membranes, the collecting area was
reduced to 5 cm by 5 cm. To accomplish this, a 1/4th
inch thick acrylic sheet was laser cut as a 25
cm by 25 cm square with a 5 cm by 5 cm square cut out of the center. This acrylic piece was
placed on top of the 20 cm by 20 cm collecting platform covered with standard Reynolds
Aluminum Foil. This setup can be seen on Appendix 2, part A. Like with the original
membranes, once a stable fiber was observed, a sheet of Non-Stick Reynolds Aluminum Foil
was placed on the collecting platform under the acrylic piece to accumulate membrane. The
power and pump were run at constant voltage of around 25 kV and flow rate of 0.04 ml/min
respectively for 30 minutes. At the end of this period of time, the power supply was shut off and
the plate was grounded. The acrylic piece and foil were then recovered and a square membrane
with side length of 5 cm and a thickness of 0.5 to 0.7 mm (about twice that of the original
membranes) was obtained. These thick membranes were used for timed capacity experiments
after the original membranes proved to have kinetics that were too fast to measure.
2.2.3 Long Membranes
In order to spin longer membranes, the collecting area was replaced with a rotary
cylinder. Metal mesh was cut and taped together to form a cylinder with length of 20 cm and
radius of 7 cm and covered with standard Reynolds aluminum foil. This cylinder was then taped
to a rotary motor and supported on the other side by a 3/4 inch steel pole attached to a grounded
stand. This setup can be seen on Appendix 2, part B. Like with the other membranes, once a
stable fiber was observed, a sheet of Non-Stick Reynolds Aluminum Foil was placed on the

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collecting cylinder to accumulate membrane. The power and pump were run at constant voltage
of around 29 kV and flow rate of 0.04 ml/min respectively for 1 hour. At the end of this period of
time, the power supply was shut off and the cylinder was grounded. The foil was then recovered
and membrane with length of 40 cm and width of 15 cm was obtained. These long membranes
were used for the filmed distance experiments.
2.3 Characterizing the Membrane and Oil
Multiple properties of the membranes were characterized. The thickness was measured
with a Mitutoyo CLM1.6”QM digital micrometer using a constant force of 0.005 N. Length and
width were measured with a 30 cm ruler. The initial mass was measured using a Mettler Toledo
(AB204-S) balance with resolution of 0.1 mg. A Rame-Hart goniometer at the Institute for
Soldier Nanotechnologies (ISN) was used to measure the contact angle of two representative
membranes. The density of the polymer was obtained from the supplier. Specific surface area
was found using an ASAP 2020 Surface Analyzer in the ISN. Fiber diameter was found using
images from a JEOL 6010LA Scanning Electron Microscope (SEM) and the SEM’s software.
Four representative samples were used and 10 different fiber diameter measurements were taken
from each sample. The final value is an average of all measurements. Permeability was measured
by flowing water through a pressure controlled cell and measuring the flow rate of water.
Darcy’s law is then used to calculate the permeability (Appendix 3). JoyFay rotary viscometer
was used to measure the viscosity of oil. The density of the oil was found by measuring the mass
of multiple volumes of oil. Both of these measurements were completed three times per oil. The
built-in pendant drop method experiment was used on the Rame-Hart goniometer to measure the
surface tension of the oil. Porosity was found using equation [12], where m is mass, ρ is density
of the polymer, A is the membrane area, and T is membrane thickness.

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𝜀 = 1 −
𝑚
𝜌𝐴𝑇
[12]
2.4 Timed Capacity
In order to collect mass-vs.-time data, an electrospun membrane was placed into oil for
multiple time periods with a mass measurement taken at the end of each one. The membrane
piece of around 4 cm by 3 cm was affixed to a metal mesh of those same dimensions and mesh
size of 0.5 cm. This attachment was done by massing the piece of mesh, placing it on a hot plate
at a high setting for around ten minutes, and pressing it on the stretched membrane for a couple
of minutes using the bottom of a beaker. The temperature of the mesh was chosen to be low
enough to neither alter the properties of the mesh nor damage the membrane. Once the
membrane was fused to the mesh, it was cooled back down to room temperature.
Around 50 mL of soybean or silicone oil were placed in a 250 mL beaker. The membrane
was dropped inside the beaker and the timer was started. Refer to Figure 2 for a schematic of this
setup. While the membrane was allowed to sorb oil, a new piece of aluminum foil was set on the
balance to serve as a clean weighing tray. After a fixed time, between one and thirty seconds, the
membrane was removed from the beaker. The exact time was recorded. The membrane was
allowed to drip until the drips were five seconds apart and then the membrane was massed. The
mass value was recorded.
This process was repeated several times. When the mass values observed were
approximately equivalent, the membrane was assumed to be at equilibrium and the experiment
was stopped. The mass-vs.-time data was then converted into capacity-vs.-time data with
equation [13], where mf is mass after sorption and mo is mass before sorption.
𝑄 =
𝑚 𝑓− 𝑚 𝑜
𝑚 𝑜
[13]

13
2.5 Filmed Distance
In order to have a structural support to collect distance-vs.-time data, an acrylic frame
with a small platform for the camera was laser cut. This frame had dimensions of 20 cm by 20
cm by 30 cm and the camera stand had dimensions of 20 cm by 5 cm by 2.5 cm. A 1 L beaker
containing 100 ml of soybean or silicone oil dyed red was placed at one end of the box. The
camera stand was fit to the other end of the box and the camera was placed on it. This set up is
shown in Appendix 1. Markings around the beaker and the camera were made to ensure that the
beaker and camera would be placed on the same spots every time and thus all experiments would
be filmed at the same angle. A stand with a clamp hanging vertically above the center of the
beaker was placed behind the frame. A ruler was taped to the top right edge of the frame. The
sample was clamped parallel to the ruler above the beaker. The sample was at the same
horizontal plane of the ruler to ensure the ruler could be used as a reference point. In order to
keep the sample stretched out, it was laid on metal mesh, but not fused into it, given that the
clamp and static attraction between the mesh and membrane were enough to hold the mesh and
membrane together.
To begin the experiment, the camera was started and the sample was lowered to
submerge the bottom face around 0.3 centimeters into the oil. Refer to Figure 3 for a schematic
showing the camera’s point of view. The camera recorded until the end of the third hour.
Screenshots of the video were taken thirty seconds apart for the first ten minutes and then ten
minutes apart until the end of filming. After the first three hours, a picture was taken each hour
for thirteen to fifteen hours. For some trials, the length expanded beyond fifteen hours. When
using silicone oil, pictures were taken during the first three hours instead of a video, since the oil
dye did not work with the silicone oil and thus it was impossible to see the advance of the front

