Physics Extended Essay
Non-Newtonian and Dilatant Fluids
Eric McCorquodale
March 6th, 2009
Candidate number: 000479-017
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Non-Newtonian Fluids
Contents
Page
Research Question
3
Abstract
3
Introduction
4
Body
5
Lab Investigation
14
Lab Journal
18
Conclusion
20
Bibliography
21
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Research Question
What gives non-Newtonian, or more specifically shear thickening and
thinning fluids their unique properties? What are non-Newtonian fluids used
for, and what other practical purposes could they have?
Abstract
This essay looks at the possible applications, and current uses
for non-Newtonian fluids. It also explains the current theories for how nonNewtonian fluids work. Shear thickening fluids should be able to achieve a
maximum possible force through a ratio of particles to lubricant. My
investigation into this matter can only go so far though. I have looked at
several non-Newtonian fluids, as well as their applications, such as the use
of silica nanoparticles in traction control, advancement in body armour, and
protective gear. In the lab portion of the essay, I showed that as the
concentration of the particles that make shear thickening fluid increases, the
force it is able to apply to an object also increases. Furthermore, we should
be able to find a concentration at which the shear thickening fluid will be
strongest. This strong concentration should be used to treat Kevlar, and
could be used in traction control systems for superior performance.
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Introduction
I first came across non-Newtonian fluids when watching an episode of
the television series Numb3rs. In the show, several people run across what
appears to be a pool of liquid. Initially I thought that I could not make such
a liquid, but after further investigation, I found out that these liquids are very
common and fairly easy to make. Several companies use non-Newtonian
fluids in their protective gear, and traction control systems as well as many
other products.
In this essay, you will see how non-Newtonian fluids are used, and I
will attempt to explain, and understand how they work. A lab investigation
will also be involved, as I try to show that the amount of particles in a shear
thickening fluid correlates with the force it is able to apply on an object.
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Body
A fluid is called non-Newtonian if it does not conform to Newton’s
equation describing viscosity, F/A=v/Z. A Newtonian fluid will conform
to this equation, and viscosity will be a constant for that liquid when a
constant temperature is achieved. “F” stands for the force applied to the
liquid, and “A” stands for the area over which said force is applied. On the
other side of the equation, “” represents the viscosity of the liquid, “v”
represents the velocity of the planes, and “Z” is the distance between the
planes.
Viscous forces in a fluid. (Earle, 1983)
A non-Newtonian fluid can be put into the equation, =k(dv/dz)n ,
where , the shear stress of a fluid, is the constant of proportionality
multiplied by the shear rate, dv/dz. For a shear thickening fluid, n will be
smaller than one, and for a shear thinning fluid, n will be greater than one.
(Earle, 1983)
Shear stress/shear rate relationships in liquids (Earle, 1983)
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Here are some important definitions for future reference.
Non-Newtonian Fluid:
A non-Newtonian fluid’s viscosity does not fall under a constant value. This
is the opposite of a Newtonian fluid, where there is a linear relationship
between shear stress and the rate of strain applied by the fluid. These fluids
can change their viscosity depending on time, shear stress, or based on a
variety of other factors. Some common examples are quicksand, ketchup,
and Silly Putty. A dilatant fluid is an example of a non-Newtonian fluid. A
dilatant, or Shear Thickening Fluid (STF), is a fluid whose viscosity
increases non-linearly as the rate of shear increases. This falls under the
definition of a non-Newtonian fluid.
Shear:
The shear is a force applied tangentially to the face of a solid object. Shear
will be applied to any solid surface (boundary or object) that a liquid comes
into contact with.
Shear Stress:
For Newtonian fluids, this is proportional to the shear rate. The shear strain
divided by the rate of shear strain is a constant for any given liquid. The rate
of shear strain is the rate of deformation for the liquid when a parallel force
is applied. For non-Newtonian fluids, the constant
Shear stress F/A = v /Z =  (dv/dz) = 
This is the equation that Newton proposed for shear.
Shear Rate:
The rate at which shear is applied to a surface. Expressed dv/dz.
