Characterization of polymer powder motion in a spherical mold in biaxial rotation.
Rotational molding, also known as rotomolding or rotocasting, is a high-temperature low-pressure plastic forming process that uses heat and biaxial rotation to pro duce hollow parts. Rotational molding is usually broken down into four basic steps Hi: (1) Loading where a pre weighed amount of powdered or liquid plastic is placed in one half of a thin walled hollow metal mold that is mounted on the arm of a molding machine. The mold is then closed using clamps or bolts. (2) Heating a biaxially rotating mold about perpendicular axes inside an oven. As the temperature inside the mold increases, the powder/liquid is tumbling up to a point where the material sticks to the mold surface in successive layers to form the part . (3) Cooling the material for part consolidation by moving the mold to a cooling station where forced air, water mist, or a combination of both is used to bring the part temperature down to a point below the crystallization or solidification point of the material . At this stage, rotation is still applied to prevent the molten material from sagging. (4) Unloading the solidified part by moving the mold to an unloading station where the part is removed. The mold is then ready to begin the process again.
Inside the mold, the forming process can be broken down into three stages. In the first stage, the powder is cascaded within the heated mold. Heat transfer from the mold surface to the tumbling particles will lead to the latter sticking to the sufficiently heated areas forming a sticky semi molten mass that will have the form of the mold. During this stage, the temperature of the powder will be close to or just above its melting point. The rotational speed and speed ratio (biaxial rotation) will be dictated by the shape of the mold and the desire to achieve a uniform coating of the walls (uniform part thickness) or not. The second stage is the coalescence of the powder particles to form a consolidated molten mass [4-7]. The controlling factor in this stage of the process is the efficiency of the heat transfer from the heated mold to the powder bed and then the subsequent heat transfer through the growing mass of the deposited powder. During this stage, the viscosity of the melt should be sufficient for the material to be retained in the location at which it is deposited but not so high as to inhibit spreading and molten particle coalescence. The rate at which this process occurs will depend also on the polymer melt surface tension. The final stage is cooling the mold to decrease the polymer temperature to solidify the part before mold opening.
Although rotational molding of plastic parts was introduced as early as 1855 by Peters , much of the analytical works on the subject started only around 1990 [9-13] The original patent of Peters  presents the basics of this molding technique such as biaxial rotational and external cooling methods . With the introduction of polyethylene powders in 1958 , rotational molding received increased interest. Today, rotomolded products are competitive in price with those made with processes such as injection or blow-molding. Unlike these processes, rotomolding does not involve pressure and does not require coring (used primarily for water cooling), thus resulting in comparatively inexpensive parts 181. Linear low -density polyethylene became the most widely used material because its molecules retain their low density and are packed more tightly than other polyethylene . Additional information about the rotational molding process may be found elsewhere (8), (14), (16).
One important part of the process, which has not received a great deal of attention, is the initial tumbling and distribution of the powder inside the rotating mold. Actually, this first step is of the utmost importance, because it will control how the particles are coming in contact with the heated mold in the first stages of the process. In order to see how particles are moving inside a rotating mold, several studies used the simple rotating drum (uniaxial rotation) as a first step [17, 18]. Because of its simplicity, the rotating drum has been a major research tool to study the effect of powder characteristics in rotating systems [19, 20]. Early investigations used this system to understand the initial stages of the rotational molding process . Throne indicated that three powder flow regimes can be encountered : (1) A static powder bed where the particles are lock together. As a result, the powder bed slides along the mold surface. (2) A free flowing powder bed where the particles easily move over one another. (3) A circulating powder bed where the frictional resistance between the powder and the mold surface is greater than the frictional resistance between powder particles. In some instances, the circulation is intermittent with frictional resistance between the particles locking them together as in the static bed case When the powder pool is drawn far up the rotating mold wall, the gravitational effect overcomes the powder resistance to flow. The powder bed then either breaks apart, with a portion cascading across the bed surface, or the powder bed simply slips down the mold surface to a lower level. The transition between each regime is con trolled by the powder characteristics, the mold geometry and surface, as well as rotational speed and degree of mold filling.
