Longitudinal segregation of polymer powder in a rotating cylinder

Powder Technology 207 (2011) 324–334

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Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c

Longitudinal segregation of polymer powder in a rotating cylinder Amara Aït Aissa a,b, Carl Duchesne a, Denis Rodrigue a,b,⁎ a b

Department of Chemical Engineering, Université Laval, Quebec City, Canada, G1V 0A6 CERMA — Centre de Recherche sur les Matériaux Avancés, Université Laval, Quebec City, Canada, G1V 0A6

a r t i c l e

i n f o

Article history: Received 12 July 2010 Received in revised form 4 November 2010 Accepted 11 November 2010 Available online 23 November 2010 Keywords: Axial segregation Particle size Band number Image analysis Froude number

a b s t r a c t This paper reports some observations on the behaviour of a binary particle bed consisting of a mixture of small and large particles in the axial plane of a rotating drum. The effects of Froude number, particle diameter, filling ratio and initial particle concentration on axial segregation are evaluated using polymer powders. The results show that the number of segregation bands formed depends strongly on bed composition and processing conditions. Based on the experimental results, a segregation model to quantify axial dispersion is proposed. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.

1. Introduction The segregation of granular materials like powders is a significant problem in many processes of the pharmaceutical, metallurgical, food and plastics industries. This problem adversely affects mixing processes related to solids sampling, handling, conveying and discharging [1]. This explains why many experimental studies on segregation have been performed in simple mixing devices like rotating cylinders [2–11]. In the last 15 years, attention was given to the fact that systems containing particles of different properties tend to show segregation, where particles with similar properties collect (aggregate) together in some part of the bulk. For such systems, random mixing is not a natural state. If the particles are originally mixed they will unmix on handling. The properties giving rise to segregation are differences in particle size, density, shape and resilience [6,12,13]. Smith et al. [14] reported some observation on size and density segregation during the preparation of powder samples. Brown et al. [15] first reported vertical segregation of particles in coal transport which depended not only upon the particles relative size and density, but also on friction coefficient, surface roughness, resilience and other properties like moisture and friability which are inherent to the media. If a cylinder partially filled with a granular binary mixture is tipped on its side so that its axis of symmetry is horizontal and rotation about that axis is imposed, individual species will segregate into alternating bands of relatively pure single component along this ⁎ Corresponding author. Department of Chemical Engineering, Université Laval, Quebec City, Canada, G1V 0A6. Tel.: + 1 418 656 2903; fax: + 1 418 656 5993. E-mail address: [email protected] (D. Rodrigue).

axis of rotation. Donald and Roseman [3] focused on the demixing of rotating mixtures, rather than problems of imperfect mixing. They reported that an initial radial segregation occurs, followed by an endlongitudinal segregation; i.e. radial segregation together with segregated bands of particles near the ends of the tube. Finally, full axial segregation of single component bands of particles extends over the entire length of the tube. The axial segregation due to a different size shows that each individual species segregate into alternate bands of relatively pure single component [7,8,16–25]. Band formation mechanisms have been proposed previously and theories were developed to explain axial segregation in terms of surface flow [9–11]. Donald and Roseman [3,4] proposed a theory based on surface velocity gradients of glass beads along the axial direction of the mixer and higher acceleration of larger particles down the slope of the bed. Fan and Shih [26] used a probability theory and the Kolmogorov diffusion equation to model the band formation. Hill and Kakalios [27] proposed an approach similar to Donald and Roseman [3,4], but used the dynamic angles of repose instead of the static angles of repose to relate the particle velocity gradients along the drum. 2. Objectives When homogenizing a multi-component mixture made of particles of different physical properties, the process is always leading to some degree of segregation. Many authors like Williams [6] stated that size difference is the most important factor in the mechanism of segregation. In the present work, the main objective is to use the RGB color space image analysis to follow the mixing dynamics of polymer powders of different particle sizes and colors inside a rotating

