Segregation of Particulate Mixtures

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					                         Segregation of Particulate Mixtures
       Jesse Debes                       Brittany Friedman                               Grace Kim
 j debes@rocketmail.com              brittybear01@hotmail.com                     gracekim33@hotmail.com
                                       Kristina Vishnevetskaya
                                     kvishnevetskaya@gmail.com
                                          Friday, July 23, 2010


Abstract                                                     tempt to thoroughly mix both the inactive and ac-
                                                             tive ingredients throughout the sample. Active in-
A challenge in pharmaceutical production is to en-           gredients perform the drug’s desired effect, and in-
sure that there are equal amounts of active and              active ingredients are included to help deliver the
inactive ingredients in each tablet. Segregation,            medicine to the correct parts of the body. By sim-
a process by which the larger particles segregate            ply reading a bottle of Tylenol, a consumer can
from the smaller ones, is often the main culprit be-         notice that there is only a trace amount of active
hind tablet to tablet concentration variations. Two          ingredient in each dosage. Not only are the compo-
main mechanisms behind segregation are percola-              nents mixed in different ratios, but the active ingre-
tion and convection. Segregation can occur during            dient is often much smaller than the inactive ingre-
transportation of pharmaceutical products because            dient. In order to make each capsule, the active and
of the vibrations given off by surrounding equip-             inactive ingredients must be mixed in a way that
ment and as a result of transportation. In order to          would ensure correct proportions, otherwise, a pa-
simulate this effect, we use glass beads to represent         tient may unknowingly overdose on a product that
components of pharmaceutical mixtures and shake              contains too much of the active ingredient whereas
them in a vibrating cylinder. The different pro-              a pill or capsule with too little active ingredient will
portions that we test reveal that a binary mixture           not deliver the necessary effect. Also, dispropor-
consisting mainly of large particles will undergo less       tionate doses of active and inactive ingredients in
segregation than a binary system with a majority             pharmaceutical products can result in drug recalls.
of small particles. This can be as large of a dif-           However, due to differences in shape and size, the
ference as 9.9% of the total large beads on top,             varieties of particles segregate, or separate, during
which stems from 26.8% of the total large beads              the pharmaceutical process. To maintain the bal-
on top in 11 89 mixtures but only 16.7% in 89 11             ance of active and inactive ingredients in each pill,
mixtures. Also, a ternary system with equal vol-             segregation must be avoided. Time and regulatory
ume fractions, which results in about 16.2% of the           constraints often limit the development process, so
total large beads on top, will segregate less than a         it is vital to reduce the segregation in the current
binary system with equal volume fractions, which             processes. The solution process begins with identi-
results in about 19.6% of the total large beads on           fying the magnitude of the problem. Different size
top. Thus, if a mixture has more components, it              beads are also employed to represent the different
will be less likely to segregate.                            sized powders. They are placed in the cylindrical
                                                             container, which is designed to replicate both per-
                                                             colation and convection, through a uniform mixing
1    Introduction                                            process. The cylinder is vibrated at a frequency
                                                             and amplitude that replicates the experience phar-
In everyday life, pharmaceutical products are used           maceutical powders undergo.
constantly, and like most scientific processes, the
average person puts minimal thought into the cre-
ation of these products. However, there are a
plethora of underlying factors that make their de-
velopment complex. In order to mass produce
these products, all their constituent ingredients are
mixed thoroughly in an industrial mixer in an at-


