ENGINEERING
Tatiana Niculescu
Mr. Almarode
Fourth Period
THE EFFECT OF VIBRATION OF GRANULAR MATERIALS ON FORCE CHAINS
WITHIN THE MATERIAL
Abstract: Granular materials are readily abundant in nature and are commonly used in
day to day life. They are poorly understood because of their diverse and erratic behavior under
different circumstances. Very little is known if vibrating grains will alleviate or exacerbate force
chains within the materials. The purpose of this study was to determine if vibrating the particles
of a granular material will reduce the number and intensity of the force chains. Photo-elastic
cells were sheared with a stepper motor. The grains were then vibrated at 5 different amplitudes
and pictures were taken every 5 seconds for 1000 seconds. The pictures were then thresholded
for black and whiteness and the average number of white pixels were was calculated for each
vibration level. Results were analyzed using a Pearson Product Moment Correlation Test that
yielded no statistical difference. The researcher concluded that there is no statistical correlation
between the vibration of grains and the abundance of force chains present in the medium.
Introduction: Granular materials exist everywhere in nature and though they appear to
be solids, they can act like liquids and gases under the appropriate conditions. In fact, they can
act like all three at the same time. These macroscopic particles are omnipresent and affect our
lives daily though we may not even know it. Grains held in silos are actually granular materials
that if put under a certain amount of stress will actually make the silo collapse. Granular
materials are poorly understood because of their diverse behavior and very little is known if
vibrating the particles will affect the forces running through them and if it will relieve the stress
in the system.
For this reason granular material, uses, processing and common industrial
problems, and related studies should be investigated.
Granular materials are primarily macroscopic objects, meaning that they can be detected
by the naked human eye. They are usually about 100 microns (µm) or larger in size (Duran,
2000). The term granular material can actually be applied to anything from grains of sand to ice
floes even to Saturn’s rings. Its behavior across this wide range of sizes is what makes studying
granular matter so worthwhile; it seems to obey universal laws no matter what size the particles
are. These laws however are poorly understood and this misunderstanding leads to a great many
practical problems.
Sands, powders and grains are not subject to traditional Brownian motion. It appears that
this phenomenon is inconsequential when it comes to granular materials and is only exhibited
when the particles are in a uniform vertical air flow (Duran 2000). This observation explains
why granular materials don’t really respond to being mixed; when shook they simply segregate
according to size. This size segregation is often the exact opposite of what is expected or sought.
When granular materials are dry, the forces between them are strictly repulsive and the shape of
the grains, sand, or aggregates is only influenced by the size and shape of the container and by
gravity (Jaeger et al., 1996).
Interactions in granular materials are unique and quite different from those of other
materials. Since they can behave like all three states of matter at the same time then it is very
hard to say how exactly grains will interact. Unlike solids, liquids and gases granular materials
must be “sufficiently” disturbed in order to move. This observation means that the behavior of
these particles will be harder to explain and will require the usage of thresholds and
nonlinearities. If a stress is applied to a system in which contacts are randomly spaced then the
force of the stress will follow an irregular path. As the stress on the system increases, the
particles begin to deform and redistribute themselves in order to relieve the stress which simply
leads to new force chains being formed.
Granular materials are readily abundant in the world; in fact, the worldwide production of
grains and aggregates is about ten billion metric tons. Granular materials actually classify
second after water in importance to human activity. As the understanding of these materials
advances, profits and efficiency in the industry also advance. In recent years, it has been
suggested that the techniques used to deal with grains and aggregates are severely out of date;
many haven’t been changed since the 19th century (Duran, 2000).
Construction materials are one major use of aggregates. Natural aggregates such as
alluvial soil are extracted from the earth and then must be processed. The huge amounts of
granular material may be forced through pipes, ground down, sifted, and washed. Eventually it
will be stored and finally transported to its final destination. All of these processes are plagued
by problems that cost the industry billions of dollars.
Some major problems encountered in the production, transportation and storage of
granular materials are flow obstructions, the formation of plugs and segregation of the matter.
Blocked flows are a common annoyance in industrial settings during loading and unloading. The
formation of highly stable arches in the chutes used to load and unload can either make flow
sporadic or completely block it. The frequency and strength of these arches is due to the
properties of the grains and the size of the chute. In silos the formation of these blockages can
lead to devastating results when the arches trap the fermentation gases inside; the silo will
explode.
Physicists have studied the formation of blockages and jams within granular materials.