At low speeds and low mold filling, Henein et al. [22, 23] showed that the powder bed in a rotary drum slipped continuously. This is due to low friction between the particles and the drum walls, which results in minimal movement of the solids with respect to each other. At slightly higher speeds, the bed goes through a stumping stage, which occurs periodically. Increasing further the velocity results in a rolling bed where the solid material continuously moved upward with the drum walls and rolled down the inclined surface. Then, cascading is a more severe form of rolling and this occurs at slightly higher velocities where some particles at the surface of the bed become airborne due to high kinetic energy. Finally, the centrifuging regime occurs when the drum is rotating at a velocity greater than the critical speed. In this regime, all the solids adhere to the wall to form a static annular region. The critical rotational speed ([w.sub.c] can be calculated by:
[w.sub.o] = [square root of (term)]g/R (1)
where R is the radius of the drum and g is the acceleration due to gravity.
In most cases, the rotational speeds are selected to stay in the rolling regime. In this work, our uniaxial rotational system has been modified by adding a second motor to produce biaxial rotations [24, 25].
The glass cylinder is replaced by a glass sphere as a first step toward understanding particle movements in the first stage of roto molding.
To achieve good powder distribution inside the rotating mold and produce good parts, it is imperative that certain aspects of powder mixing/segregation be understood. Recently, there have been several discussions about powder flow characteristics in rotational molding [26-28] and several important contributions in the general field of granular material physics have been published [19, 29]. So, the main objective of this work is to determine how the powder bed moves inside a biaxially rotating mold. As a first step, a glass sphere will be used to follow the particles using video images and particles of different colors. Linear medium density polyethylene (LMDPE) with similar or different particle sizes will he used, arid experimental parameters such as particle diameter (d), ratio of larger over smaller particles diameter ([d.sub.r]), and initial powder position inside the mold and camera viewing position will be studied.
To investigate the particle dynamics, image analysis using the gray-level co-occurrence matrix (GLCM) method is used to determine the mixing degree (mixture homogeneity) as a function of time. Then, the red, green, and blue (RGB) color space image analysis is used on the same images to follow the motion of polymer powders inside a spherical mold [20, 24, 25, 30-33]. From the results obtained, it will be possible to determine the conditions leading to particle mixing/segregation and estimate the time for their occurance.
MATERIALS AND METHODS
The polymer used in this work as a general rotomolding grade of LMDPF: Hival 103508 from Ashland Canada. This polymer has a specific gravity of 938 kg/[m.sup.3] (ASTM D792A) and a melt index of 3.5 g/10 min (ASTM D1238). To differentiate between the LMDPE powders different colors such as red, blue, white, and yellow were used. Particle sizes where characterized and separated by sieving the original powder. The experiments were carried out in a glass sphere of 130 mm inner diameter driven by a Lab Line CEL-GRO Rotator. As described above, several processing parameters were studied. First, rotational velocities were selected as to produce a specific range of Froude numbers, which represents the ratio between centrifugal and gravitational forces. For biaxial rotation, the Froude number (Fr) is defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [w.sub.1] and [w.sub.2], are the horizontal and vertical rotational velocities. In this work, [w.sub.1], and [w.sub.2] were taken equal but can be controlled independently.
The range of Froude number was fixed between 0.017 and 0.7, because these conditions were found to represent the limits of the rolling regime determined experimentally (visual observation). In order to ensure good motion, the filling ratio (volume of powder divided by the sphere volume) was limited to the 10-50% range.
To capture the particle dynamics, a Sony Full HD 1080 Cyber-Shot camera with a resolution of 640 x 480 pixels was used. A black screen with a hole of 52 mm in diameter was placed parallel to the free surface of the powder bed and used as a mask to eliminate the exterior of the sphere. A complete schematic of the experimental set-up is presented in Fig. 1 with the definition of the parameters used.
Each video recording was between 20 and 30 min long For image analysis purposes, the videos were discretized into single images using the ImageGrab30fr software every 2 s, giving a total of 600/900 images for each experiment, respectively. The images were then cropped, enhanced, and converted to eight-bit grayscale using WCIF ImageJ[R] software.
