copyright 2017, michael sweeney
TRANSCRIPT
Effects of Rheology on Wet Granular Material and Energetic Slurries
by
Michael Sweeney, BSME
A Thesis
In
Mechanical Engineering
Submitted to the Graduate Faculty
of Texas Tech University in
Partial Fulfillment of
the Requirements for
the Degree of
Masters of Science
Approved
Dr. Gordon Christopher
Chair of Committee
Dr. Michelle Pantoya
Dr. Craig Snoeyink
Mark Sheridan
Dean of the Graduate School
December, 2017
Copyright 2017, Michael Sweeney
Texas Tech University, Michael Sweeney, December 2017
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ACKNOWLEDGMENTS
I am very appreciative for all the help provided from my mentors and
colleague throughout my graduate school experience. I would like to thank Dr.
Gordon Christopher for the guidance, advice, and mentorship along with the great
opportunity to enhance my engineering skills. Thank you for setting such a great
example of professionalism, technical savvy, and ingenuity for an aspiring young
engineering such as myself.
I sincerely appreciate Dr. Pantoya for the guidance, advice, and great passion
for research. Thanks for all the help and advice, through guiding me in a direction to
enhance the project I worked on. Many thanks to all my colleagues in the rheology lab
and combustion lab who helped me with this project. I would like to thank Mr. Kevin
Hill and Mr. Colt Cagle for the help with the SEM imaging.
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TABLE OF CONTENTS
ACKNOWLEDGMENTS ................................................................................ ii
ABSTRACT ..................................................................................................... iv
LIST OF TABLES ........................................................................................... vi
LIST OF FIGURES ........................................................................................ vii
NOMENCLATURE ....................................................................................... viii
CHARACTERIZING THE FEASIBILITY OF PROCESSING WET
GRANULAR MATERIAL FOR ADDITIVE MANUFACTURING .............. 1
ABSTRACT ...................................................................................................... 1
BACKGROUND .............................................................................................. 3
Rheology Effects on Printability and Print Quality ............................... 3 Rheology .................................................................................................. 11
RESULTS AND DISCUSSION ..................................................................... 11
Printability ................................................................................................ 11 Print Quality and Extrusion ................................................................... 18
CONCLUSIONS ............................................................................................. 24
EFFECTS OF RHEOLOGY ON THE SYNTHESIS OF MG MNO2 THIN
FILMS .................................................................................................................. 26
ABSTRACT .................................................................................................... 26
INTRODUCTION .......................................................................................... 26
EXPERIMENTAL PROCEDURES ............................................................... 28
Materials and Synthesis................................................................................... 28
Rheological Measurements .................................................................. 29
RESULTS ....................................................................................................... 30
Rheological Processing ................................................................................... 30
Energetic Characterization .................................................................... 36
CONCLUSION ............................................................................................... 37
REFERENCES ................................................................................................ 39
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ABSTRACT
Rheological measurements were used to evaluate the viability of high mass
fraction wet granular material for extrusion based 3D printing. Such materials have
diverse applications from making dense, strong ceramic custom parts to 3D printing
uniquely shaped energetic materials. Traditionally, 3D-printed colloidal materials use
much lower mass fraction inks, and hence, those technologies will not work for
systems requiring higher mass fraction solids content. These wet granular materials
are highly non-Newtonian presenting non-homogenous flows, shear thinning, yield
stress, and high elasticity. Such behaviors improve some aspects of print quality, but
make printing very difficult. In this work, the relationship between the rheological
behavior of wet granular materials and the processing parameters that are necessary
for successfully extruding these materials for printing is examined. In the future, such
characterizations will provide key indicators on how to alter printer design/operating
conditions and adjust material behavior in order to improve printability. This study is a
fundamental first step to successfully developing 3D printing technology of wet
granular energetic materials.
To better understand how rheological techniques effect energetics during 3D
deposition, a thermite thin film composed of magnesium (Mg) and manganese dioxide
(MnO2) powders mixed with polyvinylidene fluoride (PVDF) binder and n-methyl
pyrrolidone (NMP) solvent were used to understand the effects of processing on
energetic thin films. Varying shear rate over a prolonged period was used as a
parameter to study the flowability and the suspension of particles to better understand
the behavior of the non-Newtonian fluid. Flame speed and the heat of combustion
were investigated for a variety of shear rates. The composition of the thermite thin
film was held constant at an equivalence ratio of one with a 0.45 solids-liquids mixing
ratio at a wet film thickness of 300 microns. Rheology measurements show that
particle suspension due to high shear rate creates a much more homogenous
microstructure, allowing flame speeds to increase of upwards of 39.9%. Changing the
shear rate to a significantly lower frequency creates an immobilized flow that is driven
by frictional forces between particle resulting in a thin film that is very porous
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throughout. These results show that a varying shear rate affects the microstructure and
energetic potential of thermite thin film created in an additive manufacturing process
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LIST OF TABLES
1. Results of fit of power law model to quasi-static flow regime ............. 10
2. Magnesium & Manganese dioxide particle size distribution ................ 28
3. Flame speed and heat of combustion results ......................................... 37
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LIST OF FIGURES
1. SEM images ............................................................................................ 9
2. Images of PDMs with different particle sizes. ..................................... 10
3. Flow sweep data .................................................................................... 13
4. Effects of pre shear................................................................................ 17
5. Recovery test ......................................................................................... 18
6. Small amplitude oscillatory shear ......................................................... 19
7. Extrusion pictures.................................................................................. 23
8. Flow sweep of thin film ........................................................................ 28
9. Mg MnO2 slurry flow sweep ................................................................ 31
10.Viscosity versus inertial number .......................................................... 32
11. Surface SEM images ........................................................................... 34
12. Cross section SEM images .................................................................. 35
13.Flame speeds ........................................................................................ 36
14. Heat of combustion ............................................................................. 37
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NOMENCLATURE
Pmin = Minimum driving pressure
yield = Material yield stress
eff = Effective viscosity at a particular shear rate
= Shear rate
k = Consistency index
n = Power law exponent
Q = Flow rate
ΔP = Pressure drop
I = Inertial number
= Average density of the composite
�̇�= Shear Stress
G’ = Modulus
R = Radius
P = Pressure
L = Length
PET = Pentaerythritol
PDMS = Polydimethylsiloxane
SEM = scanning electron microscope
PETN = Pentaerythritol tetranitrate
TNT = Trinitrotoluene
RDX = Cyclotrimethylenetrinitramine
HMX = Octogen
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CHAPTER 1
CHARACTERIZING THE FEASIBILITY OF
PROCESSING WET GRANULAR MATERIAL FOR
ADDITIVE MANUFACTURING
ABSTRACT
Rheological measurements and extrusion tests are used to evaluate the viability
of high mass fraction (80% solids content) wet granular materials for extrusion based
3D printing. Such materials have diverse applications from making dense, strong
ceramic custom parts to 3D printing uniquely shaped energetic materials. Traditionally,
3D printed colloidal materials use much lower mass fraction inks, and hence those
technologies will not work for systems requiring higher mass fraction solids content.
