copyright 2017, michael sweeney

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

Texas Tech University, Michael Sweeney, December 2017

ii

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.


iii

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


iv

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


v

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


vi

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


vii

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


viii

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


1

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


2

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


3

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.


4

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


5

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


6

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


7

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]


8

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.


9

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.


10

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


11

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


12

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.


13

(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


14

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


15

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.


16

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.


17

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.


18

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


19

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


20

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.


21

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


22

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.


23

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.


24

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


25

solids density and to open up new applications such an energetics printing warrants

further study of such system beyond these initial feasibility tests.


26

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


27

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.


28

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


29

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


30

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)


31

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)


32

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


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.


34

(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


35

(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


36

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)


37

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)


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.


39

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