The picture above shows how the
Newton’s equation for shear stress
relates to a liquid. 1
1
http://upload.wikimedia.org/wikipedia/commons/a/a4/Laminar_shear.png
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Rheology:
Rheology is the study of the flow of unusual materials, particularly nonNewtonian fluids. Rheology is the science of deformation and flow of
matter.
Non-Newtonian Fluids Explained
There are two types of Non-Newtonian fluids, shear thickening fluids
and shear thinning fluids. Shear thickening fluids are a specific type of nonNewtonian fluid whose viscosity increases as the shear stress applied
increases. For all practical purposes, a dilatant fluid is a shear thickening
fluid. Dilatant fluids act as a liquid when pushed at low velocity, but when a
high velocity object hits the liquid, friction between the particles increases
dramatically and the object is unable to move. An example of a dilatant
fluid and the fluid that I will be researching is a polymer mixture of
cornstarch and water commonly referred to as oobleck. (Oobleck was
originally used to describe an imaginary liquid in Dr. Seuss’s book,
Bartholomew and the Oobleck)
There are many experts who argue that dilatant fluids are simply
powder polymers that dilate and expand in volume when an uneven force
acts upon it. In any case, dilatant fluids demonstrate the properties of shear
thickening fluids, and, for this paper, will be considered to be a shear
thickening fluid.
The water and cornstarch solution that we used in our lab is a dilatant
fluid. As a dilatant fluid, the force keeping it together comes from the
friction between particles when a force is applied to it. When a force is
applied to a dilatant fluid, the cornstarch particles hit each other, and the
force holding it together comes from the friction between the particles of
cornstarch. In the water and cornstarch solution, the water acts as a
lubricant, so that the cornstarch can move relatively easily when no uneven
force is applied. The water allows the normally solid cornstarch to act as a
liquid in this case. When an uneven force is applied, however, the
lubricating water particles between the cornstarch particles move aside, and
the cornstarch acts as a solid once again. The name dilatant is given to this
and other similar fluids, because of its dilation, or expansion. In other
words, these fluids expand when a force is applied, or if you attempt to
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splash it. This expansion is due to the pores between the particles getting
bigger. Since it is being both compressed and expanded, there is no net
deformation of the liquid. When the pores between particles are expanded,
the cornstarch particles come into contact and form a lattice-like structure,
and act as a solid.
Applications
Many companies use non-Newtonian fluids with their personal
protection and padding products. Among the most prominent of these
companies are Zoombang, d3o, and Dow Corning. The basic idea behind all
of their products is that under normal conditions the padding will remain
flexible, and comfortable, but upon impact, the padding will stiffen to
provide protection from any blow. The particles form a lattice-like structure
that will remain together as long as the impact remains.
Zoombang protective gear uses an undefined shear-thickening
polymer. They say this polymer will “stiffen in proportion to the energy
applied.” Zoombang calls their polymer a “Viscoelastic” polymer because
of its elastic and flowing properties. (MacKinley, 2009) This polymer will
stiffen when a force, or some other shock, but remain as a liquid in normal
conditions. Zoombang claims to have hundreds of professional athletes who
use their products. As with all protective gear that uses shear thickening
technology, Zoombang provides protection along with flexibility and the
freedom to move. (zoombang.com)
D3o describes the active particles in their product only, “intelligent
molecules”. Upon further investigation, the only thing I could find out about
their technology was that it used silica nanoparticles. D3o, which is based in
Hove, East Sussex, has many products for athletes such as goalkeeper
gloves, ski helmets and boots, that all use shear thickening fluids to protect
the wearer from impact. D3o’s managing director said, “Sometimes it’s
hard to convince people what a truly amazing innovation this is until you
demonstrate it. I was wearing a prototype shirt incorporating d3o, and at one
point I stood up and slammed my elbow onto the table as hard as I could,
sending coffee cups flying. Once they saw me doing that - without flinching
- they understood what I was saying.”2 These products truly are
revolutionary, and without a doubt very interesting. (d3o.com; Palmer, 2004)
2
2004, http://www.azom.com/details.asp?ArticleID=2555
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Dow Corning claims that their Active Protection System, or APS, is
superior to other shear thickening fluid based padding and protective gear.