These wet granular materials are highly non-Newtonian presenting non-homogenous
flows, shear thinning, yield stress, and high elasticity. Such behaviors improve some
aspects of print quality, but make printing very difficult. In this work, the relationship
between the rheological behavior of wet granular materials and the processing
parameters that are necessary for successfully extruding these materials for printing are
examined. In the future, such characterizations will provide key indicators on how to
alter printer design/operating conditions and adjust material behavior in order to
improve printability. This study is a fundamental first-step to successfully developing
3D printing technology of wet granular materials.
INTRODUCTION
Additive (i.e., 3D) printing technologies have immense potential to impact a
wide range of industrial, scientific and medical applications due to their ability to reduce
material usage, decrease manufacture costs, enable on-demand production, and
fabricate unique shapes. The major research thrusts in this area have been the
development of new tools and techniques that will allow the use of a wider range of
polymers, biomaterials, ceramics and metals.[1-5] In particular, colloidal materials have
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been a major interest,[6-13] because through variation of the type of colloid and
solvent/binder system, fabrication of ceramics,[9,14,15,12,16,17,13,18,19] conductive
pastes,[20,21] and medical materials[3,9] are possible. However, 3D printing of
colloidal materials has been limited to volume fractions of approximately 60% or
less,[6] and such prints often require post processing to create final products with
desired colloid mass fraction, void fraction, or surface properties.[22] Characterizing
higher mass fraction colloids helps fill this gap towards processing a wider range of
materials using additive manufacturing strategies.
One advantage to processing higher colloidal mass fractions is that the final
product will be denser with less void space, allowing mechanically stronger materials
with less need for post processing. This issue is important in creating stronger ceramic
materials and also 3D printing energetic materials. Energetic composites are typically
at least 75 wt. % energetic components with the remaining binder required to hold the
formulation together. The energetic components could include fuel particles such as
aluminum (Al) or boron (B) combined with an organic explosives such as PETN, TNT,
RDX or HMX and may also include a propellant such as ammonium perchlorate
(AP).[23] Energetic composites are typically casted or molded, which can be time
consuming, expensive, wasteful, and difficult to adapt to new designs. But, 3D printing
can create more complex, unique geometries on demand, facilitating fast optimization
of performance for mission specific criteria that cannot be attained using traditional
processing. Overall, 3D printing of energetics would reduce the need for excessive
handling, post processing and stockpiling, conferring benefits to safety, cost, waste and
flexibility. For these reasons, advanced manufacturing of energetic composites as an
important goal.[24-29,23] However, any energetic formulation designed for printing
would need much higher mass fractions to create a viable material and avoid post
processing; thus, the need for research on processing wet granular materials with solids
loadings of at least 80 wt. %.
Such high mass fraction colloidal formulations are best described as wet
granular materials, where solvent and/or binder does not fully penetrate the entire void
space between particles. The combination of both “hard” collisional based interactions
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and “soft” viscous and surface tension based interactions between particles creates a
material that has a complex, non-Newtonian response to deformation. Such materials
exhibit a range of unique challenges in their response to deformation that may make
their utilization in 3D printing techniques particularly difficult. The goal of this paper is
to explore the feasibility of extrusion based 3D printing of wet granular materials by
characterizing the rheology of a model material as well as its behavior under extrusion
similar to what would be found in actual 3D printing technologies.
BACKGROUND
Rheology Effects on Printability and Print Quality
Many printing materials exhibit non-Newtonian, viscoplastic, or viscoelastic
behaviors such as shear thinning, yielding, or shear thickening. The ability and quality
of any additive manufacturing process such as 3D printing is very dependent on material
rheology in terms of both printability and print quality. Unfortunately, the necessary
properties that result in good final print quality are often at odds with those that make
for easy printing, requiring a delicate optimization.[6,7]
The process of extrusion based printing is always easier for materials with low
yield stresses and viscosity. This is due to the effect of these parameters on the minimum
pressure to create flow and the sustained pressure drop needed to drive flow through the
nozzle. The minimum pressure needed to create flow for a material with a yield stress
in a circular tube is described by Eq. (1).[30]
𝑃𝑚𝑖𝑛 = (4𝐿
𝐷) 𝜏𝑦𝑖𝑒𝑙𝑑 (1)
In Eq. (1), Pmin is the minimum driving pressure, L is the length of the extrusion nozzle,
D is the diameter of the nozzle, and yield is the material yield stress. As can be seen in
Eq. (1), lower yield stress values reduce minimum driving pressure.[8,9,15,30] This is
desirable in 3D printing, since the flow is not continuous but frequently starts and stops
during a print. High yield stresses will require the machine to constantly apply large
pressures to overcome yield, which will require a more robust system capable of
constantly and reliably applying such pressures in a controlled manner.
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After yield, the continuous driving pressure necessary for a given flow rate in a
circular tube will depend on desired flow rate and viscosity. A basic non-Newtonian
model is a power law fluid,
𝜇𝑒𝑓𝑓 = 𝑘𝛾𝑛−1 (2)
where eff is the effective viscosity at a particular shear rate, is shear rate, k is the
consistency index, and n is the power law exponent that determines the degree of shear
thinning or thickening. Newtonian fluids have n =1. For n <1, fluids shear thin with
smaller values of n indicating more significant shear thinning. For n > 1, materials
shear thicken. Although this model is simplistic and only captures shear behavior, it
allows us to understand in a simple way how these behaviors will affect the flow in a
nozzle in terms of the relationship between flow rate and pressure,[31]
𝑄 =𝜋𝑅3
1
𝑛+3
(Δ𝑃
𝐿
𝑅
2𝑘)
1
𝑛 (3)
In Eq. (3), Q is the volumetric flow rate, r is tube radius, ΔP is pressure drop, and L is
tube length. As can be seen, lower consistency indices (k) will result in a lower pressure
requirement for higher flow rates; and, smaller n will create materials that are easier to
flow as applied pressure increases. In general, to reduce continuous driving pressure for
a desired flow rate, low k and n are advantegous.[8,9,15,30]
Printability is also affected by how an extruded material exits a nozzle of a
printer. Viscoelastic materials forming threads are prone to a wide array of unhelpful
behaviors, in particular jet breakup and satellite drop formation. Jet breakup due to
capillary forces is a natural phenomenon that would make sustained printing difficult.