14
without flash from the camera. These pictures were taken every minute for the first 10 minutes,
and every 10 minutes after that for the next three hours. The Image Analyzer tool from
Mathwork’s MATLAB (Version R2017a) was used to measure the distance of the oil front in
each picture using the ruler to correlate pixels to distance in centimeters. From every picture, 10
distance points were measured and the average was taken to obtain one value per picture.
2.6 Tensiometer
In order to relate the timed capacity and filmed distance experiments, a TA.XT Plus
Texture Analyzer available in the McKinley Lab was used. The setup was the same as the filmed
distance experiment, yet the membrane and mesh were attached to the Texture Analyzer’s clamp,
which was connected to a spring that recorded the changes in mass of the sample over time. The
tensiometer took a mass measurement every 0.005 seconds with a resolution of 0.001 mg. A long
membrane was used for this experiment, and pictures were also taken of the advancement of the
front to be able to compare the mass vs. time data with distance vs. time data. This experiment
was run for 90 minutes with one picture taken every five minutes.
3. Results
The main results of this project include characterization of material and oil and data from
two experiments, the timed capacity and filmed distance experiments, in addition to a
preliminary trial of the third experimental method, the tensiometer. The timed capacity results
include capacity-vs.-time data and fits to the first and second order models. The filmed distance
results include distance-vs.-time data and fits to the Marmur model as well as parameters
calculated from material and oil properties. A brief set of calculations is included attempting to
relate the two methods together. The tensiometer method provides mass-vs.-time and distance-
vs.-time data from the same trial and an attempt to quantitatively relate the two.

15
3.1 Characterization of Material and Oils
Multiple properties of the long membrane were experimentally determined. The material
properties are listed in Table 1. The values given for width, length, thickness, and mass are the
average values for eight long membranes. The long membranes are the only ones used for trials
of the filmed distance method. As material properties are used in Marmur calculations, these
membranes’ properties are the most pertinent. Porosity was calculated for each sample using
equation [12] and the value in Table 1 is an average. Contact angle and diameter were measured
for four representative samples. A sample SEM image, used to find diameter, is shown in Figure
5. Permeability was experimentally measured by flowing water through a set area of membrane
and measuring the flux. Darcy’s law was then used to calculate permeability based on this flux.
A detailed calculation is shown in Appendix 3. Specific surface area for five original membranes
was determined using a surface analyzer. An approximation for surface area was derived and is
shown in Appendix 4. In order to determine the surface area of the long membranes, which have
a different fiber diameter, the same approximation was used but was multiplied by the ratio of
the surface analyzer result to the approximation result for the original membranes. The resulting
equation is equation 14. Both the value from the surface analyzer and from equation 14 are
shown in Table 1.
𝑆 = 2.71 ∗
(1−𝜀)𝐴
𝜋𝑅2 ∗(2𝜋𝑅𝐿+ 2𝜋𝑅2)
(1−𝜀)𝐴𝐿
[14]
Table 1: 25/75 PAN/PS Long Membrane Properties
Property Value
Porosity (%) 94.8 ± 1.2
Width (cm) 8.23 ± 0.64

16
Length (cm) 31.0 ± 1.0
Thickness (mm) 0.127 ± 0.034
Initial Mass (g) 0.171 ± 0.024
Diameter (microns) 1.238 ± 0.097
Contact Angle (degrees) 0 (for all oils)
Measured Surface Area (m2
/m3
) 1.10 x 107
Approximated Surface Area (m2
/m3
) 8.74 x 106
Permeability (m2
) 1.39 x 10-13
± 0.03 x 10-13
Figure 5: A SEM image of a 75:25 PS/PAN membrane. It is obtained with a scale of 5 microns. Using the built
in software, the diameter of ten fibers was measured from this image. It is clear here that there are relatively
uniform fibers, with limited beading, and that the material is very porous.
Properties for soybean oil, the original oil for kinetics measurements, have all been
experimentally determined. These are listed in Table 2 along with literature values for each (8).

17
Temperatures for each value are reported as well. Density and viscosity were measured three
times and the average is reported with the error as the 95% confidence interval. The goniometer
takes multiple measurements of surface tension with one trial and these were used to find an
average and 95% confidence interval.
Table 2: Soybean Oil Properties
Value Literature Value from (8) Experimental Value
Viscosity (Pa*s) 0.0585 (20°C) 0.0524 ± 0.0001 (20°C)
Density (kg/m3
) 916.5 (20°C) 898.7 ± 3.8 (20°C)
Surface Tension (N/m) 0.0276 (30°C) 0.03762 ± 0.00006 (20°C)
The same properties for 5 cSt grade silicone oil and 20 cSt grade silicone oil are in Tables
3 and 4 respectively. The density values are from the supplier. The literature viscosity value was
calculated by multiplying the supplier kinematic viscosity by the specific gravity of silicone oil.
Surface tension was found in a technical report by Shin Etsu (9).
Table 3: 5 cSt Silicone Oil Properties
Value Literature Value Experimental Value
Viscosity (Pa*s) 0.00457 (25°C)1
0.00442 ± 0.00042 (20°C)
Density (kg/m3
) 913 (25°C)1
892.3 ± 1.7 (20°C)
Surface Tension (N/m) 0.0197 (25°C), from (9) 0.02049 ± 0.00003 (20°C)
Table 4: 20 cSt Silicone Oil Properties
Value Literature Value Experimental Value
Viscosity (Pa*s) 0.019 (25°C)1
0.01961 ± 0.0021 (20°C)
Density (kg/m3
) 950 (25°C)1
898.9 ± 3.5 (20°C)
Surface Tension (N/m) 0.0206 (25°C), , from (9) 0.01917 ± 0.00002 (20°C)
1
Value obtained from Sigma Aldrich

18
3.2 Timed Capacity Experiment
3.2.1 Timed Capacity for Soybean Oil
Many trials of the timed capacity
experiment have been run, however many of them
suffer critical flaws and therefore, only five trials
supplied usable data. Early trials involved placing
the membrane into the oil without attempting to
keep it flat. These trials resulted in large
fluctuations in mass, with some fluctuations being
nearly 3 g differences between data points. It was
concluded that if left unconstrained, the
membrane would fold onto itself. The folding would lead to inconsistent dripping and therefore
inconsistent mass values. In later trials, the membrane was melted onto metal mesh in an effort to
keep it in flat. Figure 6 shows one representative trial of data from this experiment. Here, the
mass data has been converted to capacity using equation [13]. While the data shows less
inconsistency and fewer fluctuations than observed without the mesh, it is apparent that the
kinetics happen too quickly to observe from this experiment.
The first and second order fits for this experiment are shown in Figure 7. These are plots
of equations [3] and [4] using the data from Figure 6. The best fit lines for each was found using
Mathwork’s MATLAB (Version R2017a) Curve Fitting Toolbox using a polynomial fit of order
one. The first order model clearly does not fit based on the R2
value, while the second order fit
appears to be a very good one. However, as the majority of the data points were at equilibrium
capacity, the “t/Q vs. t” fit devolves to “t vs. t” and therefore these results are inconclusive. The
Figure 6: Capacity vs. time data for a
membrane of average thickness (0.0161 cm)
attached to a metal mesh. It is clear that there
is little kinetics observed as most of the points
are close to equilibrium.