They use the same basic principles seeing as Dow Corning’s padding will
become rigid if a high velocity force hits it, but they use fabric so that the
skin underneath it can breathe. The fabric is made of cross-linking bonds of
a dilatant silicone polymer. They claim the fabric will absorb and dissipate
shock through the material. They do highlight a limitation for other shear
thickening fluid protective gear. Allowing the skin underneath to breathe
could be a major marketing tool for products aimed at athletes, and industrial
workers, as well as soldiers and policemen. Dow Corning also states that
their technology has potential to be used for body armour, but do not
actually manufacture any such products. The only unique idea that Dow
Corning had was that their technology could be put to use in architectural
design. The same can go for the other similar products. (Dow Corning
APS)
(Dow Corning APS)
Body armour is possibly the most interesting application for shear
thickening fluids. Body armour that is completely flexible, but turns
extremely hard when struck by a bullet or shrapnel sounds like it is straight
out of a science fiction movie. No movie is needed to make this possible
though, only shear thickening fluids. The body armour that is currently used
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usually consists of several layers of Kevlar, and heavy ceramic plates.
Rheologists are working on ways to use shear thickening fluids to provide
the same service as body armour without the weight and inflexibility that our
current body armour has.
Obviously the padding and protective gear mentioned above wouldn’t
be suitable for combative purposes. Those products are only meant to
protect the body from impacts of relatively small force, like being hit in
hockey, or American football. We should look at some other applications of
shear thickening fluids that could help protect the body from high velocity
impacts, such as bullets.
The U.S. Army Research Labs are working with the University of
Delaware to produce body armour. Their armour consists of only a couple
of layers of Kevlar fabric that has been treated with a shear thickening fluid.
The fabric is soaked in shear thickening fluid, then pressure is applied, and
the fabric is put through a wringer. This way, only about ten layers of
Kevlar are needed to protect the wearer from the force of a stab, rather than
about forty layers in regular police body armour. The problem that arises
with an impact from a bullet is that bullets are dense, and the force of the
blow is very concentrated over a small area.
The image below3 shows that two layers of Kevlar that have been
treated with shear thickening fluid can withstand shots from multiple arrows.
The untreated Kevlar, even with double the layers, could not withstand the
arrows, and all four arrows were able to puncture the fabric. Of course it
would not be wise to send soldiers into battle with two layers of treated
Kevlar. Bullets can travel over ten times the speed of the arrow used in
these tests.
3
http://www.ccm.udel.edu/STF/image_gallery/testing4.jpg
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This is a picture of a container of polyethylene glycol with
400 nanometer silica nanoparticles. This was one shear
thickening fluid used by the U.S. Army Research Labs to treat
the Kevlar. This shear thickening fluid is also suspended in
water but will not clump up like the cornstarch because the
particles repel each other slightly. Upon impact the particles
will hit each other and harden.
(Wilson)
(Wilson)
This is treated Kevlar after the impact from a bullet. For slow moving
impacts, such as a slow, forceful stab, the treated Kevlar will sustain a small
amount less damage than untreated Kevlar, possibly due to the liquid
holding the fabric together.