From the images obtained, the homogeneity of the powder bed, called here the mixing quality, can be quantified using the concept of mixing degree, which is based on the ratio of a mixing index (I) provided by the GLCM texture analysis . GLCM is a second-order statistics that com pares two neighboring pixels at a time and compiles the frequency for which differing gray levels can be found within a restricted area. Using the GLCM method, a complete mixing curve for a given experimental setup needs to be obtained before identifying the degree of mixing at t = [varies]. In practice, its value is taken as the highest value provided by the index (I) within the fully mixed plateau. According to Haralick , three parameters must be taken into account when computing the GLCM of an image: the number of gray levels, the translation length, and the angle of displacement. Haralick also proposed to calculate several parameters allowing to build vector characteristics of the treated images. The most commonly used are contrast, energy, correlation, and homogeneity. For more details, see Ref. 14 where the parameters proposed by Haralick have been studied using the contrast textural feature. The optimum conditions were found to be: a transition distance of 1 pixel, a displacement angle of 0 [degrees], and 16 gray levels.
The mixing degree (M) used here is the ratio of the mixing index (1) provided by the algorithm at a given time t in relation to its initial value (t = 0) and that of a perfectly dispersed blend (t = [varies]) as:
[M.sub.(t)]= [I.sub.(t)] - [I.sub.(0)]/[I.sub.( [infinity])]-[I.sub.(0)](3)
The use of the RGB color space analysis method, developed in past works, is applied in order to measure the area occupied by each color (i.e., surface concentration of each type of particles) in order to detect segregation of the particles. Surface concentrations are calculated by the following equation [30-33]:
Surface concentration=Number of pixels of given color/Number of pixels of given image(or field) (4)
In this work, all the LMDPE powders used are assumed to have the same physical properties, only color and size are different as described next. More details on the experimental set-up and image processing/analysis methods are available in our previous studies [20, 24, 25, 30-34].
PARTICLES OF SIMILAR SIZES
An example for a quaternary blend of polymer powder (blue, white, red, and yellow) of similar sizes in the spherical mold is presented in Fig 2. The initial and final states of the bed are also presented.
The [t.sub.1]-[t.sub.2] score histogram plots represent the density of pixels having a certain combination of ROB color intensities along with segmented regions corresponding to the color of the particles. The number of pixels falling into each of these regions can be used to estimate the surface particle composition as described by Eq. 4. In each case, the black mask (sphere exterior) is eliminated before the analysis. From the same images, each color intensity can be obtained and their variation with time is presented in Fig. 3. It is clear that each curve can be broken down in two pans: a rapid variation in color intensity within the initial moments of mixing and stabilization at after a certain mixing time. One can assume that the first part of the signals corresponds to a fast reduction of heterogeneity due to the reorganization of the particles, while the second part corresponds to color intensity stabilization with small scale fluctuations representing a competition between the mechanisms of mixture and segregation. With time, the signals stabilize around their theoretical (initial) values (25% here).
Effect of Camera Viewing Position
In order to verify mixing homogeneity at various positions of the granular bed, videos were taken under different angles, namely: top view and side view. Typical results in terms of mixing index versus time are presented in Fig. 4 for particles of similar sizes (275 [micro]m) and similar experimental conditions (filling ratio, concentration, and rotation speed). Figure 4 clearly shows that the mixing dynamics are similar independently of viewing position. For this reason, only the top view results will be presented in the rest of the article. Figure 4 also shows that the blends are homogeneous (mixing degree higher than 0.98) around 210 s (3.5 min), which is a typical time before the polymer starts sticking to the walls in a typical rotational molding process [36-38].
Effect of Initial Powder Position
The initial powder arrangement is an important point to consider, because it controls the initial stages of mixing. The initial condition is especially critical for highly diluted mixtures, because it can advantage or disadvantage the mixture. To study this parameter, experiments were performed using the same conditions, but with different initial powder configurations. Figure 5 presents some of the possibilities tested, and Fig. 6 presents their respective mixing curves.
The results of Fig. 6 clearly shows that for similar particle sizes (d = 275 [micro]m) and initial concentration (1/4 for each color) in the rolling regime (Fr = 0.35 and f = 20%), the mixing dynamics are very similar. This implies that the initial distribution of the particles have little influence on the final state of the blend and homogeneous mixtures with mixing degrees higher than 0.98 can be achieve within 4 min. Furthermore, the blends are stable for the time period tested, 20 min being a typical "cooking" time for polyethylene  in rotomolding equipment.