Elasticity tends to stabilize jets against breakup, which is advantageous. However, it
also means stopping printing quickly is more difficult since elastic fluids will be more
stable. Alternately, shear thinning can accelerate breakup, which would be problematic
if breakup occurs before printing is finished. Furthermore, high elasticity materials with
long relaxation times can exhibit the formation satellite drops or beads on a string
phenomenon during breakup, which would also be problematic to printing. Obviously,
any of these phenomena would negatively impact the ability of a material to be printed
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continuously with controlled diameter. In general then, if materials have high relaxation
times and elasticity without yield, breakup and satellite drop formation may be a
concern. Yielding fluids will avoid some of these issues, but are prone to snap off
behavior at critical thread dimensions, which could also affect continuous printing.[32-
35]
Print quality is the ability of the printed material to match the intended design,
stay in place once printed, and maintain its printed shape. However, many printability
problems bleed into print quality. For instance, material viscosity will also affect print
fidelity and processing times by limiting the rate at which the print head can move, since
mismatch between printed heads and extrusion rate can cause changes to extruded
filament diameter. Therefore, shear thinning can create resolution difficulties if the
pressure in the extrusion nozzle is not well controlled.[8,9,15,30,7] Thread breakup will
affect the ability of the printer to match the programmed design, and may cause
significant deviations in design. Other problems that may occur at the nozzle include
die swell,[36,37] in which an extruded viscoelastic material expands immediately at the
tip of a nozzle due to large normal stresses; this would affect print resolution. In general,
filament breakup and die swell are related to the overall elasticity of extruded materials;
larger storage moduli and relaxation times would cause more complicated filament
breakup behaviors and greater die swell in general.
Print quality is generally improved by printed materials being able to support
their own weight and avoid road spread, the widening of the printed thread due to
gravity. High yield stress is a benefit in avoiding this issue, since a material with a yield
stress will not flow under quiescent conditions, avoiding road spread. Shear thinning,
is also beneficial, since such materials will be more resistant to flow under quiescent
conditions as well. In general, elastic materials better maintain their shape and recover
the initial shape after stress relaxation from the printing process. [8,9,15,30,7] Print
quality is most benefited by larger yield stresses and elasticity; however, these
properties typically increase the necessary driving pressure, and can also create
instabilities which can both stop printing and/or affect surface properties of the material.
Wet Granular Materials for 3D Printing
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In broad perspective, 3D printed colloidal materials can be categorized in three
ways: (1) low volume concentration suspensions of non-attractive particles; (2) low to
higher concentration of attractive particles that form colloidal gels: and, (3) higher
concentrations of repulsive particles that can form colloidal glasses. All of these
materials are non-Newtonian in shear, and depending on the specific composition can
exhibit shear thinning, shear thickening, yield stress and other viscoelastic or
viscoplastic behaviors. The mechanisms and range of these behaviors have been widely
documented and studied in other literature.[38-40] Above the volume fractions
typically used in the majority of 3D printing of colloidal materials (~60 %) the volume
fraction of particles becomes so large that the liquid does not fully occupy the void
space.
These materials are classified as “wet granular” materials, in which particles are
the primary component and liquid bridges gaps between particles. The magnitude of the
soft cohesion forces caused by capillary bridges are affected by individual particle
dimensions, liquid volume, and formation/breakup, creating a hysteretic and statistic
nature to the cohesion. Due to the combination of hard and soft interactions this creates,
wet granular materials exhibit several regimes of flow behavior, which are characterized
through the use of the non-dimensional Inertial number (I) defined by Eq. (3).[41] In
Eq. (3), is the average density of the composite and all other terms have been
previously defined.
𝐼 =𝛾�̇�
√𝑃𝜌⁄
(3)
Initially, stresses are not large enough to breakup local particle jamming, and
there is no flow.[41] Yield stress will depend on the confining pressure applied as well
as the magnitude of friction and cohesion interactions.[42,43] After yielding, wet
granular systems typically present non-homogenous flow response to deformation s due
to local jamming, capillary force behavior and the statistic nature of the collisions.
Because of this, the local shear stress can be independent of global shear rates.[44-46]
Simple continuous shear is rarely seen in such systems, instead local areas of low mass
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fraction particles will typically shear first due to their less restricted movement,[47]
which often occurs near the boundaries of the material.[48]
For I <<1, flow is in a quasi-static regime where particle friction and cohesion
forces dominate flow response. Particle movement is restricted by the size of local
aggregates, frictional contact and the magnitude of the cohesive interactions. The size
of jammed clusters will decrease with increasing I, allowing greater movement and
reduced resistance to deformation. [49-51] It is possible in the quasi-static regime to
have regions of non-yielded material flow by being carried by bands of yielded
materials,[52] creating sliding layers of particles[53] that can also show stick-slip
behavior.[54]
For I >>1, particles become fluidized and resistance is collision based. Non-
homogenous behavior will present itself as shear banding in the intermediate and
collisional regimes.[45,48,46,47,50,55] The size and nature of the bands is directly
related to the amount of solvent in such systems, with increasing larger bands with
increasing solvent content and variation in solvent viscosity.[55,46] Streamline
curvature will generally also result in increased shear banding due to particle migration
caused by curvature in the streamlines.[45] Intermediate regimes occur at I ~ 1, where
particles are somewhat mobilized to flow, but still subject to friction and cohesion
forces.
Because of the above behaviors, rheological measurement of such materials is
quite difficult and still a major challenge.[56] In fact, the measurement technique and
processing method will often determine the value of such materials measured, indicating
that it is difficult to some degree to translate rheology results to other
processes.[43,44,49] Furthermore, the rheology of wet granular materials is
unsurprisingly very system specific, but does tend to exhibit a range of common
behaviors. Typically wet granular materials will exhibit some degree of shear
thinning, with viscosity decreasing with increasing shear rate or inertia number.[57,55]
These flows can often be modeled as power law fluids or Herschel-Bulkley in these
regimes.[57]
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The overall magnitude of the viscosity will vary greatly as particle properties
and solvent are changed. Increasing particle roughness typically increases overall
dissipation due to increased friction and also changes to the structure of capillary
brdiges.[46] Particle size will also effect overall viscosity. Increasing particle size
creates less viscous material by decreasing the effect of the viscosity and capillary
bridge and creating more deformable clusters of particles.[58,54] Larger particles will
also often exhibit lower yield.[54] Bimodal distributions of particles will also tend to
decrease viscosity. Changes to particle surface chemistry can result in changes to
solvent wettability. Increasing wettability tends to make systems more viscous and
elastic due to increased strength of capillary bridges and large granule size.[59,60]
MATERIALS AND METHODS Material Preparation
An inert formulation was designed for this study to avoid the influences of
reactivity and focus on the rheological characteristics of processing a mock energetic
mixture. The formulation is composed of a rough, polydisperse colloidal powder that is
representative of the metallic colloids found in energetic composites. The colloidal
particles are pentaerythritol (PET) and are millimeter sized particles obtained from Alfa-
Aesar. For energetic material combustion a particle diameter that is 100 microns or
smaller is ideal for fastest burn times.[61] To create the representative energetic mixture,
the powder particle size was reduced with a Retsch CryoMill using a frequency of 18
Hz for 30 seconds for a 5 gram sample size. The sample is then placed in a Retsch AS
200 Basic sieve shaker for 60 minutes at a frequency ranging from 2-3 Hz. This is done
through several different sieve sizes to create several representative particle size ranges:
38-75 microns, 75-90 microns, and 250 – 350 microns. The distribution of diameters
has not been characterized for this study. In typical energetic formulations there would
be a wide distribution of particle diameters as in this mock mixture. Figure 1 show
scanning electron microscope (SEM) images of the powder post milling.
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Figure 1: SEM images of (Left) particles recovered from 38 - 75 micron sieves and
(Right) particles recovered from 75 - 90 micron sieves.