19
parameters k1 and Qe were calculated using the slope and y-intercept found from the curve fitting
and their corresponding values from equation [3]. The same was done to find parameters from
equation [4]. The parameters are shown in Table 5, along with the maximum capacity observed
to compare with the equilibrium calculated by the fits. It can be seen that the fitted values for Qe
match well with the experimental values. A second, experimentally identical trial was conducted
and the same parameters are included in Table 5. The graphs look very similar to the
representative trial shown. However, the values obtained for the parameters are not very
consistent between trials.
a) First Order Fit b) Second Order Fit
Figure 7: The first and second order fits for average thickness membrane, capacity data presented in figure 6.
As can be determined by the R2
value, the data fits the second order model much better than the first order
however this fit may be skewed by the amount of data collected at equilibrium.
Table 5: First and Second Order Parameters for Average Thickness Membrane
k1 (1/s) Qe from 1st
order (g/g)
k2 (1/s) Qe from 2nd
order (g/g)
Maximum Q
(g/g)
Trial 1 (data
shown)
2.46 x 10-4
47.61 6.97 x 10-2
52.88 54.19
Trial 2 5.21 x 10-4
21.98 1.40 x 10-3
33.80 33.52

20
In an attempt to observe more of the kinetics process
before the membrane reaches capacity, thicker
membranes were spun. It was hypothesized that if the
membrane was thicker, it would take longer to reach
maximum capacity. The three thick membranes had
thickness of 0.576 mm (trial one), 0.740 mm (trial
two), 0.708 mm (trial three) in comparison to the
original membrane thickness which is between 0.1 and
0.3 mm. Figure 8 shows the capacity-vs.-time data for
trial one, which is used a representative trial. While there is some observation of measurements
before equilibrium, the first point (at two seconds) is at 62% of maximum capacity and by 10
seconds it is at 84% of capacity. The maximum capacity is reached within 20 seconds. In the
other two trials, even fewer measurements were kinetically relevant, with both trials reaching
maximum capacity within 5 seconds.
Figure 9 shows the first and second order fits for the trial in Figure 8. Like with the
average thickness membranes, the first order fit has a low R2
value, showing that the data does
not fit this model. The second order fit is much better, however, with so many values at or near
equilibrium capacity, it is unclear if this is a meaningful result.
Figure 8: Capacity vs. time for a thick membrane
(0.0576 cm). This representative trial shows that
while some kinetics can be observed, the majority of
kinetics happens before the first data point.

21
a) First Order Fit b) Second Order Fit
Figure 9: The first and second order fits for a thick membrane, capacity data presented in figure 7. As can be
determined by the R2
value, the data fits the second order model much better than the first order however this fit
may be skewed by the amount of data collected at equilibrium.
Two other trials were run of this experiment and if plotted, the capacity-vs.-time data and
the fits would look very similar to the representative trial. The parameters for the first order
model, k1 and Qe, and the parameters for second order model, k2 and Qe were calculated for all
three trials and are in Table 6. In addition, the maximum capacity for each trial is shown to
compare to Qe. It is clear that while Qe matches relatively well with the maximum capacity, the k
values are not physically meaningful as many are negative, furthering the suggestion that these
models do not truly fit the kinetics of this process.
Table 6: First and Second Order Parameters for Thick Membranes
3.2.2 Capacity
k1 (1/s) Qe from 1st
order (g/g)
k2 (1/s) Qe from 2nd
order (g/g)
Maximum Q
(g/g)
Trial 1 (data
shown)
4.28 x 10-4
41.88 -0.0461 45.25 53.69
Trial 2 -7.61 x 10-4
15.75 -0.013 14.14 16.66
Trial 3 5.53 x 10-5
37.19 -0.0023 36.43 39.95

22
While the timed capacity method does not result in any usable kinetics data, it does
provide a measurement of the capacity of the membrane. This method was carried out for each
oil and the maximum capacities for each trial are compiled in Table 7 along with an average and
standard deviation for each oil. For soybean oil, there are five trials presented (two for the
original membranes and three for the thicker membranes). For both silicone oils, there were only
three trials conducted. No fits were done with the silicone oils as the soybean trials showed these
fits were not useful. For each oil, there is a large standard deviation between trials. While this
standard deviation may go down if more trials were conducted, it does seem to indicate that the
timed capacity method is not very accurate even in determining maximum capacity.
Table 7: Maximum Capacity
Oil Soybean 5 cSt Silicone 20 cSt Silicone
Trial 1 Q (g/g) 54.19 13.86 36.34
Trial 2 Q (g/g) 33.52 7.64 26.70
Trial 3 Q (g/g) 53.69 13.50 27.29
Trial 4 Q (g/g) 16.66
Trial 5 Q (g/g) 39.95
Average Q (g/g) 39.602 11.67 30.11
Standard Deviation 13.9623 2.85 4.41
3.3 Filmed Distance Experiment
3.3.1 Fits to Gravitational and Non-Gravitational Model for Soybean Oil
In order to find the best fit curves for the filmed distance data, Mathwork’s MATLAB
(Version R2017a) Curve Fitting Toolbox was used. The custom equation setting was used for
each model. For the non-gravitational model, the data was fitted to equation [9], written
explicitly x = f(t) by taking the square root of both sides. For the gravitational model,
Wolfram|Alpha’s online program was used to solve equation [5] explicitly for X (10). The result
is equation [15].

23
𝑋 =
𝑊(−𝑒(−𝐴𝑡−1))+1
𝐵
[15]
Early trials of the filmed distance experiment were run under strict timed constraints.
While these trials fit well to both the gravitational model and non-gravitational model, these
trials did not reach equilibrium and the values of the parameters did not match those calculated
using equations [6], [7], and [10]. In order to remedy this, the experiments were run for longer
time periods. These longer trials can be seen in Figure 10. However, these trials (even trial two at
56 hours) did not reach equilibrium either. It was clearer, thought, that at longer times that the
gravitational model does in indeed model the process better than the non-gravitational model.
a) Trial One b) Trial Two

24
c) Trial Three
Figure 10: Filmed distance-vs.-time data for three soybean oil trials for varying time periods. Each shows an
excellent fit to the gravitational Marmur model and a good, albeit worse, fit to the non-gravitational model. While
not quite at equilibrium, there is a clear indication that the curve is beginning to flatten at longer time points. The
error bars represent the 95% confidence interval between the ten distance points measured at each time point.
3.3.2 Comparison of Fitted and Calculated Parameters for Soybean Oil
For each of the three trials in Figure 10, the Mathwork’s MATLAB (Version R2017a)
Curve Fitting Toolbox was used to find the parameters A, B, and D from equations [5] and [9].
These parameters, along with calculated parameters using equations [6], [7], and [10] with the
values in Tables 1 and 2, are in Table 8. A complete set of sample calculations, including error
propagation, is included in Appendix 5. It is clear that there is not agreement between the
calculated parameters and the parameters obtained from the fitting, however each trial’s values
deviate from the calculated value in the same direction.
Table 8: Parameters for Soybean Oil Marmur Model
Trial 1 Trial 2 Trial 3 Calculated
A (x108
1/s) 1640 394 176 1.20 ± 0.89
B (1/m) 8.12 3.70 3.25 0.488 ± 0.114
D (x 107
m2
/s)
2.30 2.84 2.67 1.01 ± 0.34