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Traction control systems often use shear thickening fluids in their
viscous coupling units. The fluid used is quite often a silica polymer, much
like the polymers used in protective gear. The viscous coupling unit consists
of two rotating plates. If the two plates are rotating at the same speed, the
silicone will act as a liquid. Very little power will be transferred to the
secondary drive wheels. However, if the two plates are rotating at different
speeds, the silicone will start to solidify, and power will be transferred as
needed to the secondary drive wheels. (ChemistryDaily, 2007)
Shear Thinning Fluids
The opposite of a dilatant fluid would be a shear thinning fluid, such
as whipped cream. When no uneven forces act on the whipped cream, it is
stationary, and does not flow like a liquid would. You can see it acts as a
solid, because it can stand up without support instead of making a puddle as
a liquid would. When a force is applied to the whipped cream, it moves and
deforms like a liquid would. NASA recently did a study on shear thinning
fluids, using xenon as their test liquid, because xenon is a very simple
molecule to understand. (Phillips, 2008)
A shear thinning fluid’s fluidity depends upon the stress being applied
to it. Some common examples include but are not limited to pseudo plastics,
lubricants, paint, whipped cream, and Bingham fluids. As the force and
velocity applied over an area of the fluid increases, the fluid will become
easier to flow through, as the viscosity will decrease. The main difference
between shear thickening fluids and shear thinning fluids is that shear
thickening fluids appear to change into solids upon shearing, whereas shear
thinning fluids will appear to be more gaseous when shear is applied.
It is not entirely clear how shear thinning fluids work. One very
plausible theory says that shear thinning fluids are comprised of large
molecules in a solvent of smaller molecules. At rest, the larger molecular
chains will be aligned at random. Under a shear force, however, the larger
chains will be forced to align with one another, reducing volume, and
producing less friction against the shear. The explanation given by the
NASA group is that upon shearing forces, a shear thinning fluid will become
partially gaseous, and flow more easily. (Phillips, 2008)
In automotive terms, it could be very useful to find effective shear
thinning fluids. Shear thinning lubricants could be very useful to produce
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and maintain high efficiency vehicles. Finding and investigating nonNewtonian fluids could also be useful in geology. (Balmforth, UBC)
A study aboard Space Shuttle Columbia called Critical Viscosity of
Xenon, or CVX2, highlighted a way in which shear thinning fluids can be
studied. NASA scientists describe a fluid’s critical point as a “special
combination of temperature and pressure where fluids can exist as both a
liquid and a gas simultaneously. At their critical point, simple fluids are able
to "shear-thin" (a verb) just like whipped cream does.” 4 This means that at
certain temperatures and pressures, any fluid can act as a shear thinning
fluid. I also liked Phillips’s explanation of the shear thinning process.
Phillips wrote, “When part of the foam is forced to slide or "shear" past the
rest of the foam, the foam "thins." It becomes less like honey and more like
water, allowing it to flow easily until the shearing stops.” (Phillips, 2008)
(Phillips, 2008)
The critical point for xenon is shown here.
This critical point can theoretically be achieved for any liquid.
Tony Phillips, 2008,
http://science.nasa.gov/headlines/y2008/25apr_cvx2.htm?
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Shear Thickening Fluids Lab Investigation
Purpose: To find the force holding a shear thickening fluid together with
different ratios of the active particles in the polymer in comparison to a
Newtonian fluid.
Hypothesis:
The water acts as a lubricant for the particles of
cornstarch. As more cornstarch particles are added to the solution, the force
holding the fluid together should increase.
=k(dv/dz)n , n>1, This equation is important when calculating shear, but we
are only comparing forces, so it will not be needed. In this experiment, the
shear will be acting on the surface of the weight. The force of the liquid’s
shearing on the weight will be found.
Since the surface area of the weight, and the depth are constant, the force
holding the weight back in these conditions should be equal to the force of
subtracted from the net force of the weights.
Materials: Pasco Data Studio interface
Pasco Photogate sensor, and smart pulley system
Computer with Data Studio application
Several containers to hold liquid (Ice cream containers, etc.)
Beakers (400mL, 500mL, 1L)
Water
3 kg of cornstarch
Spoon
Meter sticks
A 400g electronic scale
Procedure:
Equipment setup
1.
A retort stand is placed on a table.
2.
A horizontal clamp is attached near the top of the stand.
3.
On the clamp, put the photogate along with the smart pulley.
4.
The photogate is attached to the Data Studio interface, which is
connected to the power outlet and a computer with the Data Studio
application installed.
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5.
Two weights are tied to a string, which has been strung through the
smart pulley apparatus.
Fluid setup
1.
500mL of water is measured out into a 4L ice cream container.