To complete the system, a silicone based binder (PDMS) was obtained from
Dow Corning (Sylgard 182); this material is added without curing agent. The final mass
fraction of all tested systems was 80% by mass solids and 20% by mass PDMS. When
preparing the mixture, the colloids were mixed with silicone binder using a THINKY
ARE-310 planetary centrifugal mixer at 2000 RPM for 2 minutes and 2200 RPM for 30
seconds in the opposite direction to deform the mixture and eliminate air bubbles. Figure
2 shows photographs of the materials used in Table 1. In general, as particle size
decreases, the mixtures resemble more cohesive materials. For the smallest particle
system, the final material represents a silly putty like material (Fig. 2b). As size
increases, the material looks more like wet sand (Fig. 2d); finally at the largest particle
size (Fig. 2f), the mixture is very course and loosely held together.
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Figure 2: (a) 38 – 75 m particles without any binder, and (b) same particles 80% by
weight with 20% PDMS. (c) 75-90 m particles without any binder, and (d) same
particles 80% by weight with 20% PDMS. (e) 250 - 350 m particles without any
binder, and (f) me particles 80% by weight with 20%PDMS.
Table 1: Results of fit of power law model to quasi-static flow regimes
Particle
Size [m] K n
38-75 2502 -0.14
75-90 948 0.075
250-350 308 .13
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Rheology
To characterize the rheological properties of the mixture, a TA Instruments
Discovery HR-3 rheometer was used with a 20mm parallel plate geometry and a Peltier
plate set to 25 Celsius. The sample was placed between the parallel plate and Peltier
plate at a gap set to 1000 microns. Using the system in both steady shear and oscillatory
shear allows characterization of viscosity and elastic and viscous moduli. Furthermore,
normal pressure is recorded during tests, which can be used in the calculation of I (see
Eq. (3)).
As noted above, the non-homogenous shear response of these materials is well
established. There are no means to visualize these flows during tests, so there is no way
to ascertain if shear banding or plug like flows occur. Hence all reported viscosities and
moduli should be considered apparent values based on the assumption of a typical
Couette flow field as would be created by a parallel plate geometry used here. A concern
with these materials is fracture. This can typically be observed during experiments on
the edge of the material visible under the parallel plate. No evidence of fracture
throughout experimentation is observed by visually inspecting the edge of the materials.
RESULTS AND DISCUSSION
Printability
In order to gauge printability of wet granular solids, their behavior under steady
shear at a range of shear rates is examined. Using the three ranges of powder sizes at
80% solids loading by mass, viscosity was measured over a range of shear rates as
shown in Fig. 3. The first thing to note is that for all particle sizes the materials are non-
Newtonian with pronounced shear thinning across all shear rates. As particle size
decreases, overall viscosity magnitude increases at all shear rates, which can be
attributed to the larger surface area of the smaller particle size groups creating more
inter-particle friction and hence resistance to flow. Also, liquid bridges in this system
will have smaller radii and hence larger Laplace pressures and surface tension forces,
which will also increase viscosity. The degree of shear thinning in all sample materials
is approximately similar despite the difference in viscosity magnitudes. However, at
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the lowest shear rates tested, the viscosity begins to diverge for the smaller two particle
distributions, indicating these materials definitely have a finite yield stress. The
materials all have a distinctive transition in the degree of shear thinning that occurs at a
shear rate between 1 and 10 s-1, which may indicate a transition to the collisional regime.
The viscosity data is replotted as a function of inertial number (Eq. (3)) using the
density of the materials as calculated by their combined mass fractions and normal stress
data from the rheometer, in Fig. 3b. At low I in the quasi-static to transitional regimes,
there is a clear dependence on particle size, where friction would be important. The
previously seen transition in behavior now occurs at an inertial number of ~100. After
this point, the data collapses onto a single line for all particle sizes. This indicates a
transition to the collisional regime where the inter-particle collisions determine
rheology rather than friction and surface tension forces. The reduced dependence on
particle size is due to the reduction of these two forces that are dominated by particle
size. Although particle size does effect likelihood of collision between particles, it
would appear mass fraction is the more important controller of this behavior. Since, all
systems shown in Fig. 3 are at identical mass fractions, the viscosity curves collapse
into a single trend for I > 100.
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(a) (b)
Figure 3: (a) Viscosity data for all particle sizes compositions at 80% by weight solids
and 20% PDMS as a function of shear rate. (b) Identical data to (a) but plotted vs. Inertial
number using normal force data obtained from rheometer.
The nature of the observed shear thinning in the quasi-static regime is further
explored by attempting to fit the data to the simple power law model from Eq. (2). Table
1 shows the results of the fit to all data before the change in slope between at 1 s-1 (i.e.,
before the material is in the collisional regime). All fits in this range of data had R2 >
0.99. As Table 1 shows, the shear thinning exponents are exceptionally small, and in
fact negative for the smallest particles. Shear thinning exponents approaching or less
than 0, indicate a yielding, since for a yielding materials stress will be proportional to
inverse of shear rate;[62] therefore, it is concluded that the smallest two materials indeed
have a yield stress, and are deforming in the quasi static regime. Hence the local
behavior of this material will be very different than the average global data recorded by
the rheometer. The largest particle data shows significant shear thinning, but with a very
small, although non-zero exponent. It is possible that this material either has a very
small yield stress is not being captured by the rheometer, or perhaps does not have a
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yield stress. In either case, the material also would be considered to be in the quasi
static flow regime, but shows a truer shear thinning like behavior. For all materials,
being in the quasi-static to transitional regimes would also indicate a high dependence
on particle friction, which is why the pronounced dependence on particle size is
observed. The high values of k indicate the overall large resistance to flow this materials
have, which decreases with increasing particle size. When the data in the collisional
regime is fitted to the power law fluid model of Eq. (2), all materials have n < 0,
indicating all materials have yielded, as expected.
The data in general indicates that these materials have very high viscosity and will
make printing difficult, especially for smaller particles. The high viscosities at low shear
rates indicates tremendous pressures will be needed in order to create flow. However,
at higher I or shear rates, transition to collisional flows alleviates this problem since all
materials exhibit significant shear thinning. In general, printing smaller particle mixes
may be possible provided shear rates are high enough. However, the overall larger
viscosities of smaller particle systems will likely reduce extrusion rates which will
reduce print head speed. In general, the materials present the possibility to be presented
but will likely have a restrictive operational phase space within which printing will be
possible.
Looking at the viscosity results in Fig. 3, the major concern for printability is the
high viscosity that make printing very difficult due to high driving pressures required.
One way to deal with such a condition is to apply a pre-shear to the material before
printing. Pre-shearing/conditioning applies a known flow to a material to modify its
state in order to create lower initial viscosities. In this case, pre-shear could rearrange
particles out of the jammed state and into a more collisional mode before actual printing
begins.
Figure 4a, shows the effectiveness of pre-shear based on time of applied pre-shear.