25
3.3.3 Fits to Gravitational and Non-Gravitational Model for 5 cSt Silicone Oil
The same process was followed for 5 cSt silicone oil as soybean oil. Figure 11 shows the
data for two trials of the filmed distance experiment for 5 cSt silicone oil. Each trial was run for
fifteen hours. The gravitational model fits much better to the data. In fact, the discrepancy
between the two trials is greater than for soybean oil.
Figure 11: The data for the two trials run with 5 cSt grade silicone oil. Both show a good fit for the Marmur
model with gravity, though the non-gravitational fit is not as good. The error bars represent the 95% confidence
interval between the ten distance points measured at each time point.
3.3.4 Comparison of Fitted and Calculated Parameters for 5 cSt Silicone Oil
Table 9 provides similar information as Table 8 does for soybean oil. Two trials were
completed for silicone oil and the A, B, and D for each trial is presented. A calculated value is
also provided based on values in Tables 1 and 3. Like with the soybean oil, there is a discrepancy
between the calculated parameters and those obtained by fitting. However, each trial deviates
from the calculated value in the same direction.
Table 9: Marmur Parameters for 5 cSt Silicone Oil
Trial 1 Trial 2 Calculated

26
A (x107
1/s) 906 810 2.58 ± 1.92
B (1/m) 6.67 6.43 0.891 ± 0.208
D (x107
m2/s) 8.63 9.23 6.52 ± 2.26
3.3.5 Fits to Gravitational and Non-Gravitational Model for 20 cSt Silicone Oil
The same process was followed for 20 cSt silicone oil as for the other two oils. Figure 12
shows the data for two trials of the filmed distance experiment for silicone oil. Trial one was run
for 24 hours, while trial two was run for over 120 hours to allow for collection of additional B
values. As before, the gravitational model fits better than the non-gravitational model.
Figure 12: The data for the two trials run with 20 cSt grade silicone oil. Both show a good fit for the Marmur
model with gravity, though the non-gravitational fit is not as good. The error bars represent the 95% confidence
interval between the ten distance points measured at each time point.
3.3.6 Comparison of Fitted and Calculated Parameters for 20 cSt Silicone Oil
Table 10 provides similar information as Table 8 does for soybean oil. Two trials were
completed for silicone oil and the A, B, and D for each trial is presented. A calculated value is
also provided based on values in Tables 1 and 4. Like with the soybean oil, there is a discrepancy

27
between the calculated parameters and those obtained by fitting. However, each trial deviates
from the calculated value in the same direction.
Table 10: Marmur Parameters for 20 cSt Silicone Oil
Trial 1 Trial 2 Calculated
A (x108
1/s) 1219 905 6.32 ± 4.74
B (1/m) 5.01 4.84 0.959 ± 0.224
D (x107
m2
/s) 4.83 1.77 1.37 ± 0.049
3.3.7 Estimated Equilibrium Height and Time for Both Oils
To estimate the maximum height the oil would rise, the limit of equation [15] as time
goes to infinity is used. The result is x = 1/B. Based on the calculated parameters, the maximum
heights and times to reach 90% of these heights is presented in Table 11. If these heights are
accurate (or even accurate to within 25% of the actual equilibrium height), it is clear that the
experiments run were not long enough to capture the entire kinetics process to reach equilibrium.
The time for these experiments are far too long to feasibly do the entire experiment, which is a
large source of error when comparing between the fitted and calculated parameters.
Table 11: Maximum Height and Time
Oil Maximum Height Time to Reach 90% of
Maximum Height
Soybean 2.05 m 3.66 years
5 cSt Silicone 1.12 m 8.98 weeks
20 cSt Silicone 1.04 m 1.39 years
3.3.8 Changes in Marmur Parameters over Time
To investigate the hypothesis that the filmed distance experiments were not long enough
to capture the full process and that this time issue causes the deviations between the calculated
parameters and the parameters obtained from fitting, a filmed distance trial was run for 122
hours. The trial was run using 20 cSt silicone oil. The experimental data was broken up into

28
subsections and each subsection was fitted to equations [5] and [9] to obtain A, B, and D. The
results from each fitting are shown in Table 12 along with the calculated parameters. It can be
seen that A and B both approach the calculated parameters over time whereas the D value most
closely matches the calculated value at shorter times.
Table 12: Marmur Parameters over Time
Time A (x 108
1/s) B (1/m) D (x 107
m2
/s)
1 hour 15180 14.35 8.46
3 hours 2488 6.943 6.87
15 hours 1774 6.056 4.72
25 hours 1659 5.912 4.21
35 hours 1343 5.462 3.21
48.5 hours 1273 5.36 2.93
59.5 hours 1114 5.139 2.57
73 hours 1066 5.065 2.42
96.5 hours 980.3 4.923 2.16
106.5 hours 931 4.879 1.89
122 hours 905 4.842 1.77
Calculated 6.32 0.954 4.83
3.4 Comparison of Timed Capacity and Filmed Distance Methods
If the timed capacity method is thought of as a one-dimensional diffusion problem, it can
be mathematically related to the filmed distance method. Since the membrane is flat in the oil
and very thin, gravity can be neglected, and equation [9] can be used. Oil enters the membrane
from the top and the bottom therefore there are two simultaneous paths for diffusion. If the two
paths meet in the middle, the “height” of diffusion is half the thickness of the membrane. Using
the thick membrane from trial one (with a thickness of 0.576 m) and D for soybean oil calculated
from measured properties, it is predicted that the time of diffusion is 0.82 seconds. While this is
certainly faster than what is observed, it does not discredit the conclusion that the timed capacity

29
method is too fast to observe enough pre-equilibrium data points to properly fit it to a kinetics
model.
3.5 The Tensiometer Method
One trial of the tensiometer method was completed. While the tensiometer was taking
mass measurements, pictures were taken so the mass could be compared to the distance
measurements. Figure 13 shows the mass and distance data plotted together. Both sets of data
follow a similar, exponential growth trend which shows that these two sets of data are likely
related. One attempted calculation to relate these two values is shown in Figure 14. The
approximated data is obtained using the tensiometer mass data and equation [11]. However, it is
clear from this figure that this initial attempt at an approximation between distance and mass is
not accurate.
Figure 13: Mass and distance data for the tensiometer
experiment. It is clear that both data sets increase
exponentially over time suggesting that there is a
relationship between mass and distance.
Figure 14: Distance and distance approximated by the
mass measurements of the tensiometer experiment. It
is clear that equation X is not an accurate way to
convert between mass and distance.