                                                         1
2     Background                                              2.2    Segregation
                                                              Segregation in pharmaceutical products affects the
2.1    Prior Research                                         amount of medication in each pill. The Brazil Nut
After mixing pharmaceutical powders in industrial             Effect, derived from the common occurrence within
sized blenders, the mixture is usually transported            a cylindrical can of mixed nuts, is a concept that
in large bins to the next step of the process. While          explains the movement of granular materials in a
transporting between machines, the natural vibra-             vibrated system. It states that when solid parti-
tions of movement cause a shaking within the blend            cles are shaken in a vertical motion, the different
of powders. This shaking results in the larger parti-         sized particles will segregate[3]. In this specific ex-
cles rising to the top of the system, creating a segre-       ample, the larger nuts, Brazil nuts, rise to the top
gated mixture. This specific type of segregation is            of the mixture, while the smaller nuts fall through
known as the Brazil Nut Effect[2]. In the final prod-           the voids between the large nuts to the bottom.
uct, segregation results in an uneven distribution of         This incidence is known as percolation and can be
active and inactive ingredients, leading to ineffec-           applied to any granular mixture to explain segrega-
tive products. Then, the products are funneled into           tion. Another common granular mixture in which
machines that compress them into tablets. These               this effect is evident is a bed of glass beads. Typi-
tablets consist of both active and inactive ingredi-          cally, one would look at how a single large bead rises
ents. Active ingredients are the chemicals designed           in a bed of otherwise monodisperse beads. This
to cause an effect within the body, while inactive             is called the intruder system. However, real sys-
ingredients are chemicals that do not directly affect          tems have a distribution of sizes, and one bead is
the consumer, but assist in getting the drug to the           not enough to capture the whole story. Therefore,
desired site of action within the body. Equivalent            you need to analyze the effect of variations in vol-
distribution of active ingredients ensures that all           ume fraction on the segregation observed within a
dosages in the medications contain uniform weights            system. Also, we wish to isolate the effects of mix-
of the respective active and inactive components.             ture properties on segregation extents, so we do not
Equal dosages in pharmaceutical products are es-              change the operating conditions, but rather how a
sential to the medication and its effect on the hu-            mixture is prepared, which may make it less likely
man body. Currently, final dosages and uniformity              to segregate.
among medication are required to be checked and
placed on an official compendium[1].                            2.3    Convection
   In order to examine the effects of segregation, we
used glass beads instead of pharmaceutical pow-               In addition to percolation, another mechanism con-
ders. Both of these substances are granular ma-               tributing to segregation is convection, as seen in
terials, which can be defined as collections of dis-           Figure 1. Unlike percolation, which only occurs in
crete particles that can behave like liquids under
certain conditions and solids under others. For in-
stance, sand can flow like water when poured, but
can also support walking along the beach. These
substances react similarly under like circumstances,
thus allowing an observation of the movement of the
glass beads to correlate to pharmaceutical powder
movement. Not only do glass beads share many
similarities with pharmaceutical powders, but they
are also easier to work with. There are numerous
health hazards for potentially inhaling high doses of
such toxic materials and complex phenomena as a
result of their small sizes, such as cohesion and elec-
trostatics. In addition, variations in shape, density         Figure 1: Convection current of a 50 50 binary mixture
and surface properties hinder the ability to isolate                    simulation.
the root causes of segregation within a mixture with
size differences. In contrast, marbles are perfectly
spherical, uniform, and have a consistent density.            the presence of vibration and size differences be-
Thus, marbles are beneficial for removing compli-              tween mixture species, convection affects all par-
cations and focusing on the fundamental causes of             ticles and carries them from deep inside the bed,
segregation in a particulate mixture.                         to the surface and back. Convection is caused by


                                                          2
the friction between the granular materials and the          particles among an entire mixture. Within a simu-
walls of their container, resulting in a rolling effect       lation, we were able to see the inside of the mixture
that forces particles to move down the sides of the          and also track the movement of each and every par-
container and rise in the center. When the width of          ticle.
the downward flow is not large enough to accommo-
date a large particle, these large particles become          3.1    The Relevance of Sandpaper
trapped on top of the granular mixture and are dis-
allowed to fall. Convection can act to redistribute          Due to their perfectly spherical shape, beads cre-
smaller particles that percolate to the bottom of            ated less friction upon collision than more realistic
the bed back to the surface. In addition, convec-            particles with some angularity. In order to account
tion can transport large particles normally trapped          for this dearth, we lined the inner walls of the vi-
on the surface into the bed, decreasing segregation.         brating cylinder with sandpaper. The rough tex-
In our experiments, we studied convection and seg-           ture provided sufficient friction for spherical parti-
regation using both binary and ternary mixtures.             cles that would otherwise be provided by the nat-
Binary mixtures are an assortment of two differ-              urally angular shapes of the powders. When the
ent sized particles and ternary mixtures are an as-          marbles came in contact with the walls of the con-
sortment of three different sized particles. The size         tainer the sandpaper ensured that convection would
variations and combinations in a mixture affect the           still occur. It was vital for this process to occur
overall amount of convection and flow of particles            because it provided a method for continually mix-
in the mixture. To simulate the flow of particles af-         ing the materials. Since we were using marbles
ter the mixing process and during transportation,            rather than pharmaceutical powders the circum-
we used a vibrating cylinder. This cylinder repli-           stances were slightly different. Instead of having
cates the pharmaceutical drum, which is used to              a completely natural system we have had to syn-
transport the pharmaceutical powders. It also had            thesize certain aspects of it. Our artificial system
enough width to eliminate wall effects and support            provided an identical process that was able to be
convection.                                                  studied in a simpler manner.