Corwin et al. (2005) studied the forces formed within a cylinder full of glass beads. A slowly
rotating plunger exerted a constant shearing force on the beads. By studying the bottom layer
and employing a photo elastic sheet and polarization, it was found that the beads near the sides
flowed while those in the center tended to jam and rotated as a whole. It can be said that
networks formed by contact forces between separate particles are the key to jamming and
yielding of granular matter.
There have been studies conducted on the vibration of dissimilar grains. Daniels and
Behringer (2005) at Duke University conducted an experiment in which they vibrated a mass of
particles in a cylindrical container that were being sheared at the same time to see the effects.
They had proposed that the vibration would in fact emulate a phase change so that instead of
being jammed or “frozen” the grains would “melt” and flow like a liquid. They found that
vibrating the matter would in fact just lead to segregation. This finding could have a great many
practical applications; some common industrial methods of un-jamming grains in silos and
hoppers could actually make the problem worse.
Physicists at Rutgers University have conducted research into the mixing of various food
and pharmaceutical products. It was found mixing grains longer or faster does not always
produce a smooth blend. Some ingredients actually end up separating. One interesting finding
was that under conditions that would seem to be conducive to a thorough mixing, fine particles
actually separated into distinct layers (Conway et al., 2005).
Granular materials are poorly understood macroscopic particles that do not behave as
expected. They can take on the properties of all three states of matter all at the same time.
Granular materials are all around and are the basis for many industries such as agriculture and
construction. The better understood these particles are, the better and more efficient industries
can become. The purpose of this study is to determine if vibrating the particles of a granular
material will reduce the number and intensity of the force chains. The following null hypothesis
was examined:
there is no statistical difference between the observed force chains in the
vibrated and un-vibrated particles.
Methods and Materials: The subjects for this study were pentagonal Vishay ps-4 low
modulus photo-elastic cells made of an unknown polymer. The exact makeup of these cells is
unknown due to a trade secret of the Vishay Measurements Group Inc. 150 cells were used. The
5 different vibration points were chosen by first detremining determining the vibration point
amplitude where there were relatively few zero force chains and then going reducing the
vibration by various increments.
A SS X-Ray light was used in conjunction with a 3M polarizer sheet over the set up and
one on the light below that are crossed to produce the polarizing effect. These cells are used in
2D plane stress model analysis. The SS X-Ray light with the 3M polarizer shows the force
chains in the photo-elastic cells. The light and the polarizer sheet are very similar to those used
in the medical field.
A Compumotor ES 33B-DF-310 stepper motor with Motion Architect
software application was used to shear the grains. The Compumotor Zeta Series allows control
by any standard step in the clockwise or counterclockwise direction. The Zeta6000 family series
stepper motor is the highest performing, single axis system in the industry. Pictures were taken
every 5 seconds for 1000 seconds with a Pixelink high speed camera. The PL-A741 Mono 1.3
Megapixel PL-A781 Mono 6.6 Megapixel MV Camera with Global Shutter has a resolution of
1280x1024 3000x2208 pixels with a pixel pitch of 6.7 µm. It’s the one of the most popular
machine vision cameras. A GW Instek function generator was used to produce and oscillating
signal that was amplified by a Harrison 6823A amplifier that was in turn sent to the speakers and
the Teketronix oscilloscope that measured the driving force exerted on the speakers. The testing
equipment was used because it was the available equipment for the study. The data collection
method similar to Majmudar and Behringer (2005) was employed. The cells were placed on a
plexiglass sheet and motorized linear slides moved the walls. The whole set up was illuminated
from below and a high speed camera was used to capture digital images. This set up is very
similar to the one that is to be employed in this study.
Methods and Materials: The data collection method similar to Majmudar and Behringer
(2005) was employed. The cells were placed on a plexiglass (Plexiglas is technically a brand
name with capital P and only one s) sheet and motorized linear slides moved the walls. The
whole set up was illuminated from below and a high speed camera was used to capture digital
images. This set up is very similar to the one that is to be employed in this study.
The subjects for this study were 150 pentagonal Vishay ps-4 low modulus photo-elastic
cells made of an unknown polymer. The exact makeup of these cells is unknown due to a trade
secret of the Vishay Measurements Group Inc.
A correlational experimental design was employed. The independent variable was the
amplitude of the vibration applied to the cells. The dependent variable was the average number
of white pixels (signifying the observed force chains). The same set of photo-elastic cells was
used for each of the four tests.