Degree of Homogeneity
To see the reliability of the image processing method used in this work, experiments were carried out with different numbers of colors: binary, ternary, and quaternary blends. Using the mixing degree definition of Eq. 3, Fig. 7 presents typical results for each case.
In a blend, the homogenization process always occurs in competition with segregation or a demixing process, and this secondary phenomenon prevents perfect mixing from being obtained The mixing quality depends directly on this dynamic equilibrium, which is the result of the operating parameters and the nature of the mixing components. According to the results of Fig. 7, it can be deduced that for particle having similar sizes, similar dynamics are obtained, because binary, ternary, and quaternary blends have identical mixing degree curves. Their initial and final states are presented in Fig. 8 for comparison.
According to the pictures of the final states given in Fig. 8, the uniformity of the mixtures in all cases con firms the results of the GLCM method given in Fig. 7, it is clear that the mixing dynamics of binary, ternary, and quaternary mixtures are similar. For this reason, only results for the quaternary mixtures will be presented and discussed, the conclusions being equally valid for binary and ternary cases. For example, Fig. 9 presents a typical evolution of the mixing state for a blend of blue, red, yellow, and white particles having an average diameter of 275 [micro]m at a filling ratio of 20% with equal initial concentration for each color (25%) at Fr = 0.35.
Following the mixing state with time makes it possible to determine the mixing kinetics. This information can highlight the various mechanisms taking place inside the mold. Moreover, the kinetics can be used to determine the optimal mixing time beyond which, for specific conditions, segregation can occur. Mixing time is a convenient parameter commonly used to characterize the mixing performance and can be defined as the time taken to achieve a given degree of homogeneity. One can say that Fig. 9a is a completely segregated state. With time, the blend goes through intermediate states (see Fig. 9b-d), which is called the transition phase where homogeneity increases due to convection. Finally, the system tends to be macroscopically homogeneous (see Fig. 9e-i) with stabilization of particle content and distribution. A discussion is now made on the effect of particle size distribution on the motion dynamics.
PARTICLES OF DIFFERENT SIZES
When the particles are not of similar dimensions, size segregation can occur . As particle size distribution (broad or not) is always present in commercial grades of polymer powders, this must be quantified. As a starting point, a study was done on a mixture of two different particle sizes characterized by the diameter ratio ([d.sub.r]) defined as the ratio between the diameter of the largest particle over the diameter of the smallest particle. As presented above, a typical evolution of the mixing degree is presented in Fig 10 for binary blends of red (small) and blue (large) particles with [d.sub.r] between 1.18 and 5.57.
From Fig. 10, it is clear that different mixing behavior can be obtained based on the value of [d.sub.r]. The results show that for particles of different diameters and equal concentrations in the rolling regime, a good and stable mixture (mixing degree = 0.9, ) can only be obtained for [d.sub.r] values between 1.0 and 2.0. On the other hand, for [d.sub.r] values higher than 2.0, mixing degree increases up to a point where a maximum is obtained before a slow and continuous decrease is observed. The maximum value for the mixing degree ([M.sub.mAx]) and the time to achieve it ([t.sub.mAx]) is presented in Table 1 for different [d.sub.r] (1.18-5.57) values in the range studied.
TABLE 1. Maximum mixing degree and its corresponding time for different [d.sub.r] values in binary mixtures. [d.sub.r] (-) [M.sub.MAX] (-) [t.sub.MAX](S) 1.18 0.96 234 1.41 0.94 298 1.68 0.91 406 2.00 0.90 700 2.15 0.83 780 3.02 0.72 501 4.28 0.60 367 5.57 0.52 215
According to the results of Table 1, it can be concluded that for homogeneous mixtures ([d.sub.r]= 2.0), the maximum mixing degree decreases and the time to achieve it increases with increasing [d.sub.r] values. On the other hand, for higher diameter ratios ([d.sub.r] > 2.15), the maximum mixing degree cannot reach 0.9 due to the presence of size segregation between small and large particles . For the range studied, the maximum mixing degree decreases and the time to achieve also decreases with increasing [d.sub.r] values. Based on these informations, segregation may or may not occur in the powder bed depending on particle diameter ratio and processing time, because segregation needs time to be established.
Again, the reliability of the image processing method used in this work can he seen by carrying out experiments with different numbers of colors and different particle sizes: binary, ternary, and quaternary blends as presented in Figs. 11-13.