0032-5910/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.11.014

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Fig. 1. Typical t1–t2 pixel density histograms. The lighter is the color in the histograms (from black to red, yellow and white), the greater is the pixel density having a particular combination of t1–t2 (i.e. a particular pixel color). Initial state (left) and final state (right).

cylinder. Several experimental parameters will be studied: Froude number (10− 4 to 10− 2), particle size ratio (1.0 to 4.28), initial particle concentration (0.3 to 0.5) and filing ratio (0.17 to 0.43). Based on the data obtained, a model is proposed to quantify mixing quality as a function of time. As a first step, only binary mixtures will be used.

3. Materials and methods The experimental work was carried out using linear medium density polyethylene (LMDPE) in a powder form: Hival 103508 from Ashland Canada with a specific gravity of 938 kg/m3. The original powder was sieved into several range of particle (sieve diameter between 90 and 500 μm) to give different diameter ratios (dr) defined as the ratio of the larger particles (dL) divided by the diameter of the smaller particles (ds). In our case, the available range was between 1.0 and 4.28. Three rotating glass cylinders were used with dimensions of 69.3, 180 and 270 mm in length (L) and 54.5, 50.2, and 50.3 mm inner diameter (2R), respectively. The extremities of the cylinders were

closed with low-friction Teflon sheets to reduce end-effects. The mixing dynamics were captured using a Sony Full HD 1080 CyberShot camera with a resolution of 640 × 480 pixels. The working distance of the camera gave a pixel spatial resolution of 60 μm. Each experiment was left running for 30 min and the videos were discretized using the ImageGrab30fr software every 2 s. These images were later cropped, enhanced and converted to 8 bit greyscale using WCIF Image J® software. More details on the experimental setup and procedures can be found elsewhere [28,29]. 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 as [28–30]: MðtÞ ¼

IðtÞ − Ið0Þ Ið∞Þ − Ið0Þ

ð1Þ

where I(t) and I(0) are the mixing indices at time t and for the initial state of the mixture, respectively. I(∞) is the final state of best binary mixing. These indices corresponds to the contrast textural feature [31]

Fig. 2. Images and mixing degree as a function of time from the GLCM method for a binary mixture of red and black particles of different sizes with dr = 1.68, Fr = 10− 4, f = 20% and x = 50/50.

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Fig. 3. Color intensity of a binary mixture of red and black particles as a function of time from the RGB color analysis method with dr = 1.68, Fr = 10− 4, f = 20% and x = 50/50.

computed on a single grey level co-occurrence matrix (GLCM) using 32 grey levels, 1 pixel translation and 0° angle. The mixing degree scale insures that: 0≤MðtÞ ≤1

ð2Þ

and equilibrium is defined as: dMðtÞ ≈ 0: dt

ð3Þ

The RGB color space analysis, as developed by Aït Aissa et al. [29,32,33], is used to estimate the surface concentration of each type of particles as a function of time. Surface concentration is obtained by classifying the color of each pixel within RGB images using a method known as multivariate image analysis [34]. It basically consists of collecting the RGB color intensities of each pixel of an image in a matrix X of dimensions (640 × 480 × 3), where the columns correspond to the three color intensities, and the rows to each pixel of the image. Then principal component analysis (PCA) is applied jointly to the matrices obtained from each image of a set collected during a mixing experiment using a so-called kernel algorithm [34]. Scatter