30
4. Discussion
4.1 Timed Capacity
4.1.1 First vs. Second Order
The second order fit was better than the first order fit for the timed capacity method as
indicated by the R2
value of nearly one for second order fits and R2
values of 0.5 or worse for
first order fits. This was as expected; nearly all literature that measures kinetics concludes a
second order model fits the best (3,5). However, as shown in Figures 6 and 8, the change in
capacity over time is frequently very small, because it reaches equilibrium capacity at early time
points, which has been observed in literature (3,5). Observationally, every trial has resulted in
small capacity changes after the initial jump at the first measurement. While it was hypothesized
that there would be more significant capacity changes over time with a thicker membrane, this
was not true for any membrane used in this project. The second order fitting involves graphing
time/capacity vs. time. If the changes in capacity are very small, this is essentially plotting time
vs. time, which will always produce a perfectly straight line (y = constant*x). This means that
this fit is likely meaningless, and the observed fit is just a graph of time vs. time.
4.1.2 Problems with Timed Capacity Experiments
It has not been trivial to find a reliable measurement method for this experiment. The
original method involved crumpling the membrane, submerging it in oil, and removing and
weighing it at various time points. Crumpling the membrane allows oil to get caught in between
the folds rather than actually being sorbed by the membrane. This leads to inaccurate
measurements, as the membrane would often unfold uncontrollably leading to inconsistencies in
the amount of oil that dripped out. To fix this, the membrane was melted onto a hot metal mesh

31
to hold it flat. This method is an improvement and generally results in consistent data, but is not
foolproof and there was some observation of folding or inconsistent dripping in certain trials.
The inconsistency is also noted when comparing the equilibrium capacity between trials
as seen in Table 7. For each oil, the standard deviation is very large compared to the average
capacity between trials. For soybean oil especially, the maximum capacity changed dramatically
between trials with the standard deviation being equal to one third of the average value. While
there is some improvement for the silicone oils (with standard deviation for the 20 cSt silicone
oil being about 13% of the average value), it still generally very inconsistent. The large
deviations between trials is surprising as all the membranes had very similar intensive properties,
such as porosity, and capacity should not be affected by size of the sample as capacity is a
normalized mass. Therefore, this result shows the unreliability of the timed capacity method.
Besides the inconsistencies in equilibrium capacity, the data from these experiments has
not been ideal as there is very little change in the capacity over time. To confirm the hypothesis
that kinetics are too fast to observe, a sample was left submerged in oil for several nights. As
there was no change in capacity after four days, it can be safely concluded that the process is
very fast rather than very slow.
To attempt to combat this problem, thicker membranes were spun. However, the majority
of data points collected were still at equilibrium. In addition to this, thicker membranes also
resulted in negative second-order rate constants further showing that while the model fit well
quantitatively, the results had little physical meaning. Using a similar analysis as set out in
section 3.4, equation [9] was used with the D calculated via the measured material and oil
properties. Setting time equal to one minute (which should be an adequate amount of time to
collect at least five data points), the distance obtained is 2.46 mm, meaning a nearly 4.92 mm

32
thick membrane would need to be used. As the thickest membrane achieved was less than 1 mm,
this is a significant barrier to this method. An attempt was made to spin a membrane that was
twice as thick as the thickest membrane obtained by adding an additional acrylic plate, but as this
obstructed the electric field the attempt did not produce a membrane.
4.2 Filmed Distance and the Marmur Model
4.2.1 Gravitational vs. Non-Gravitational Model
It is clear from the data presented in Figures 10, 11, and 12, that the gravitational model
fits the distance vs. time data for each oil better than non-gravitational model, which is expected
since the oil front moves in the vertical direction against gravity. While the gravitational model is
somewhat better in every trial, the discrepancy between the two models is clearer with the
silicone oils than with the soybean oil. This observation is in line with the derivation of the
Marmur model. In it, the pressure drop in the Darcy equation is related to a force balance
between capillary action and gravity. The gravity term includes the height of the oil. In the non-
gravitational model, the gravity term is set to zero, indicating that at low heights gravity can be
neglected.
Both silicone oils reach a higher height than the soybean oil in the same amount of time.
Therefore, for equally-timed experiments, the gravitational term of the force balance is higher for
the silicone oil than for the soybean oil resulting in more inaccuracy associated with the non-
gravitational model. In addition, the capillary action term for the silicone oils is smaller due to
lower surface tension. The surface tension effect makes it so that even at the same height, the
gravitational term is larger relative to the capillary action term for the silicone oils. Therefore,
when comparing between two equal heights, it will also hold true that the silicone oil will fit
worse to the non-gravitational model. When comparing between the two silicone oils, the 5 cSt

33
oil fits worse to the gravitational model than the 20 cSt oil. As the 20 cSt oil moves slower than
the 5 cSt oil, this result further verifies the height effects described above. Overall, these effects
result in a very clear picture regarding the gravitational model’s advantage over the non-
gravitational model especially when doing very long experiments.
4.2.2 Comparison Between Oils
The filmed distance method was performed with three oils, soybean oil, 5 cSt grade
silicone oil, and 20 cSt grade silicone oil. These oils were chosen because they had viscosities
ranging from 4.42 mPa*s to 52.4 mPa*s. The reason for the change in oil is twofold. First, it was
desired to see if the filmed distance method produced reliable data and a reliable fit to the
Marmur model with multiple oils. At least two trials were completed for each oil and each
produced reliable results that fitted well to the Marmur model.
Second, a main advantage of the Marmur model is its ability to relate kinetics empirically
to oil and material properties. If kinetics is reliably modeled using properties, these properties
can then be used to predict relative kinetic ability. By changing a property, it was possible to test
whether these predictions are accurate. By looking at equation [15], it can be seen that B is
inversely proportional to equilibrium height based on the limit as time goes to infinity. When
looking at equation [5], it can be seen that A is inversely proportional to the equilibrium time as
the equation is solved explicitly for time when both sides are divided by A. The parameter A,
shown in equation [6], is inversely proportional to both surface tension and viscosity and directly
proportional to density. The parameter B, shown in equation [7], is inversely proportional to
surface tension and directly proportional to density. The density hardly varies between the three
oils. However, the viscosity and surface tension are different for every oil.