A 2 foot high by 3 feet long by 2 feet wide metal frame with a clear plexiglass tray inside
was constructed. The belts of the Computar stepper motor were placed on opposite sides of the
plexiglass tray to act as walls. A group of 150 pentagonal ps-4 low modulus photo-elastic cells
were placed into the tray and the top was then replaced. A 3M polarizing sheet was taped over
the clear top. A SS Xray light with another polarizing sheet was placed below the whole set up
and turned on. The light shined through the plexi-glass then through the photoelastic cells and
then through the top 3M polarizing sheet thus illuminating the force chains between the cells (see
Appendix A for a picture of the experimental set up). The Compumotor stepper motor’s then
rotated at a speed of 0.05 revolutions per second which drove the belts at 0.36 cm/s. The belts
were sheared in opposite directions, causing force chains to form.
A high speed, black and white, Pixelink 782 MV camera with a 10-100 mm Computar
zoom lens in conjunction with a computer was used to take pictures every 5 seconds for 1000
seconds. This was the data set for no vibration.
A plastic block with two screws was then placed in between the belt on one side of the
set up.
A speaker was connected to both of the screws; these speakers were connected to a
Harrison 6823A amplifier which was connected to a GW Instek function generator. See
Appendix B for a picture of this set up. A Teketronix oscilloscope was used to measure the
signal driving the speakers in Volts. The oscilloscope was first set to 7.6Volts and pictures were
taken every 5 seconds for 1000 seconds. The same procedure was then repeated for 7.2Volts, 6.0
Volts, 4.8 Volts, 3.6Volts, 2.4Volts, and 1.2 volts.
See Appendix C for a picture of the
experiment in progress.
The pictures were then opened using Adobe Photoshop and a threshold for whiteness of
the pixels was determined by finding the place on the 0-255 presence of color scale (0 is black
and 255 is white) where the force chains were most pronounced. This threshold was found to be
46.
A Linux computer using the athreshold.c program was used to analyze the vast amount
of pictures that were taken. The average of the presence of color data was then averaged for
each group and analyzed using the appropriate statistical test.
Results: A Pearson Product Moment Correlation Test was used to test the null
hypothesis. This procedure allowed for a correlation to be detected between the amount of
vibration of the grains and the % of pixels above the 46 threshold. No statistical correlation was
found between vibration and the % of pixels above the threshold. Therefore the null hypothesis
was accepted, r=-.75. See Appendix D for Pearson Product Moment Correlation results and
Appendix E for a graph of the average data.
Discussion and Conclusion: According to Daniels and Behringer (2005), vibrating
sheared particles does not lead to a virtual phase change. Vibrating the grains only leads to
segregation of particles by size and shape. The results from this study were consistent with the
conclusions of the previous experiment. They showed that there is no clear correlation between
the vibration of sheared particles and the abundance of force chains within the sample. One may
conclude that too little data was collected to come to a precise result. Possible procedural
improvements to this study could be to take pictures more often during the experiment or to
repeat the test more times. Recommendation for future study could include the use of different
sized grains in a three dimensional environment. By doing this, researchers would have a truer
picture of how granular materials behave under lifelike circumstances.
LITERATURE CITED
Corwin, E. I., Jaeger, H. M. & Nagel, S. R. (2005). Structural signature of jamming in granular
media. Nature, 435, 1075−1078.
Conway, S., Shinbolt T., & Glasser, B. (2004). A taylor vortex analogy in granular flows.
Nature,431, 433-437.
Daniels, K., & Behringer, R. (2005). Hysteresis and competition between disorder and
crystallization in sheared and vibrated granular flow. Physical Review Letters, 94, 168001.
Duran, J. (2000). Sands, powders, and grains: An introduction to the physics of granular
materials. New York City, NY: Springer-Verlag New York, Inc.
Jaeger, H.M., Nagel S.R., & Behringer R.P. (1996). The physics of granular materials. Physics
Today, 49, 32-38.
.
Appendix A
Picture of the Whole Experimental Set up
Appendix B
Picture of Speaker Set up
Appendix C
Picture of the Experiment in Progress
Appendix D
Results
Column 1
Column 1
1
Column 2 -0.753522214
Column 2
1
Appendix E
Chart of average pixels above threshold [Missing chart title…]
% of pixels above threshold
Chart Title
y = -0.3744x + 4.1013
R2 = 0.5678
6
5
4
% above thresh
3
Linear (% above
thresh)
2
1
0
0.00
2.00
4.00
Voltage (V)
6.00
8.00