plots of the first two latent variables t1–t2 (also known as score vectors) of any image of a set are used to perform an unsupervised pixel classification based on their color in the original image. The first latent variable t1 is defined as the linear combination of RGB color intensities that explains the greatest amount of variance of X, whereas t2 is that linear combination explaining the second greatest amount of variance orthogonal to the first. Since there are as many observations in the t1–t2 scatter plots as the number of pixels within an image (i.e. 307,200 points in this case), it is common to display t1–t2 plots as 2D density histograms using a color map to indicate pixel density: dark regions means no pixel in this region and the brighter the color, the higher the pixel density for a particular t1–t2 combination (i.e. color). Fig. 1 shows an example of a 2D score density histogram for the initial and final state of a typical segregated binary mixture. Pixels having a similar color in the original image will project in the same region of the t1–t2 density histograms while those having a different color will fall in another region. Pixel classification based on color is obtained by establishing boundaries around such regions as also shown in Fig. 1. The boundaries were established by trial-and-error consisting of: 1) selecting a region in the t1–t2 density histograms, 2) automatically identifying the pixels falling within these boundaries, 3) highlighting these pixels in the original image using a very different color, and 4)

Fig. 4. Influence of initial powder position on axial segregation. (a) Parallel, (b) superimposed and (c) in series. All conditions are: dr = 1.68, Fr = 10− 4, f = 20% and x = 50/50. The first line of pictures represents the initial condition (t = 0) and the second line is for t = 30 min.

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Fig. 5. Mixing degree as a function of time from the GLCM method for particles of different diameter ratios for Fr = 10− 4, f = 20% and x = 50/50. The lines represent fits to Eqs. (8)–(11).

Fig. 7. Mixing degree as a function of time from the GLCM method for particles of different sizes in a binary mixture with Fr = 10− 4, f = 20% and x = 50/50. The lines represent fits to Eqs. (8)–(11).

verifying whether the particles of each type were well classified based on their color. This procedure was repeated until a satisfactory particle classification was obtained [29]. A count of the number of pixels falling within each region (i.e. boundaries) provides a measure of the area occupied by each color and the surface concentration of the selected pixels can be calculated by:

4. Results and discussion

obtained with axial segregation starting to appear and causing the mixing to decrease. At position D, axial segregation is developing. Finally, position E shows clear segregation between the larger and smaller particles into sharp bands. Fig. 2 also shows that broad bands, which are formed at the beginning, are dissipated into smaller bands with time. For this purpose, it is possible to determine an optimum mixing time for each specific mixture and mixing conditions before segregation occurs. This time is a function of mixer configuration (length and radius), products (particle size, geometry, density, and surface properties) and mixing conditions (rotating speed, initial content, and filling ratio). Kulvanich and Stewart [35,36] studied the influence of mixing time on the adhesion of the particles in an ordered system and showed that adhesion was higher by increasing the time of mixture. According to these authors, this increase in adhesion can be related to increasing electric charges at the surface of the particles due to contacts and more frequent particle collisions. To get more information on the process, the dynamic mixing evolution given by the RGB color analysis method is presented in Fig. 3. The results from the RGB method confirm the transitions observed in Fig. 2. Fig. 3 also shows two short periods of signal stabilizations. The first stabilization (shortly after point B) represents the optimum mixing time (highest homogeneity obtained), while the second stabilization (between D and E) represents complete segregation. One can say that segregation is a stable phenomenon for short periods but not stable in the long run [37]. The effects of operating conditions on the transition points are discussed next.

4.1. Effect of time

4.2. Effect of initial powder position

Typical evolution of the mixing degree with time for a binary mixture (red and black particles) of different sizes is given in Figs. 2–3 using the GLCM texture and RGB color analyses, respectively. From Fig. 2, it is clear that the mixing curve can be decomposed into several regions. First, point A represents the initial state of the system. The powders were placed side by side to start with the worst case scenario; i.e. a completely segregated state. Then, mixing degree increases up to point B, where homogeneity of the mixture increase due to convection mixing. Up to point C, a pseudo-equilibrium state is

Initial powder position is important for a mixing operation since it has a direct effect on mixing time. To highlight this effect, experiments were carried out using three initial state of the mixture as described in Fig. 4: parallel, superimposed or series. At the end of each experiment (30 min), conditions a (parallel) and b (superimposed) gave rise to bands forming along the axis of the cylinder which are more or less rich in some of the components. On the other hand, condition c (powders in series) led to negligible mixing, with the exception of the interface between both powders.