Figure 11 shows that segregation can occur depending on particle diameter and number of different particle size (color coded here; [d.sub.B]/[d.sub.R] = 3.02, [d.sub.Y]/[d.sub.R] = 3.02, and [d.sub.W]/[d.sub.R] = 3.02) with the red particles being the smallest particles and the others (blue, yellow, and white) having the same particle sizes (larger particles). It can be con cluded from Fig. 11 that in a biaxial spherical mixer and when [d.sub.r] is higher than 2, larger particles are projected on the peripheral of the granular bed, which can be explained by difference in movement and trajectories for small and large particles (size, inertia, etc.). This type of segregation was well explained by Harnby 1411. When a jet containing particles of different sizes falls vertically, each particle travels at different speeds. If the jet of particles is continuous, there will he no or little segregation, because at every moment and in any section of the jet, there will be particles of different sizes. However, if the particles are projected with no horizontal speed, segregation can occur because the horizontal component of velocity decreases more rapidly for smaller than for the larger particles.
Segregation can also occur for a wider range of particle size distribution. For example, a quaternary blend with different [d.sub.r] values is illustrated in Fig. 12.
Figure 12 shows the case of a quaternary blend with different [d.sub.r] values ([d.sub.B]/[d.sub.R] = 4.26, [d.sub.Y]/[d.sub.R] = 3.02, and [d.sub.W]/[d.sub.R] = 2.15) giving a wider particle size distribution. It is clear that segregation occurs as in Fig. 11 when a mixture of different sizes runs out along an inclined plan. From the video images, it can be observed that the larger particles tend to go further towards the walls compared with smaller particles. This leads to the formation of various layers of particles due to different [d.sub.r] values. The traveling distance (D) can be approximately calculated by :
where [V.sub.O] is the initial speed of the particle, d is the particle diameter, [eta] is the fluid viscosity (flow resistance), and [[rho].sub.s] is the particle density. Thus, a particle of diameter 2d will be able to travel a distance four times longer than a particle of diameter d under the same conditions. More detailed calculations with respect to particle size and densities can be found elsewhere .
Mixing degree as a function of time from the GLCM method for the cases presented in Figs. 11 and 12 is given in Fig. 13 to compare the mixing/segregation kinetics.
From the results of Fig. 13, two types of comparison can be made:
Comparing the kinetics of binary, ternary, and quaternary (1) mixtures with the same particles diameter ratios ([d.sub.r] = 3.02). The results show that the mixing dynamics are similar for all three cases with a maximum mixing degree 0.69 reached around 310 s. The equilibrium mixing degree is also similar: an equilibrium mixing degree around 0.68. So, the proportions (number of colors) are not influencing the particle mixing dynamics.
Comparing the kinetics of quaternary mixtures (1 and 2) under similar conditions but with different particle size distribution. In this case, the same maximum mixing degree is reached, but for different times: 316 s for quaternary (1) and 453 s for quaternary (2). As quaternary (1) has a narrower particle size distribution, this parameter not only influences the mixing dynamic but also seems to delay the appearance of segregation. Finally, quaternary (1) has a higher equilibrium mixing degree than equilibrium (2) meaning stronger segregation for wider particle size distribution.
This study was meant to be a first step toward our understanding of particle motion and mixing/segregation dynamics for polymer powders moving freely in a spherical mold under biaxial rotation. As the distribution of the particles in a solid bed inside the rotating mold is expected to influence the nature of particle deposition on the mold surface, it will definitely have an effect on final part's properties. Although interesting results were obtained in this preliminary work, much more work remains to be clone for improving our understanding of flowing particles in the rotowolding process. Parameters such as particle shape, particle surface, and mold surface quality and mold geometry must be investigated in the future. In addition, wider range of size distribution must be studied, because this parameter will highly influence the size and the number of bubbles formed in the sintering stage. Finally, all the experiments here were per formed at room temperature and more work needs to he done to include the effect of varying temperature. Although it appears that the powder is cohesionless at room temperature, there is strong evidence that there is increasing cohesion during heating. This changes the nature of powder flow with frictional or shear flow occurring between the mold surface and the powder layer against it.