2.4    Equal Volume Fractions vs. Un- 3.2 Bead Size Disparities
       equal Volume Fractions         We used different sized beads, which are able to
Equal volume fractions and unequal volume frac-     manipulate various mixture properties in the binary
tions define the percentage of different sized beads  and ternary mixes. For each case, both binary, con-
among each mixture. Equal volume fractions are      sisting of small and large glass beads, and ternary,
mixtures in which the percentage of beads is equal  consisting of small, intermediate, and large glass
among all sizes whereas unequal volume fractions    beads, the amount of segregation was observed af-
are mixtures in which the percentage of beads variester vibration. This was done by counting the num-
among all sizes.                                    ber of large beads that had risen to the surface of
                                                    the vibrated bed. After figuring out the calcula-
                                                    tions and analyzing the trends of the graphs, we
3 Methods and Experimen- discovered which mixture, binary or ternary pro-
      tal Design: The Use of duced the most segregation and the intermediate,
                                                    the comparative result. The small,
                                                                                            difference in

      Glass Beads in Understand- and large glass beads all have the same densities so
                                                    the mass fraction is the same as the volume fraction
      ing Pharmaceuticals                           within any run, and size is the only factor driving
Using glass beads is a simpler way to understand segregation between the different species.
the mixing process in the pharmaceutical industry.
By counting and calculating the percentage of the 3.3 Choosing Frequency and Ampli-
beads on top of a small simulated mixture we de-            tude
termined how well the system was mixed. Experi-
ments only permitted us to observe the top beads We were operating at Γ = 3, derived from formula
of a mixture because the sandpaper along the walls 1.
                                                                             4π ∗ f 2 A
of the container stopped it from being transparent.                    Γ=                            (1)
Going through the container to see the particles                                 g
would disturb the mixture and make our results In the equation, f=frequency, A=amplitude, and
flawed. Thus, we used simulations to follow the g=gravity. Operation continued for approximately


                                                         3
200 seconds of vibrations at an amplitude of 1mm              ternary mixtures only. After weighing out these
and a frequency of 38.7Hz, which corresponded to              mixtures, we pre-mixed the beads in a glass cylin-
over eight thousand oscillation cycles. We chose              der beaker. Next, we poured the combination of
this amplitude and frequency to ensure the bed                beads into the cylindrical container. The cylinder
moved as a single body and the particles on the               was separated into four divisions labeled the front
surface did not behave vastly different than those             left, front right, back left, and back right. The idea
near the bottom of the bed. Also, vibrations of               of creating a simulated mixture is to start with a
much lower frequency would not create convection              mixed initial state which is why we use the divider
and thus, our investigation would be limited to the           to separate the particles. First poured into the front
effects of percolation, not the balance that might             left, the beads went next to the front right, back
exist between convection and percolation. With the            left, back right and then to the beginning again to
capability to choose specific numbers that applied             be repeated four times. This ensures that there will
directly to a particular situation, in this case trans-       not be segregated layers before running the simula-
portation, we were better able to simulate the con-           tion and that the glass beads are well mixed. This
ditions of the pharmaceutical particles after they            ensures that we start with a mixed initial condition
had already been mixed.                                       that allows us to study the segregation of partic-
                                                              ulate mixtures undergoing vertical vibration, the
                                                              situation most relevant to the production of phar-
3.4    The Vibrating Device
                                                              maceutical tablets.
The use of a correctly sized vibrating cylinder was
one of the most influential parts of our experi-               3.6    D-average
ment. We made the cylinder 20cm tall with a ra-
dius of 6cm. This made it tall enough to hold all of          The d-average is a parameter which helps us un-
the beads in our experiment, while having enough              derstand why one mixture is better mixed than
width to eliminate wall effects and support convec-            another. Calculating the d-average is performed
tion. Without convection, the investigation would             through formula 2,
be limited to percolation, which had been shown to
                                                                        (#L ∗ DL ) + (#I ∗ DI ) + (#S ∗ DS )
lead to complete segregation between the compo-                Davg =                                        (2)
nents. Convection can act to redistribute particles                               #L + # I + # S
and maintain a relatively mixed system, striking a            where # equals the number of beads, D equals the
balance with the percolation mechanism.                       diameter of the bead, and L, I, and S equal the size
                                                              of the bead (large, intermediate, small). In a binary
3.5    Creating a Simulated Mixture                           mixture the d-average increases with an increas-
                                                              ing volume fraction of large beads. In a ternary
Each mixture contained 1200 grams of beads which              mixture the d-average increases with an increasing
were divided in half for binary equal volume frac-            volume fraction of intermediate beads. A higher
tion mixtures (vfm), in thirds for ternary equal              d-average causes a larger downward-flowing convec-
vfm, and multiple fractions for unequal vfm. By               tion layer. This results in better chances for a larger
varying the types of volume fraction mixtures we              sized particle to participate in the flow as opposed
observed particles in pharmaceutical mixing pro-              to being stuck at the top causing a better mixed
cesses efficiently and legitimately. Among bi-                  system.
nary mixtures we tested volume fractions such as
11 89, 30 70, 50 50, 70 30, and 89 11 (small large).
Likewise, we also tested ternary volume frac-                 4     Results and Discussion
tions such as 49 2 49, 45 10 45, 40 20 40, 33 33 33
(small intermediate large). To create and mix                 Among all the experiments and simulations we
these systems, we weighed out the small glass                 performed, the ternary equal volume fraction,
beads, which are about 5mm in diameter, in weigh-             33 33 33, stayed the most mixed. In our binary
ing dishes on a balance. This was to ensure that the          mixtures, the 30 70 system remained the least seg-
masses corresponded with the correct given masses             regated.
we calculated after using the d-average formula
shown in Figure 2, which is explained in greater              4.1    Binary vs. Ternary Equal Vol-
detail later in the paper. We repeated these steps
                                                                     ume Fractions
for the large green beads, which are about 10mm in
diameter, and the clear intermediate beads, which             Our results demonstrated a wide range of segrega-
are about 7.5mm in diameter and are included in               tion for the vibrated system. Largely correlated