surface concentration =

number of pixels of given color : number of pixels of given image ðor fieldÞ ð4Þ

In this paper, it is proposed to use the RGB color analysis to follow the segregation dynamics of binary blends of polymer powders having different colors and particle sizes. The operating parameters studied are the particle size ratio (dr = dL /ds), the rotational speed (ω), the initial concentration of each color (x), the filling ratio (f), the cylinder's length over diameter ratio (L/D) and the initial powder position. For dynamic purposes, the Froude number (Fr) is generally used and defined as: Fr =

Rω2 g

ð5Þ

where g is the gravitational acceleration.

Fig. 6. Final mixing state of powders for different diameter ratios (dr) near unity at Fr = 10− 4, f = 20% and x = 50/50.

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Negligible mixing or segregation occurred within the time frame studied. Band formation can be interpreted using several explanations from the literature. Savage [11] interpreted the phenomenon of band segregation as the result of a balance between a process of un-mixing by diffusion and un-mixing caused by a preferential trajectory for one of the species. On the other hand, Zik et al. [38] explained axial segregation by the presence of an instability created in the cylinder by weak space fluctuations of the concentration of one or both species. Periodic space fluctuations created artificially on the wall of the rotating cylinder induced segregation in a mixture which remained completely homogeneous in the case of perfectly smooth walls of the drum. Moreover, they showed that the bands followed perfectly the periodicity of the modulations of the wall. Many theoretical works show that the dynamic angle of repose is a function of particle

size [9–11]. This variation of repose angle is mainly related to the presence of side walls and the angle is a fundamental parameter in the force balance acting on a granular bed. To limit the amount of work and produce segregation, the study will focus only on the parallel initial condition (Fig. 4a) because it is practically the easiest and most encountered state.

4.3. Effect of particle size Our previous works [28,29] showed that powders of similar particle sizes (dr = 1) and densities produced homogeneous mixtures (M(t) N 0.9) in agreement with Schutyser et al. [39]. In these cases, mixing occurred in less than 10 min for the range of particle size studied (82.5–550 μm). In order to see the evolution of particles

Fig. 8. Color intensity as a function of time from the RGB color analysis method for particles of different sizes in a binary mixture with Fr = 10− 4, f = 20% and x = 50/50.

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mixing when dr slightly deviates from unity, Fig. 5 presents typical curves for the mixing degree. Fig. 5 shows that the mixing degree decreases as dr deviates from unity. Contrary to the work of Dury and Ristow [40] which showed that segregation takes place whatever the particle diameter ratio is taken between the large and small particles, the cases dr = 1.06 and dr = 1.11 can be considered well mixed since their mixing degrees are above 0.90 [39]. On the other hand, axial segregation appears as shown in Fig. 6 for dr = 1.18. The size distribution of the powders used in this work allowed us to vary dr between 1.0 and 4.28. The evolution of the mixing degree with time is presented in Fig. 7 for three diameter ratios (dr = 1.18, 1.68 and 4.28) leading to segregation. Their corresponding analysis using the RGB color analysis is presented in Fig. 8. The results of Fig. 7 show that the process of segregation increases in intensity as the diameter ratio becomes larger as reported by Williams [6]. Campbell and Bauer [41] studied the segregation in a rotating drum for a particle size ratio between 0.84 and 1.41. In their work, segregation was also due to density difference but their definition of dr represented the diameter ratio of the different materials used. Their results showed that segregation appears for very small ratios, but the sampling method used probably underestimated the intensity of the phenomenon. Nystrom and Malmqvist [42] showed that a reduction in particle size influences homogeneity, highlighting an increase in powder agglomeration (5, 20 and 40 μm for small particles and 225 μm for large particles). The mixing homogeneity and axial segregation were confirmed by the RGB results of Fig. 8 where the signals stabilize at the same concentration (initial value) for each color (equi-mixture). Then, segregation starts and the signals stabilize at a different concentration for each color.