34
5 cSt silicone oil has an order of magnitude lower viscosity and a surface tension
approximately half that of soybean oil as shown in Tables 2 and 3. It is expected that both A and
B will increase when changing from soybean oil to 5 cSt silicone oil. The prediction for the
parameters is proven to be accurate for both the calculated values and the values obtained from
fitting. These increases should result in faster kinetics and a lower equilibrium height. The height
is observed to increase more quickly, reaching an average height of 17.51 cm after 12 hours
compared to 10.99 cm. However, as none of these experiments reached equilibrium height, it is
difficult to determine if the relative equilibrium heights match predictions.
The 20 cSt silicone oil has a viscosity in between that of the 5 cSt silicone oil and the
soybean oil as shown in Tables 2 and 4. Its surface tension is slightly lower than that of the 5 cSt
silicone oil. Therefore, its A value should be in between that of the other two oils and its B value
should be slightly higher than that of the 5 cSt oil. The A value follows this trend for both the
calculated and fitted values, however the B only follows it for the calculated values. For the
fitted values, the B value is slightly higher for the 5 cSt silicone oil than the 20 cSt silicone oil.
However, as the 20 cSt silicone oil trials were run for longer than the 5 cSt silicone oil trials, it is
difficult to determine if this discrepancy is meaningful. Additionally, the difference in surface
tension measured is so small that a small inaccuracy in either measured surface tension could
result in the opposite trend being true for B. It is expected based on the change in A that the
speed of the kinetics should be in between the 5 cSt silicone oil and the soybean oil. The height
increase is observed to be at an intermediate speed, with an average height of 13.53 cm at twelve
hours, just in between the 17.51 cm of 5 cSt silicone oil and 10.99 cm of soybean oil.

35
4.2.3 Comparison of Fitted Parameters to Calculated Values
For each oil, the parameters obtained from do not match those calculated from the
material and oil properties. For the A values, the fitted value is at least two orders of magnitude
different and is three orders of magnitude different in a few cases. Each B value is an order of
magnitude different. The D values are all within an order of magnitude, though none match the
calculated value exactly. However, as it is believed that the non-gravitational model should not
match the data well, the fact that the D values did not match is a very reasonable result.
It is impossible to know if the calculated value or the fitted value is more correct. There is
a compelling argument for why each will have error. The fitted values are fits to an incomplete
data set. It is approximated in section 3.3.8 that the experiment could take years to run. Even if
this is very inaccurate, even 10% of the approximate time for the soybean oil to reach
equilibrium height is over a hundred times longer than any of the experiments run. The data
presented in Table 12 furthers the hypothesis that a longer experiment would result in different,
and likely more accurate, results. When sub-sections of the data are fitted to the Marmur model,
different values of the parameters are obtained. As longer times are used, the values for A and B
approach the calculated value. While the changes slow down over time, there is still an
exponential decay approaching the expected values. Since no experiment run actually reached an
equilibrium height, it is difficult to know whether even longer trials would result in even closer
values of A and B. In contrast, D is nearly identical to the calculated value at shorter times, but
gets less accurate at longer timeframes. This result ties into the hypothesis that at short times,
when the height is low, the non-gravitational model better fits the process. It is also helps to
support the hypothesis that with an accurately timed experiment, the fitted and calculated values
of A and B may match.

36
It is also possible that there is some discrepancy between the calculated and fitted
parameters due to inaccuracies in the measured and calculated material and oil properties. While
some material properties are measured for every sample, and small deviations exist from sample
to sample, others have only been measured a few times. The surface area measurement presents
an especially high area of uncertainty. An approximation for surface area (see Appendix 4 for
derivation) was used in calculation until surface area was experimentally determined. The
approximated and experimental values differed by an order of magnitude. The surface area was
only measured once and so it is uncertain how accurate the measurement was. There was an
additional complication as the membranes used for the experiment had a different fiber diameter
than those used for the filmed distance experiments. In order to correct for this, a ratio of the
experimental to the approximated surface area for the original membranes was used as a
correction factor. Between the disagreement with experimental and calculated values and the
need to approximate a correction for different membrane geometry, the surface area value is a
potentially large source of error.
4.2.4 Problems with the Filmed Distance Method
The filmed distance method seems to satisfy the main objectives of this project; it
provides data which fits well to a theoretical model and that theoretical model is empirically
related to material and oil properties. However, it is not a realistic experiment to run properly.
For instance, for soybean oil, the experiment would ideally be run for years based on the B
calculated from material and oil properties.
In addition, longer experiments reveal that it is difficult to get consistent distance data.
The obvious part of this obstacle is that it is difficult to reliably take pictures over extended
periods of time. However, an additional problem occurs in that the oil front is not uniform at

37
long times. This problem was especially obvious with the silicone oil, which rises faster.
Excessive fingering (an example of which is shown in Appendix 6) makes it difficult to decide
where the oil front actually is. To try to fix this problem, multiple distances are averaged. The
error bars in Figures 10, 11, and 12 show the 95% confidence intervals for distance at each time
point. It is clear from these error bars that the actual distance is less certain at late time points.
Since it is unclear what causes this fingering, it is unclear what the oil front actually is. While
this method certainly serves the objectives of this project well, it is by no means perfect.
4.3 The Tensiometer Method
The tensiometer method presents an interesting alternative to the filmed distance method.
It requires less work by the experimenter as a machine records data for an essentially limitless
amount of time. It is also far more accurate as the experimenter does not need to manually take
distance measurements and arbitrarily decide where the oil front is when fingering occurs.
However, it also presents a challenge in that it does not result directly in distance measurements.
Therefore, it cannot be used in conjunction with the Marmur model without finding a reliable
way to convert the mass data to distance data. One attempt of this is shown in equation [11].
However, when looking at Figure 14, which compares the distance taken by the picture
method and the distance based on mass and equation [11], it is clear that this approximation is
not accurate. Since this was a short time experiment and no fingering was observed, it seems
unlikely that the issue lays in the distance measurements. One possible explanation for the
discrepancy is that the assumption that the oil fills the entire pore volume specified by the cross-
sectional area and the height is invalid. This result makes sense based on experimental
observations. When using the dye with the soybean oil, it was observed that lower sections of the
membrane appeared darker than the highest section the oil front had reached. This observation

38
makes it seem that over time, the oil continues to fill lower sections. Therefore, even if the oil
front is clearly at a certain height, it is not true that the entirety of the membrane from that height
down is full of oil. In addition, the fact that there is fingering and uneven rise in the oil front
makes it impossible to treat the volume of oil as a three-dimensional box as is done in equation
[11]. However, despite the fact that this approximation does not work, it seems that based on
Figure 13 there should be a relationship between the distance and the mass as both increase in a
similar fashion over time. With more experiments, it will likely be possible to find this
relationship and to successfully use the tensiometer with the Marmur model.
4.4 Comparison of Methods and Future Recommendations
Two methods, the filmed distance and timed capacity, were analyzed in detail over the
course of the project. These two methods should ideally be related to one another as both seek to
model similar processes. One way to relate the two empirically is presented in section 3.4. Here,
the timed capacity method is modelled based on the non-gravitational Marmur model. If
Marmur’s model works well for sorption through the smallest face of the membrane, it should
also describe the timed capacity model as it is simply oil sorption through the top and bottom
faces. Since the height is always small for this process, the non-gravitational model can be used.
The time found by this calculation is less than a second, which is slightly faster than what has
been found experimentally. However, the inability of the timed capacity method to even result in
reliable capacity measurements means that it is possible that the capacity at one second, which is
typically at least 70% of the maximum capacity, is indeed the maximum capacity. It is possible
that inaccuracies due to folding and dripping make it such later time points are artificially high.
Nonetheless, it is clear that even with this small discrepancy, these two methods are relatively in
agreement with one another.