A 2 s-1 shear was applied for varying durations, and viscosity is reduced by an order of
magnitude as pre-shear time varies from 0 to 10 minutes. The reduction in viscosity is
attributed to particle rearrangement creating a less jammed state, allowing flow to occur
in the transitional/collisional regime at I earlier than indicated in Fig. 3. The pre-shear
Texas Tech University, Michael Sweeney, December 2017
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time has a moderate effect on the viscosity reduction, which is most evident at the lowest
shear rates tested. However, at higher I where transition to the collisional regime was
seen in Fig. 3, all viscosity curves collapse onto a single trend. This indicates that a
particle rearrangement at the applied pre-shear was not enough to move the
microstructure fully into a collisional regime, and hence all data collapses once that
regime occurs.
In Figure 4b, the effect of pre-shear magnitude is examined by applying two shear
rates, one below the collisional regime and one above the collisional regime, to the
system for 2 minutes and then examining the flow curve again. At the 2 s-1 shear rate,
the same behavior is observed in Fig. 4a. However, the 10 s-1 shear rate behavior is very
different; a low shear viscosity plateau is seen, and the high shear rate collisional regime
does not collapse onto the previous collisional regime. Instead, the viscosity is always
lower than the previous tests. At the lower pre-shear shear rate, the primary effect is the
breakup of clusters, which allows material to flow more easily. However, the
microstructure is still in the same basic state at the beginning of the flow curve. Above
10 s-1, the material is already in the collisional regime, which means there is near
complete cluster breakup and particle migration due to shear. The microstructure is
substantively different. Therefore, when the lower shear rates are immediately tested,
the flow response is completely modified, creating the zero shear viscosity plateau and
lower overall viscosity at all shear rates.
One common means of reducing viscosity of any material is to heat it up rather
than applying pre-shear (as shown in Fig. 4c). Although with energetic materials this
may be unwise, Fig. 4c explores the concept in general as a means of increasing
printability by reducing viscosity (Fig. 4c). Unsurprisingly, temperature does not have
a large effect on these systems. This is because the particles are quite large and not in
solution, so increased thermal motion/energy is not a major factor in their flow
resistance, and because the binder (PDMS) is not known to be affected by temperature
over this range.[63] Although this is particular to the system chosen for this study, other
systems with more heat sensitive binders may be better suited by such a technique.
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For the effects shown in Fig. 4 to be useful, the wet granular material should
maintain the pre-shear induced properties for a substantial amount of time, allowing
pre-shear of a material and then multiple print runs to maintain the new microstructure.
It is important then to study how long the microstructure takes to revert back to its initial
state after such flow is applied. To observe the timescales for how long the pre-shear
conditions last, the same 10 s-1 pre-shear is applied to the material, and then structure
recovery is monitored with small amplitude oscillatory shear shown in Fig. 5. Recovery
time is found to be approximately ~ 60s. Figure 5 indicates that pre-shear is effective,
but microstructure recovery is quite fast, and hence any pauses in printing may negate
the effects induced with pre-shear observed here. Therefore, any thought of taking
advantage of such behaviors will require significant planning of print head motion and
starting/stopping during prints.
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Figure 4: Effects of pre-shear on viscosity for 80% by weight 75 – 90 m particle size
with 20% PDMS. (a) Pre-shear of 2s-1 was applied for 0, 2 and 10 minutes, and then a
shear rate sweep was immediately conducted. (b) Pre-shear is applied with 3 different
shear rates for 2 minute each, and then results of flow sweeps conducted immediately
after are shown. (c) Effects of temperature on steady shear viscosity as a function of I.
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Figure 5: Recovery test for 80% by weight 75 – 90 m particle size with 20% PDMS.
Pre-shear was applied at 10 s-1 for 2 minutes and followed by a frequency sweep at 10
radians per second, 0.01% strain for 10 minutes.
Print Quality and Extrusion
Final print quality is primarily determined by material viscoelasticity, yield stress
and relaxation time. Those values as a function of particle size are shown in Figure 6.
In general, all materials are viscoelastic with pronounced elasticity over a range of
frequencies and strains. Looking at strain sweep data (Fig. 6a), all materials behave
relatively similar, being primarily elastic over all strains. All the materials yield from
the linear to non-linear regime at an approximate a strain of 0.1%. Using this strain
value and the storage moduli of the material, a yield stress for these materials can be
estimated using the following relation, 𝜎𝑦 = 𝐺′𝛾, where G’ and are taken from the
yielding point on the strain sweep curves. For the values in Fig. 6a, the approximate
yield stress is found to be 10 kPa. The linear regime is very small for these materials.
After yield, all data collapse at large strains as materials move into transition/collision
regime, similar to results in steady shear and pre-shear.
The frequency sweep data is in a regime in which the materials are slightly more
viscous than elastic. There is moderate frequency dependence, but generally the moduli
are consistent over the frequencies tested (Fig. 6a). The material should be in the quasi-
static/jammed regime due to the low strains applied in this test, and so the response is
expected to be similar to the initial points of the steady shear data. Indeed, similar
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particle dependence to steady shear tests is observed. From this data, it is observed that
the cross over frequencies for these materials are likely occurring close to but below 0.1
rad/s, which means this materials should have a relaxation time of at least 60 seconds.
This is in good agreement with the structural recovery experiments shown in Fig. 5. In
general the high yield and relaxation times are favorable for print stability of such
materials.
Figure 6: Small amplitude oscillatory shear data for mixes identical to those in figure
3. Solid symbols are for storage moduli, and hollow for loss moduli. (Left) Strain sweep
(1 rad/s) and (Right) frequency sweep (1% strain).
Given the results from rheology analysis in Figs. 3-6, printability is characterized
further by extruding the materials through a nozzle using a plunger driven by a high
applied pressure (Fig. 7). Although, wet granular materials are not typically used in 3D
printing, they have been used in extrusion based processes, particularly in the drug
fabrication field where extrusion and spheronization are often used in the manufacturing
of drug loaded pellets.[57,64,65] Yield and elasticity make extrusion of such systems
difficulty, and overall processes are quite dependent on rheology of a given material.
Also, due to the high pressures required in such systems, there is often extrusion of the
liquid phase from the solid mass, which can cause surface fracture and other problems.
Overall, the extrusion of wet granular materials requires high pressures to overcome
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yield and large apparent viscosities, and can be difficult to control final material
properties due to weeping of wetting materials and non-local structure.[57,66,30,64,65]
Given the rheology results, printing is expected to be difficult and require large
pressures due to high viscosities and yield stress, especially without any significant pre-
shear. Using Eq. (1) and the yield stress found above, the minimum pressures needed to
drive flow in these tests are estimated. For the 3 mm nozzle, a Pmin of 38 PSI and for
the 1.6 mm nozzle, a Pmin of 72 PSI is calculated. These pressures are reasonably close
to the minimum pressures used in Fig. 7, indicating the merit of rheological testing for
such systems. They also indicate the relatively high pressures required to create flow,
which as mentioned above can cause weeping and other issues.