2.
500g of cornstarch is measured out, and mixed into the water.
3.
The container is placed under the retort stand so the smaller weight
can drop into the liquid, but the heavier weight will fall outside of
the container.
Trials
1.
The 50g weight is suspended so that the 20g weight is resting just
below the surface of the liquid, and just above the bottom of the
container.
2.
The “play” button is pressed in the Data Studio application to start
recording the velocity and acceleration of the weights.
3.
The 50g weight that was being suspended is now released, and the
weights will move.
4.
After the weights have stopped moving, the data being recorded is
stopped.
5.
This is repeated four more times for every liquid.
Recalibration
1.
After every five successful trials, cornstarch is added to the
solution to change the ratio of cornstarch to water.
Variables:
Independent:
Ratio of cornstarch to water
Dependent:
Fl, force produced by the shear thickening fluid
Control:
Depth of liquid
Force applied
Area of force
Surface area of object
All of these will remain constant in order to compare the force of the STF to
the force produced by a Newtonian fluid.
The mass is suspended just above the bottom of the container to ensure that
no suction occurs, where the weight could get stuck to the bottom of the
container, and affect the experimental values.
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Data:
Mass 1=20g
Mass 2=50g
Height of Mass 1=21 ± .1mm
Diameter of Mass 1=14 ± .1mm
Distance between table and pulley = 54 ± .2 cm
Distance between 50g weight and table = 23 ± .2 cm
Length of string = 84 ± .2cm
Net force upward on mass 1= 0.2943N
Surface area for shear on mass 1= .92 ± .01m
Average acceleration of mass 1 out of a Newtonian fluid = 3.56 m/s/s
Experimental net force of weights = .1068 N
Fl=.1068N - .03 x a
Where a is acceleration of the weight
This is an example of what the velocities of the trials looked like. These
trials were for the solution of 1.4:1 ratio of cornstarch to water.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Sample calculation:
F=m x a
F= .03kg x .44 ms-2
=.013 N, Fl=.1068N-F
Fl= .092 N
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Ratio
5:5
6:5
6.5:5
7:5
Unknown
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Force (N)
0
0.042
0.064
0.098
0.092
The Unknown ration is just slightly under 1.4:1. As you can see there was a
big change in force when adding only 50g of cornstarch, so the difference
between the 7:5 ratio and the unknown ratio was very small.
As the amount of cornstarch increases, the force applied to an object
moving through the liquid also increases. This could suggest that the theory
of the cornstarch particles forming a lattice structure is correct, but it does
not prove it.
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Lab Journal
One very interesting serendipitous event occurred while in the process
of preparing this lab. The proper ratio of cornstarch to water had already
been achieved to form a non-Newtonian fluid. A thin layer of cornstarch
was spread evenly across the surface of the fluid. When the layer of
cornstarch was hit with a meter stick it would not move, spread, or split, but
apply the force of the blow across the entire fluid. When the meter stick
pushed the layer of cornstarch, however, the layer would sink to the bottom
of the fluid. This suggests that if a layer of material were placed across such
a non-Newtonian fluid, it would help disperse the blow more evenly. My
thoughts went directly to Kevlar. If a thin piece of Kevlar were reinforced
by pockets of shear thickening fluid then the force and kinetic energy of a
bullet would be dissipated through the armour.
Once we got to a ratio of cornstarch to water of about 1.4:1, it became
very difficult even to stir the solution slowly. A lot of the cornstarch had
clumped up, and it was obvious that we couldn’t test solutions over this
ratio. All that was left in the bucket looked to be almost completely
cornstarch, although it was obviously a bit wet.
The practical applications of a cornstarch and water polymer are very
limited. For one thing, the consistency must remain constant, so any
addition of water or contact with water for that matter would ruin the
consistency. Also, the cornstarch particles sink to the bottom of the water
after a while if it is not stirred properly. This would affect the consistency,
making it dry and starchy in some places, while leaving the solution watery
in others. One way to get around this could be to seal the solution in small,
airtight packets. This would prevent the water from evaporating, but will
not prevent the particles of cornstarch from settling, and forming clumps so
the force of a blow will not be distributed evenly. For this reason, a silica
polymer would be better for use in armour and padding rather than a
cornstarch based product.