39
While both models have drawbacks, the filmed distance method seems to drastically
outperform the timed capacity method. The largest difference between the two is that the filmed
distance method can reliably produce enough data points to describe kinetics rather than
equilibrium, as the timed capacity method does. While a very thick membrane could produce
some kinetics data, it would be difficult to fabricate such a membrane as a thicker membrane
tends to interfere with the electric field. The second advantage for the filmed distance method is
that it is related to a superior model. The Marmur model specifically models the sorption process
for a permeable membrane and therefore incorporates many important material and oil
properties. The first and second order models are relics from reaction kinetics and do not have
the same richness. In addition, the Marmur model’s ability to predict how changes to material
and oil properties would affect kinetics is a large advantage over the timed capacity method.
Even though the method may not produce entirely correct results in regards to the parameters in
the equations, it definitely provides an accurate prediction for how changes in properties will
change kinetics. Therefore, it is possible to easily and accurately compare membranes without
experimental testing.
However, the filmed distance method is not without its faults. One major flaw is that it
takes too long to run completely. While there is still some doubt regarding exactly how long the
experiment needs to be run for accuracy, it is clear that it must be run at least for several days
and likely several weeks or months, which is a very unreasonable timeframe. Several different
changes can be made to make this method better. One is to find a way to take a small amount of
data and extrapolate to find the value of the parameters at longer times. In order to do this, a
good mathematical model for how the parameters vary with time is needed. A few attempts were
made over the course of the project but none yielded useful results. A second change would be to

40
design a membrane that sorbs oil faster. Since it is shown by the change in oils that the Marmur
model has excellent predictive capability, it can be assumed that the same would hold true for
changes in membrane properties. It is known that a larger A will result in faster kinetics. Based
on equation [6] it is clear that a smaller surface area or a larger porosity will result in a larger A.
If a membrane with those characteristics were fabricated, the Marmur experiment should take
less time.
The third method, the tensiometer method, also may result in an improvement on the
filmed distance method while still being able to use the very rich Marmur model. With this
method, data is easily collected over very long time frames. It is also requires less work by the
experimenter than the picture method. In addition, it has less of a human error element because a
machine records all of the data. However, it is currently unclear how to relate mass data to
distance data. If this relationship could be quantitatively determined accurately, the tensiometer
would likely be an improvement over both the timed capacity and filmed distance methods.
5. Conclusion
Overall, the objectives of the project were successfully met. Two methods for measuring
the kinetics of oil sorption were fully tested and compared. Each method corresponded to a
different theoretical model describing the process. One of these methods, the filmed distance
method, was proven to be reliable and to fit very well to its corresponding model, the Marmur
model. The Marmur model also fits in well with the original objectives as it corresponds to
material and oil properties. While the calculated and fitted parameters did not match exactly, the
discrepancies can be described using collected data. In contrast, the second method, the timed
capacity method, was not as successful. This method resulted in no kinetics data, as the process
happened too quickly. In addition, the best model for this process has no empirical relation to

41
material and oil properties. Preliminary studies were also begun on a third method, the
tensiometer method. This method supplies very accurate mass-vs.-time data over both fast and
slow time frames. However, attempts to relate the mass to distance were unsuccessful, which
limited the use of the tensiometer method with the better model, the Marmur model.
In the future, these methods can be further optimized. Changes to the geometry of the
membrane may decrease the time needed to accurately run the filmed distance method. In
addition, the timed capacity method could be augmented to supply more useful results if it were
possible to fabricate a much thicker membrane. Lastly, more work can be done to understand the
relationship between mass and distance in order to use the tensiometer to collect data more easily
for use with the Marmur model. Despite room for improvements, this project was a success and
has provided an excellent start for the exploration of the kinetics of oil sorption.
References
(1) Sarbatly, R.; Krishnaiah, D.; Kamin, Z. A Review of Polymer Nanofibres by
Electrospinning and Their Application in Oil-Water Separation for Cleaning up Marine
Oil Spills. Mar. Pollut. Bull. 2016, 106, 8–16.
(2) Raza, A.; Si, Y.; Tang, X.; Yu, J.; Ding, B. Electrospun Nanofibers for Energy and
Environmental Applications. Nanostructure Sci. Technol. 2014, 525.
(3) Wu, J.; An, A. K.; Guo, J.; Lee, E.-J.; Farid, M. U.; Jeong, S. CNTs Reinforced Super-
Hydrophobic-Oleophilic Electrospun Polystyrene Oil Sorbent for Enhanced Sorption
Capacity and Reusability. Chem. Eng. J. 2016, 314, 526–536.
(4) Qiao, Y.; Zhao, L.; Peng, L.; Sun, H.; Li, S. Electrospun Polystyrene/Polyacrylonitrile

42
Fiber with High Oil Sorption Capacity. J. Reinf. Plast. Compos. 2014, 33, 1849–1858.
(5) Lin, J.; Tian, F.; Shang, Y.; Wang, F.; Ding, B.; Yu, J.; Guo, Z. Co-Axial Electrospun
Polystyrene/polyurethane Fibres for Oil Collection from Water Surface. Nanoscale 2013,
5, 2745–2755.
(6) Lin, J.; Shang, Y.; Ding, B.; Yang, J.; Yu, J.; Al-Deyab, S. S. Nanoporous Polystyrene
Fibers for Oil Spill Cleanup. Mar. Pollut. Bull. 2012, 64, 347–352.
(7) Zhu, H.; Qiu, S.; Jiang, W.; Wu, D.; Zhang, C. Evaluation of Electrospun Polyvinyl
Chloride/polystyrene Fibers as Sorbent Materials for Oil Spill Cleanup. Environ. Sci.
Technol. 2011, 45, 4527–4531.
(8) Hammond, E. G.; Johnson, L. A.; Su, C.; Wang, T.; White, P. J. Bailey’s Industrial Oil
and Fat Products, Edible Oil and Fat Products: Soybean Oil. In Bailey’s Industrial Oil and
Fat Products, Sixth Edition.; Shahidi, F., Ed.; John Wiley & Sons Inc., 2005; pp. 577–653.
(9) Shin-Etsu. Silicone Fluid KF-96 Performance Test Results. Shin-Etsu Silicone 2014, 36.
(10) Wolfram|Alpha LLC. Wolfram|Alpha Result
https://www.wolframalpha.com/input/?i=A*t+%3D+-B*x+-+ln(1-B*x)+solve+for+x
(accessed Jan 1, 2017).