                                                          4
to the Brazil Nut Effect, the amount of segre-                4.2    Binary Unequal Volume Frac-
gation amongst pharmaceutical products, partic-                     tions
ularly powders, is highly dependent on the vari-
ety of sized particles in the mixture. An equal              The amount of segregation can be lessened with
volume ternary mixture segregates less than an               unequal volume fractions. Shown in Figure 4 is a
equal volume binary mixture because the ability of           trend capturing a reduction in segregation (percent
each component in the mixture to enter the con-              of total large beads on top) as the percentage of
vection current is larger in the ternary mixture.            large beads is increased in the mixture. There is
This is demonstrated by the extent of segregation
decreasing with an increase in the d-average from
the binary to ternary mixture, as seen in Figure
2. Among binary alone, the d-average affects the




                                                             Figure 4: Comparison between percentage of total large
                                                                       beads on top and the volume fraction of large
                                                                       beads in binary mixtures.


Figure 2: Comparison between mixing and diameter
                                                   some variation between some of the intermediate
          weighted averages in both binary and ternary
          mixtures.                                points, but, in general, there is a decreasing trend.
                                                   Varying the numbers from larger amounts of small
                                                   beads to larger amounts of large beads affects the
                                                   entire system, including percolation and convec-
amount of segregation drastically, as seen in Fig- tion. Theoretically, as the percentage of large beads
ure 3. We hypothesize that mixtures that include in the system increases, the ability of all particles
                                                   to participate in the upward and downward convec-
                                                   tion current increases as well. This is in contrast
                                                   with the Brazil Nut Effect, where only the small
                                                   particles are included in convection, isolating the
                                                   large particles on the surface of the bed, and creat-
                                                   ing a segregated system. We can determine which
                                                   systems are better mixed using the percent large
                                                   on top as our experimental metric to calculate seg-
                                                   regation; the lesser this number, the better mixed
                                                   the system. Currently, it seems to be due to the
                                                   beads packing themselves in crystal structures and
                                                   preventing convection from occuring. This shows
                                                   that with more of the large species in the system,
                                                   the segregation becomes less severe.