It is difficult to estimate the extrusion speed of the materials using the power law
model because for the first 2 fluids, the extremely low and/or negative exponents
indicate its use is inaccurate. Also, it is difficult to gauge what flow regime the material
is in, and whether the fitted data for the quasi-static regime is accurate. However, for
the using the values from Table 1 and Eq. (3). We estimate average velocities of 0.03 to
20 mm/s from the lowest to the larges applied pressure. We were not able to measure
the speed of the fluid or the extrusion head using the current experimental setup, but
believe these velocities are in line with what was observed. Without having an exact
speed of the flow velocity, there was mismatch between the rate of extrusion and nozzle
head print speed. Because of this, the final width of the extruded materials in Fig. 7 does
not exactly match nozzle diameter (3 mm for Fig. 7a and 7b, and 1.6 mm for 7c).
Although die swell could cause a similar effect, we believe the inconsistent nature of
the width changes indicates this was primarily caused by the speed mismatch.
One difficulty in measuring the flow rate or the speed of the extrusion head in all
tests were the significant issues in maintaining extrusion without snap off. Snap off is
a typical mechanism of jet breakup in yield stress materials. There may be issues here
in the print head speed and flow speed mismatch adding extra stresses which aided this
behavior. However, in general snap off was worse with the increasingly smaller
particles which showed more yield like behavior.
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Figure 7a displays results from the largest particle size mixture at a range of
pressures through a 3mm nozzle. All pressures give relatively consistent results in terms
of ability to extrude. There is some variation in width of the materials, but overall width
stays relatively consistent. This consistency is not affected by pressure. The final width
of the extruded materials is slightly larger than the nozzle; this is due to variance
between extrusion speed and movement of the nozzle. The particles are clearly visible
in the extrusion, which should not be mistaken for air bubbles. This material was the
least elastic and had the least yield like behavior in all steady shear and oscillatory shear
tests. No evidence of weeping is observed due to the high pressures applied; nor are
there any visible issues due to the mix of high pressure and elasticity /yielding causing
surface roughness, jet breakup or any other problem. The pressures needed here to
create continuous flow were not used to estimate any flow rates with Eq. (2 and 3), given
the inability to predict the transient flow regime.
Figure 7b displays the same nozzle but for a smaller particle size mix. The width is
relatively consistent at all pressures. At higher applied pressures there is more variation
in the width. Although, there are less defects at edges and surfaces at higher pressures.
Furthermore, the maintaining of such dimensions indicates the high relaxation times and
yield stress are inhibiting road spreading for these materials. The driving pressures all
exceed the minimum calculated pressure based on estimated yield stress. There are no
signs of surface roughness/fracture. As mentioned these are typically high yield stress
materials in spherionization. Given this material was indicating yield in steady shear
tests, but was of significantly smaller overall viscosities in steady shear, it is not
surprising to see some evidence of the high viscosity and yield on the surface properties.
The same material is printed through a smaller 1.6mm nozzle in Fig. 7c. As pressure
increases, surface defects are observed to increase due to high stress on material edges
as extruded. Print widths however are much more consistent than all the other prints.
Final diameters are slightly smaller than the nozzle, which again is due to large
relaxation times and yield stresses inhibiting road spread. In general, material in this
nozzle requires higher pressures to print. Good agreement between the minimum
pressure required for extrusion and the estimated value from oscillatory shear is
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observed. This material, had the most obvious yielding signature in steady shear, and
unsurprisingly the greatest issues in surface quality are observed with these system. In
particular, pronounced roughness all along the surface at the highest print pressure is
seen. This indicates that the yield stress was causing significant deviations in ideal flow
at the nozzle exit and neat snap off behavior was creating problems in the surface.
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Figure 7: (a) 250 -350 micron range extruded through 3 mm nozzle at varying
pressures. (b) 38 -75 micron range extruded through 3 mm nozzle at varying pressures.
(c) 38- 75 micron range extruded through 1.6 mm nozzle at varying pressures.
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CONCLUSIONS
The feasibility of using higher mass fraction colloidal systems for 3D additive
manufacturing through extrusion printing was studied through the use of rheology and
some limited extrusion of such materials. Using a model material representative of
many real energetic formulations and possible ceramic systems, there are some inherent
difficulties in working with such materials in terms of both printability and print quality;
however, through proper processing it may be possible to work with such materials. The
high viscosity and yield stresses of these materials is problematic for successful printing
using traditional pressure only based extrusion methods. Such high viscosities indicate
the need for flow driven not just by pressure but also through a secondary mechanical
means such as a positive displacement piston, auger or some other mechanical system.
These problems can be somewhat alleviated by creating shear rates large enough to
create collisional flow regimes, which provide significant alteration of the
microstructure of these systems to lower viscosity over a wide range of flow rates.
Unfortunately, it also appears that any benefits of pre-shear may be short lived.
Overall the materials have sufficient yield stress and elasticity to maintain its
shape which bodes well for print quality. However, pronounced surface roughness at
higher flow pressures for more elastic systems were seen, which is problematic. In
general, these materials major issues appear to be on the printability side rather than
print quality. The rheological profile of these materials creates significant challenges in
print quality due to yield stress induced surface roughness at high pressures as evidenced
in extrusion tests.
These initial results indicate there is some promise in the potential of printing
higher mass fraction colloidal materials. However, the phase space of possible
processing speeds, flow rates, and resolutions will likely be severely limited in
comparison to other lower mass fraction materials due to the non-trivial issues the
complex rheology of these systems creates. Furthermore, there are still many larger
questions that need to be explored in terms of the ability of layers to weld together
during printing, resolutions, shear banding in nozzle, and curing times. Nonetheless, the
potential of such materials to overcome flaws in lower mass fraction prints in terms of
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solids density and to open up new applications such an energetics printing warrants
further study of such system beyond these initial feasibility tests.
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CHAPTER 2
EFFECTS OF RHEOLOGY ON THE SYNTHESIS OF MG MNO2
THIN FILMS
ABSTRACT
Rheological techniques were used to characterize magnesium (Mg) and manganese
dioxide (MnO2) powders mixed with polyvinylidene fluoride (PVDF) binder and n-
methyl pyrrolidone (NMP) solvent to understand the effects of processing on energetic
thin films. Varying shear rate over a prolonged period was used as a parameter to study
the flowability and the suspension of particles to better understand the behavior of the
non-Newtonian fluid. Flame speed and the heat of combustion were investigated for a
variety of shear rates. The composition of the thermite thin film was held constant at an
equivalence ratio of one with a 0.45 solids-liquids mixing ratio at a wet film thickness
of 300 microns. Rheology measurements show that particle suspension due to high shear
rate creates a much more homogenous microstructure, allowing flame speeds to increase
of upwards of 39.9%. Changing the shear rate to a significantly lower frequency creates
an immobilized flow that is driven by frictional forces between particle resulting in a
thin film that is very porous throughout. These results show that a varying shear rate
affects the microstructure and energetic potential of thermite thin film created in an
additive manufacturing process.