43
Appendix 1: Image of Filmed Distance Lab Set Up
Figure 15: Equipment to film distance vs. time. The frame provides consistency in set-up from trial to trial.
Appendix 2: Different Electrospinning Set-Up
A B
Figure 16: Image of Setup for spinning thicker and longer membranes. Setup to spin thicker membranes is shown on image A, where the
purple plate represents the acrylic plate added to our steel collector to decrease the size where the membrane can collect. Setup to spin
longer membranes is shown on image B, where we replaced the collecting platform with a rotating cylinder so that the membrane collects
around the entire circumference of the cylinder.

44
Appendix 3: Permeability Calculations
𝐷𝑎𝑟𝑐𝑦 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛: 𝐽 =
𝑘
𝑢
𝑑𝑃
𝑑𝑧
𝐽 =
𝑄
𝐴𝑡
Q = volume through cell = 115.65 cm3
and 112.75 cm3
A = area of cell = 3.5 cm2
t = time = 20 s
u = viscosity of water (used in experiment) = 8.9 x 10-4
dP = change in pressure = 2 psi
dZ = thickness of membrane = 1.32 x 10-4
Calculated k = 1.39 ± 0.03 x 10-13
Appendix 4: Surface Area Approximation
Specific surface area, the surface area of the polymer divided by the volume of the
polymer, is approximated as shown here. The volume of the membrane, Vm, is determined to be
the volume of the solid polymer. The volume of the membrane is divided by the volume of a
single cylinder, Vc, to determine the number of fibers, Nf, in the membrane, with the assumption
that the fibers can be approximated as identical cylinders. The number of cylinders is then
multiplied by the surface area of a single cylinder, Sc, and divided by the volume of the
membrane to get the specific surface area.
𝑉𝑚 = (1 − 𝜀)𝐴𝐿
𝑉𝑐 = 𝜋𝑅2
𝐿
𝑉 𝑚
𝑉𝑐
= 𝑁𝑓 =
(1−𝜀)𝐴𝐿
𝜋𝑅2 𝐿
=
(1−𝜀)𝐴
𝜋𝑅2
𝑆𝑐 = 2𝜋𝑅𝐿 + 2𝜋𝑅2

45
𝑆 =
(1−𝜀)𝐴
𝜋𝑅2 ∗(2𝜋𝑅𝐿+ 2𝜋𝑅2)
(1−𝜀)𝐴𝐿
As this approximation was not accurate in comparison to the results from the BET, the
approximation is multiplied by a correction factor that is the BET result divided by the surface
area approximation using the geometric parameters of the membranes used in BET. This ratio is
1.1 x 107
/4.06 x 106
or 2.71. The final result is:
𝑆 = 2.71 ∗
(1 − 𝜀)𝐴
𝜋𝑅2 ∗ (2𝜋𝑅𝐿 + 2𝜋𝑅2)
(1 − 𝜀)𝐴𝐿
Appendix 5: Sample Marmur Calculations Calculations
As a sample, the calculations required for the Marmur parameters along with the
propagation of error for each is presented. The oil is soybean oil so the soybean oil properties in
Table 2 along with material properties in Table 1 are provided.
𝑆 = 2.71 ∗
(1 − 𝜀)𝐴
𝜋𝑅2 ∗ (2𝜋𝑅𝐿 + 2𝜋𝑅2)
(1 − 𝜀)𝐴𝐿
= 8.74 𝑥 106
𝑚2
𝑚3
only one BET trial was completed. only one BET trial was completed.
𝐶 =
𝑘 ∗ 𝑆2
∗ (1 − 𝜀)2
𝜀3
= 0.0337
𝜎 𝐶 = 𝐶 ∗ √(
𝜎𝑘
𝑘
)
2
+ (
2𝜎𝑆
𝑆
)
2
+ (
2𝜎𝜀
𝜀(1 − 𝜀)
)
2
+ (
3𝜎𝜀
𝜀
)
2
= 0.0080
𝐴 =
𝐶 ∗ 𝜀3
∗ 𝜌2
∗ 𝑔2
𝑆3 ∗ (1 − 𝜀)3 ∗ 𝜇 ∗ 𝜎 ∗ 𝑐𝑜𝑠𝜃
= 1.20 𝑥 10−8
1
𝑠
𝜎𝐴 = 𝐴 ∗ √(
𝜎 𝐶
𝐶
)
2
+ (
3𝜎𝜀
𝜀
)
2
+ (
2𝜎𝜌
𝜌
)
2
+ (
3𝜎𝑆
𝑆
)
2
+ (
3𝜎𝜀
𝜀(1 − 𝜀)
)
2
+ (
𝜎𝜇
𝜇
)
2
+ (
𝜎 𝜎
𝜎
)
2
= 8.9 𝑥 10−8
1
𝑠
𝐵 =
𝜀 ∗ 𝜌 ∗ 𝑔
𝑆 ∗ (1 − 𝜀) ∗ 𝜎 ∗ 𝑐𝑜𝑠𝜃
= 0.488
1
𝑚
𝜎 𝐵 = 𝐵 ∗ √(
𝜎𝜀
𝜀
)
2
+ (
𝜎𝜌
𝜌
)
2
+ (
𝜎𝑆
𝑆
)
2
+ (
𝜎𝜀
𝜀(1 − 𝜀)
)
2
+ (
𝜎 𝜎
𝜎
)
2
= 0.114
1
𝑚

46
𝐷 =
2 ∗ 𝐶 ∗ 𝜀 ∗ 𝜎 ∗ 𝑐𝑜𝑠𝜃
𝑆 ∗ (1 − 𝜀) ∗ 𝜇
= 1.01 𝑥 10−7
𝑚2
𝑠
𝜎 𝐷 = 𝐷 ∗ √(
𝜎 𝐶
𝐶
)
2
+ (
𝜎𝜀
𝜀
)
2
+ (
𝜎𝑆
𝑆
)
2
+ (
𝜎𝜀
𝜀(1 − 𝜀)
)
2
+ (
𝜎𝜇
𝜇
)
2
+ (
𝜎 𝜎
𝜎
)
2
= 3.4 𝑥 10−8 𝑚2
𝑠
Parameters Used
(note that σ is used for error of each parameter, where needed in the error propagation)
σ = 0.0376 N/m σσ = 0.0001 ρ = 897.8 kg/m3
σρ = 3.4 R = D/2
μ = 0.0523 Pa*s σμ = 0.0001 ε = 0.948 σε = 0.012 A = 1.04 x 10-3
m
D = 1.238 x 10-6
m σD = 9.7 x 10-8
k = 1.39 x 10-13
σk = 3 x 10-15
L = 0.31 m
Appendix 6: Example of Fingering in the Oil Front
Figure 17: An example of fingering in the oil front. Here it is clearly shown that at later time points the oil does
not rise uniformly causing uncertainty in what the actual oil front is.

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