Figure 3: Comparison between mixing and diameter
          weighted averages in binary mixtures.              4.3    Ternary Unequal Volume Frac-
                                                                    tions
                                                      As with binary mixtures, ternary mixtures also dif-
higher degrees of intermediate particles with equal fer when volume fractions are unequal. The addi-
volume fractions of small and large species will also tion of more intermediate sized beads, while keep-
be less segregated.                                   ing the volume fraction of small and large beads


                                                         5
equal, allows for larger convection currents along            5    Conclusions
the sides of the cylinder. The larger current permits
large beads to enter the rotation of particles. After         Our results show that segregation is a massive is-
these particles fall, they are brought back to the top        sue permeating the pharmaceutical industry. Our
in the convection current, creating a better mixed            research has shown, on a simple scale, the sever-
system. In our experiments, ternary mixtures that             ity of segregation of granular materials, particu-
had larger fractions of intermediate sized beads cre-         larly in regard to pharmaceutical powders. Having
ated the best mixed systems. This observation held            too much of the active ingredient in the product
true in our simulations, as seen in Figure 5. In this         may cause the consumer to accidentally overdose,
                                                              whereas having a tablet filled with inactive ingre-
                                                              dient will have no effect on the consumer. In order
                                                              to examine this issue, we used glass beads to repre-
                                                              sent pharmaceutical powders and poured them into
                                                              a vibrating cylinder. This was meant to replicate
                                                              the vibrations that the pharmaceutical powders un-
                                                              dergo during transportation. After completing this
                                                              experiment, we found that the ternary equal vol-
                                                              ume fraction of 33 33 33 and the binary volume
                                                              fraction of 30 70 segregated the least. These results
Figure 5: Observe that the mixture with the highest           suggest that a potential solution to segregation in
          amount of intermediate sized beads is the           the pharmaceutical industry is to add more com-
          best mixed system.                                  ponents of differing size to medicines. This can be
                                                              done by either introducing a new element to the
                                                              drug product, or alter the size distribution of an
                                                              existing component.
figure, it is easy to observe the difference in the                Although glass beads adequately simulated the
width of the crystallized regions of different sizes of        system in our experiments, using sand and phar-
beads, which are signified by different colors, in the          maceutical powders is the next step to fully under-
different simulation trials (from left to right). As           stand segregation of pharmaceutical mixtures. Us-
a higher quantity of intermediate sized beads is in-          ing such materials we can now introduce and isolate
troduced, the system becomes less segregated. Our             the effects of cohesion, shape, and surface variations
results from ternary mixtures are shown in Figure             on segregation potentials. For our future work, we
6.                                                            plan to test sand and pharmaceutical powders in
                                                              our small vibrated system and, then, move on to
                                                              a larger scale. Also, finding a solution to actu-
                                                              ally prevent segregation amidst the pharmaceutical
                                                              companies is ahead.


                                                              6    Acknowledgements
                                                              We would like to thank everyone involved in helping
                                                              us to conduct these experiments. These thanks go
                                                              out to Matt Metzger and Anchal Jain (our project
                                                              mentors), Amber Cox (our RTA mentor), Blase
                                                              E. Ur (GSET Program Coordinator), Ilene Rosen
                                                              (GSET Program Director), Kristin Frank (Head
                                                              RTA), Jameslevi Schmidt (Research RTA), and
                                                              The Governor’s School Board of Overseers (Mar-
                                                              guerite Beardseley, Chair, and Laura Overdeck,
                                                              Vice Chair). We would also like to thank the spon-
Figure 6: This plot shows the relationship between
                                                              sors of the 2010 Governor’s School, particularly
          weighted diameter average and percentage of
          total large beads on top in ternary mixtures.       Rutgers University, the Rutgers University School
                                                              of Engineering, Morgan Stanley, the State of New
                                                              Jersey, Lockheed Martin, PSEG, the Tomasetta
                                                              family, the Provident Bank NJ Foundation, Silver


                                                          6
Line Building Products, and the families of Gover-
nor’s School alumni.


References
[1] Woo Sik Choi. Studies on mixing of pharmaceu-
    tical powders. Archives of Pharmacal Research,
    5(2), 1982.
[2] Anthony Rosato, Katherine J. Strandburg,
    Friedrich Prinz, and Robert H. Swendsen. Why
    the brazil nuts are on top: Size segregation of
    particulate matter by shaking. Physical Review
    Letters, 58(10), 1987.
[3] Matthias Schroter, Stephan Ulrich, Jennifer
    Kreft, Jack B. Swift, and Harry L. Swinney.
    Mechanisms in the size segregation of a bi-
    nary granular mixture. Physical Review Letters,
    74(1), 2006.




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