INTRODUCTION
Consisting of a metal fuel and metal oxidizers, different variations of thermite
have been widely researched [67] and developed for joining, brazing, and welding [68]
as well as for thin film applications [69]. With demands of miniaturization, integration
while providing localized power generation, energetic thin film composites are a
growing area of research. The most common synthesis method combines fuel and
oxidizers with a binder solvent system and blade casts the mixture into a film. The
process described has been applied in the manufacturing of capacitor, batteries, and
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ceramic films [70-72]. This method, solid loading by mass plays an important role in
the morphology of the deposition of the slurry mixture. Meeks et all. showed that
magnesium (Mg), manganese dioxide (MnO2), polyvinylidene fluoride (PVDF), and n-
methyl-pyrrolidone (NMP) at a solid loading of 45% showed optimum properties as
well as flame speeds for this method [73].
This study further details the idea of using the blade casting technique by
exploring the processing effects to optimize the technique through rheological
behaviors. In many technological application, particles are suspended in a fluid that
display complex non-Newtonian rheological behaviors, for example, paints, makeup,
and other luxurious consumer products. When these suspensions are subject to flow, the
microstructure rearranges to accommodate the applied hydrodynamic and colloidal
forces. At a moderate volume fractions of solid material within a suspension, the forces
within the colloidal dispersion can be compared to forces induced by the
hydrodynamics, where the suspension can be subjected to organization when applied
under shear flow [74]. Under certain flow conditions, the organization of suspended
particles and microstructure can be evaluated using rheological techniques.
An advantage to optimizing fluid flow conditions for thermite in its slurry form
is that the final product will be much more homogenous throughout, which will leave
the thermite thin film to be more dense with less voids and cavities. This allows the thin
film to be much more durable and easier to handle considering it only has 1% binder by
mass which also allows safer handling of the final film which won’t fall apart while
transporting. The homogeneity also plays an important role in reactivity which can be
enhanced through rheological characterization to obtain a homogenous microstructure
throughout the cross-sectional area of the thermite thin film.
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EXPERIMENTAL PROCEDURES
Materials and Synthesis
Powdered magnesium (Mg) with a purity of 99.8% sieved to a -325-mesh
obtained from Alfa Aesar and manganese oxide (MnO2) with a purity of 85% sieved to
a -1250-mesh were obtained from Sigma Aldrich were the energetic composite for all
films mixed at a stoichiometric ratio. The reaction for this base composition is shown
in Eq. (4)
𝑀𝑔 + 𝑀𝑛𝑂2 → 2𝑀𝑔𝑂 + 𝑀𝑛 (4)
Average Mg particle diameter is 3.1 microns and average MnO2 particle
diameter is 4.6 microns as shown in table 2. The binder-solvent system for creating the
thin film was Polyvinylidene fluoride (PVDF) dissolved in n-methyl-pyrrolidine
(NMP). The mass of the binder was held constant for all films so that the final loading
was 1% by mass for the dry film while the solvent was held constant for all films at 55%
by mass. The slurry was mixed in a planetary centrifugal mixer (AR250, Thinky, Japan)
at 1600RPM for one and a half minutes. The mixture was created on a thin film of
Mylar at a thickness of 130 microns which was attached to a TA Instruments Discovery
HR-3 (DHR3) where the wet film thickness was set at a constant 300 microns using a
40mm parallel plate geometry at 25 degrees Celsius. Samples were created at a constant
shear rate of 0.1 Hz, 10 Hz, and 100 Hz for 1 hour and dried at 80 Celsius for twenty-
four hours as shown in Fig. 8.
Table 2: Magnesium & Manganese dioxide particle size distribution
Mean
Median Mode Standard Deviation
Mg 3.183μm 2.359μm 2.007μm 2.694μm MnO2 4.665μm 4.047μm 5.748μm 2.907μm
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Figure 8: Flow sweeps of thin film at constant shear rate
Rheological Measurements
To characterize the rheological properties of the mixture, a DHR3 was used with a 40-
mm parallel plate geometry and a Peltier plate set to 25 degrees Celsius. The sample
was placed between the parallel plate and Peltier plate at a gap of 600 microns. Using
the system in both steady shear and constant shear allows characterization of viscosity,
static, and dynamic properties of the suspended particle mixture.
Experimental Measurements: Flame Speeds
The mixture dries to form a 40mm diameter, 300-micron thick thin film circle.
The samples were cut using a box knife creating a 10mm wide 40mm long strip. To
ensure repeatability between the three samples, the films were examined for any
rheological cracking. Samples were placed on a steel bar and secured using
nonconductive adhesive and placed perpendicular to the viewing window in the
combustion chamber. The sample was ignited using a nichrome wire and recorded using
at 28,000 frames per second at a resolution of 1280 x 720 pixels using Vision Research
Phantom VII high speed camera. The videos were converted into still images and were
processed to find the horizontal position of the leading edge of the flame. The reported
flame speeds represent an average of five samples, where the uncertainty of the flame
speed is reported as the standard deviation of the five samples.
0.1
1
10
100
0 1200 2400 3600V
isco
sity
(P
a*s)
Step Time (s)
0.1 Hz
10 Hz
100 Hz
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Experimental Measurements: Heat of Combustion
Heat of combustion measurements were collected in a 1341 Plain Jacket Bomb
Calorimeter from Parr Instrument Company. The 40-mm diameter sample was placed
into the bomb and purged with oxygen until pressurized to 35-atm and placed in a water
bath containing 2 kilograms of water. Samples were ignited using 10 cm length of Parr
45C10 fuse wire. The temperature rise of the bath was recorded using a K type thermal
couple and used to calculate the resultant heat of combustion. Heat of combustion
calculations were performed in accordance with the ASTM standard [75].
RESULTS
Rheological Processing
Particle flow in blade casting is very important to achieve a homogenous
microstructure within the thermite thin film. Particle packing can be manipulated by
altering the technique of deposition depending on the characteristic of the fluid which
can be examined through rheological methods. By enhancing the technique of
deposition of the thermite thin film it is possible to improve the energetic potential of
your product.
When creating thermite thin films, the mixture typically stays in the medium-
high volume concentration suspension of particles which exhibits non-Newtonian
behaviors such a shear thinning, shear thickening, yield stress, and other viscoelastic
properties. To better understand the dense particles under flow where granular material
makes up for a majority of the fluid, where the material is confined under a normal stress
P, between two parallel plates which apply a shear rate �̇�, the diameter of the particle d,
and the density of the solution ρ, can be characterized using the non-dimensional inertial
number (I) defined by Eq. (5) [76].
𝐼 = 𝛾�̇�
√𝑃/𝜌 (5)
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Initially at low shear rates, stresses are not large enough to breakup frictional
forces or particle jamming which causes no flow within the suspension [76]. Once the
particles have yielded, the suspension will present a non-homogenous flow due to local
jamming and capillary force behavior. Because of this phenomenon, the local shear
stress can be independent of the global shear rates [77-79]. This can be described as the
quasi-static regime, for I << 1, where particle friction and cohesion forces dominate the
flow. This is caused by the size of local aggregates, frictional contact, and the magnitude
of cohesive forces. The quasi static flow can be subject to regions of non-yielded
material, but this can be changed within increasing inertial number, allowing movement
and reduction in resistance between particles [80-83]. The dynamic regime, for I>>1,
local aggregates break the frictional forces that cause the local jamming and particles
become fluidized and resistance is collision based. Intermediate regimes occur at I ~ 1,
where particles are subject to flow but can still be somewhat immobilized by frictional
and cohesion forces. These different regimes can be seen in Fig. 9 and Fig. 10. It is seen
that the sample made at 0.1 Hz, 10 Hz and 100 Hz falls into the regimes of I<<1, I ~ 1,
and I>>1, respectively.