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Lab Applications
My idea for body armour using a cornstarch based shear thickening
fluid goes as follows. The cornstarch and water solution would be sealed in
small airtight packages, lined with Kevlar. These packages would be
hexagonal and triangular in shape to provide an interlocking pattern without
holes in between each packet. The packets would be held in place by a thin
layer of rubber, which would help to dissipate the shock of a bullet.
Obviously rheologists, and other experts have been able to come up with a
much better solution to the body armour issue, but my idea could still work.
Coating the liquid with Kevlar should help distribute the impact of a bullet
more evenly. It would be much better to use a silica polymer, rather than a
cornstarch solution though. Not only would it be stronger than the
cornstarch, but also it would not clump up and lose consistency.
If the force that a shear thickening fluid is able to apply on an object
correlates with the concentration of the active particles, then we should be
able to strengthen the force infinitely. This is not true. There should be a
point where a shear thickening fluid is strongest. I say this because at a
certain point (in our case a 1.4:1 ratio), the fluid became less like a fluid, and
more like wet cornstarch. This makes sense under the theoretical
explanation for a shear thickening fluid used. There should be a point where
the solution keeps its fluidity, and is able to stiffen upon impact from a
maximum force.
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Conclusion
I have looked at several non-Newtonian fluids, as well as their
applications, such as the use of silica nanoparticles in traction control,
advancement in body armour, and protective gear. In the lab portion of the
essay, I showed that as the concentration of the particles that make shear
thickening fluid increases, the force it is able to apply to an object also
increases. Furthermore, we should be able to find a concentration at which
the shear thickening fluid will be strongest. This strong concentration
should be used to treat Kevlar, and could be used in traction control systems
for superior performance. These interesting fluids obviously have many
possible applications that have not yet been realized.
Limitations
An advanced laboratory would have been nice to do this essay.
Unfortunately I am not currently in possession of an advanced laboratory. It
is very difficult to make an accurate prediction of what gives fluids such as
non-Newtonian fluids their properties. Although there are some more
plausible solutions, it is impossible to tell if theories are correct with the
current knowledge and resources that I have. Also, with better resources, it
may be possible for me to test other shear thickening fluids, such as silica
nanoparticles. It would be interesting to see how other shear thickening
fluids stand up to the cornstarch solution. Without the ability to test other
fluids, it is not possible to test my theory that shear thickening fluids have a
maximum strength.
Eric McCorquodale
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Sources
Balmforth, N. Non-Newtonian Fluid Dynamics and Applications, UBC
website, http://www.math.ubc.ca/~njb/Research/non-newtonian.htm
Chemistry Daily, 2007, Dilatant,
http://www.chemistrydaily.com/chemistry/Dilatant
Dow Corning APS,
http://www.activeprotectionsystem.com/index2.html
Earle, R. L. 1983, Unit Opertions in Food Processing,
http://www.nzifst.org.nz/unitoperations/flfltheory3.htm
MacKinley, G. 2009, Non-Newtonian Fluid Dynamics Research Group at
MIT, http://web.mit.edu/nnf/
Palmer, R., 2004, d3o Create Intelligent Material for Use in Protective
Clothing, http://www.azom.com/details.asp?ArticleID=2555
Phillips, T. 2008, The Physics of Whipped Cream,
http://science.nasa.gov/headlines/y2008/25apr_cvx2.htm?
Wilson, T., Liquid Body Armor: Shear Thickening Fluids,
http://science.howstuffworks.com/liquid-body-armor1.htm
Other Web Sources Used
http://upload.wikimedia.org/wikipedia/commons/a/a4/Laminar_shear.png
http://www.d3o.com/
http://www.zoombang.com/
http://numb3rs.wolfram.com/416/
http://www.ccm.udel.edu/STF/image_gallery/testing4.jpg
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