As rotational molding parts become more and more complex, understanding of processing aspects such as powder flow inside a biaxially rotating mold becomes increasingly important. In this work, a preliminary step toward better understanding of powder flow was presented in order to estimate the uniformity and dispersion of a polymer powders (low medium density polyethylene) with different particle sizes and distribution thereof. To this end, the particle were color coded (blue, red, yellow, and white) to follow their motion in a biaxially rotating glass sphere. The dynamics were captured with a video camera at room temperature and quantification was done via image analysis using the GLCM method to determine homogeneity as a function of time. In addition, the ROB color analysis gave information about the relative content of each particle. From the data gathered, it was possible to get some information on mixing dynamics (time to reach a good mixing degree), possibility of segregation and blend stability for 20-30 min, which is a typical heating period in a rotomolding cycle.
To achieve uniform powder contact with the heating mold, it is imperative that certain aspects of powder flow be understood. Here, the limits of the rolling regime (good powder flow properties) were determined (0.017 Fr = 0.7) for the range of conditions tested (10% < f < 50% and 83 < d < 463 [micro]m).
For particle of similar sizes, it was found that good homogeneity (mixing degree greater than 0.9) can be obtained and the time to achieve good mixing decreases with increasing particle diameter. In addition, good homogeneity can be obtained for diameter ratios less than 2.0. In this case, the time to achieve maximum mixing degree increases with increasing [d.sub.r].
Finally, segregation was found to occur between small and larger particles when their diameter ratio is higher than 2. In this case, narrower particle size distributions seem to retard the appearance of segregation but wider particle size distributions led to stronger segregation (lower mixing degree).
Nevertheless, as all the experiments were performed at room temperature, the particle motions determined are valid only for the first step of the rotomolding process; that is, the heating stage up to the melting point of the polymer powder where the first particles will start sticking to the mold walls and modify particle motion. The effect of heating and particle motion in subsequent steps will be the subject of further studies.
Polyethylene samples obtained from WES Industries (Princeville, Quebec, Canada) were greatly appreciated.
NOMENCLATURE a Distance between the free surface and the black screen (mm) b Distance between the camera and the black screen (mm) D Traverse distance by solid particles (mm) d Particle diameter ([micro]m) [d.sub.r] Particle diameter ratio [d.sub.B], Diameter of blue, red, yellow, [d.sub.R], and white particles ([micro]m) [d.sub.Y], [d.sub.W] [d.sub.bs] Black screen diameter (mm) F Filling ratio (%) Fr Froude number g Acceleration due to gravity (m/[s.sup.2]) GLCM Gray level co- occurrence matrix [I.sub.(o)] Mixing index at initial time (t = 0) [I.sub.(t)] Mixing index at given time t [I.sub. Mixing index of a perfectly ([varies])] dispersed blend (t = [varies]). LMDPE Linear medium density polyethylene [M.sub.t] Mixing degree [M.sub.MAX] Maximum value of the mixing degree R Radius of mixer (mm) RGB Red, green, and blue color method t Time (s) [t.sub.MAX] to get the maximum mixing degree (s) V Cylinder volume (mL) [V.sub.O] Initial particle speed (mm/s) X Initial concentration (%) [w.sub.c] Critical rotational speed (rad/s) [w.sub.1], [w.sub.2] Vertical and horizontal speed (rad/s) A Field of view angle B Angle of repose [eta] Fluid dynamic viscosity (Pa s) [[rho]. Particle density (kg/[m.sup.3]) sub.s]
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Correspondence to: Denis Rodrigue; e-mail: firstname.lastname@example.org
Contract grant sponsor: National Sciences and Engineering Council of Canada (NSERC).
Published online in Wiley Online Library (wileyonlinelibrary.com).[c] 2011 Society of Plastics Engineers
Amara AIt Aissa, (1), (2) Carl Duchesne, (1) Denis Rodrigue (1), (2)
(1.) Department of Chemical Engineering, Universite Laval, Quebec City, Canada G 1 V 0A6
(2.) CERMA--Centre de Recherche sur les Materiaux Avances, Universite Laval, Quebec City, Canada G1V 0A6
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|Author:||Aissa, Amara Ait; Duchesne, Carl; Rodrigue, Denis|
|Publication:||Polymer Engineering and Science|
|Date:||May 1, 2012|
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