Figure 9: Magnesium and manganese dioxide slurry flow sweep representing a shear
thinning non-Newtonian fluid
0.1
1
10
100
0.01 0.1 1 10 100Ap
par
ent
Vis
cosi
ty (
Pa*
s)
Shear Rate (1/s)
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Figure 10: Viscosity vs Inertial number representing magnesium and manganese
dioxide representing the different regimes of the fluid
Additionally, all three samples were examined using a SEM to further
understand how the processing techniques and inertial numbers effect the characteristics
of the thermite thin film. The images represented in Fig. 11 and Fig. 12 depicts the
surface and cross-sectional images of each of the corresponding shear rates where the
magnification of the surface images and cross-sectional images is represented by 200-
microns and 100-micron scale bars, respectively.
Figure 11(A) and Fig. 12(B), representing the shear rate at 0.1 Hz where the
inertial number is less than one. It can be observed that the structure is porous
throughout the surface area where shear was applied and the cross-sectional area near
the Mylar. This is due to the constrained forces within the suspension between particles
causing local jamming and clustering giving us a final product that represent a very
porous structure.
Where as in Fig. 11(A) and Fig. 12(B) representing a shear rate of 10 Hz where
the inertial number is very close to equally one. Frictional forces are still present but
particles are somewhat mobilized to flow. Due to this less restricted flow, it is seen that
a less cavernous type surface is observed with much more particles in view at the same
0.1
1
10
100
0.01 0.1 1 10 100
Ap
par
ent
Vis
cosi
ty(P
a*s)
Inertial Number
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33
magnification. As for the cross-sectional area near the Mylar film, it is seen that particles
have filled in the porous structure with smaller particles as compared to 0.1Hz
As for Fig. 11(C) and 12(C) which represents a constant shear rate at 100 Hz
where the inertial number is significantly above one. It is seen that particles are highly
congested together at the same magnification. Particles are tightly packed due to less
frictional forces between particles during shear which causes local jamming and
capillary forces to break. This causes individual particles to flow freely throughout the
suspension causing particles to align according to size and shape. Figure 12(C) depicts
the cross-sectional area where many of the smaller particles moved towards the Mylar
film, filling in the voids creating a much more homogenous microstructure.
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(a)
(b)
(c)
Figure 11: (a) 0.1 Hz applied shear for one hour, surface SEM image. (b) 10 Hz
applied shear for one hour, surface SEM image. (c) 100 Hz applied shear for one hour,
surface SEM image
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(a)
(b)
(c)
Figure 12: (a) 0.1 Hz applied shear for one hour, cross sectional SEM image. (b) 10
Hz applied shear for one hour, cross sectional SEM image. (c) 100 Hz applied shear
for one hour, cross sectional SEM image
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Energetic Characterization
Figure 13 represents the flame speed as a function of shear rate showing a linear
trend. Each point on the graph represents an average of five flame speed test. The
samples for each flame speed was mixed to a solid loading concentration of 45% by
weight with an equivalence ratio of 1 for the Mg-MnO2 reactants and created at a wet
film thickness of 300 microns on a Mylar thin film. All experiments were created and
tested in an atmospheric environment. The 40mm diameter film was cut into strip with
dimensions of 4cm long and 1 cm wide. Each calculation used a new 40 mm diameter
thin film to ensure the that the shear rate was the same throughout each thin film strip
due to varying shear rate with respect to diameter of the film. Flame speed increased
from 150 to 250 mm/s as a result of shear being applied to the thin film. The increase in
average flame speed at 0.1Hz showed an average flame speed of 142.2 mm/s where at
a shear rate of 10 Hz showed a flame speed average of 206.5 mm/s, showing a 39.9%
increase in flame speed. At 100 Hz of applied shear, flame speeds were measured at an
average speed of 246.3, showing a percentage increase of 17.6% from 10Hz and an
overall percentage difference between 0.1Hz and 100Hz at a 53.6% increase. These
results can be seen in table 2.
Figure 13: Corresponding flame speeds for a given shear rate representing a linear
trend
0
50
100
150
200
250
300
0.1 1 10 100
Flam
e Sp
eed
(m
m/s
)
Shear Rate (1/s)
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Table 3: Flame speed and heat of combustion results
Also seen in table 3 are the results from the bomb calorimetry experiments which show
the same linear trend as seen from the flame speed calculations. This linear trend can be
seen in Fig. 14. Each point represents an average of three experiments. The same
equivalence ratio and wet film thickness were used as stated for the flame speed
calculations. The increase in the heat of combustion for 0.1 Hz and 10 Hz was from
67.8 to 123.7 Kj/g, with standard deviation of 13.7 and 11.42 Kj/g, respectively. This is
a 53.8% increase in the release of energy. As for the 100Hz sample, the heat of
combustion in averaged at 171.3 Kj/g representing a 32.3% increase from 10Hz and
86.6% increase from 0.1Hz of applied shear.
Figure 14: Corresponding heat of combustion for a given shear rate showing a linear
trend
CONCLUSION
Rheology of Mg-MnO2-PVDF thin films should be taken into consideration to
maximize the energetic potential of the thermite. The influence of suspended free
flowing particles that are free of all frictional and local jamming forces where the inertial
number is much great than one, with a corresponding shear rate of 100Hz, have been
0.1Hz 10Hz 100Hz
Flame Speed(mm/s) 142.1 ± 23.9 206.5 ± 6.2 246.3 ± 11.2
Heat of Combustion(Kj/g) 67.8 ± 13.7 123.7 ± 11.4 171.3 ± 1.9
020406080
100120140160180
0.1 1 10 100Hea
t o
f C
om
bu
stio
n(K
j/g)
Shear Rate (1/s)
Texas Tech University, Michael Sweeney, December 2017
38
shown to produce the best results creating a homogenous microstructure throughout the
thin film. This provides the greatest energetic potential which maximizes the flame
speed and heat of combustion, which provides the greatest amount of energy for the
same amount of material.
Whereas a low inertial number significantly less than one, with a corresponding
shear rate of 0.1Hz, particles become locally jammed and are immobilized by frictional
forces creating a non-homogenous microstructure which hinders the energetic potential.
It is seen that flame speeds and the heat of combustion are both significantly lower at
the smaller inertial number. For an inertial number, closely equal to one where particles
are somewhat mobilized to flow but still have not overcome all frictional forces within
the suspension shows a slightly more homogenous microstructure. This provides a
significant increase in energetic reaction which demonstrates that a mobilize flow of
individual particles will significantly impact the thermite thin films.
Texas Tech University, Michael Sweeney, December 2017
39
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