4.4. Effect of filling ratio The effect of cylinder's loading was studied via the filling ratio (f) defined as the volume occupied by the powder divided by the volume of the cylinder. Even when mixing powders of similar particle sizes, if the cylinder is not charged enough the powders slip on the wall without mixing occurring. This was the case when the load was lower than 17% [28]. On the other hand, if the cylinder is highly charged, the flow cannot take place and an almost static bed is produced for loadings higher than 43% [28]. This explains why we limited our work in this range and only three conditions were tested: f = 17, 20 and 43%. The results are presented in Figs. 9–10.

The results in Fig. 9 show that increasing f decreases the residual space in the cylinder and increases axial segregation. This increased axial segregation can be explain by an increase in band formation due to the lack of mixing and by the reduction of the active layer with increasing bed depth [43,44]. Once again, mixing homogeneity is confirmed by the RGB results of Fig. 10 since the signals stabilize at the same concentration for each color in the mixing case and at the different concentration in the segregation case. 4.5. Effect of initial concentration Figs. 11–12 present the mixing dynamics to account for the effect of initial bed composition. Three concentrations of large/small particles were studied: 50/50, 40/60, and 30/70 for each particle size in the binary mixture. The results of Figs. 11–12 show that increasing the initial content of smaller particles increases segregation. Also, more bands of small particles along the cylinder's axis are produced as reported by Oyama [2] for limestones of three different sizes. 4.6. Effect of Froude number Figs. 13–14 present the effect of Froude number on the mixing dynamics of binary powder blends. Three conditions were tested: Fr = 10− 4, 10− 3 and 10− 2. In general, at low revolutions, the particles move jointly with the drum until the bed makes an angle with the horizontal which is related to the angle of repose of the powder, then rolls on the surface. As rotational speed increases, the particle on the surface can be projected, then fall and roll on the surface. This increased speed causes a certain vibration in the powder bed leading to segregation due to different particle acceleration. Various modes of flow can appear in a rotary drum according to the number of revolutions [45]. In this work, the same conditions in terms of Froude number (10− 4–10− 2) and filling loading (17–43%) were used to minimize segregation. 5. Band number To complement on the literature published, the present work also tries to determine the influence of the experimental parameters on the number of segregation bands. Fig. 15 presents the results obtained for the range of parameters studied. Band formation due to axial segregation, as shown in Fig. 15, is influenced by each experimental parameter studied and the results are similar to those encountered in the literature. Oyama [2] used mixtures of three different sizes of limestone particles and reported that the number of bands decreased with increasing rotational speeds. Donald and Roseman [3,4] performed similar experiments using 30 different binary mixtures of sands, salt and glass beads. They observed that the number of bands increased with increasing surface roughness of the cylinder using sandpaper. Das Gupta et al. [9,10] used four sizes of sand particles and observed that the number of bands increased with the concentration of smaller particles for a given rotation speed. Based on the results of Fig. 15, a generalized correlation can be proposed as:    NBands = ð49:1 þ 42:4 expð−1036FrÞÞð−6:1þ34:02 xs Þ 0:001þð−0:04 f Þþ 0:036f 2   L ð−55:01–0:18LÞ ð−0:001–0:001dr Þ −1:06–0:14 D

Fig. 9. Mixing degree as a function of time from the GLCM method for different filling ratios (f) with dr = 1.68, Fr= 10− 4 and x = 50/50. The lines represent fits to Eqs. (8)–(11).

329

ð6Þ

with a regression coefficient (R2) of 0.97. The average absolute deviation between Eq. (6) and the experimental data is 8.4% for the range of parameters studied: 10− 4 ≤ Fr ≤ 10− 2, 0.5 ≤ xs ≤ 0.7, 0.17 ≤ f ≤ 0.43, 1.18≤ dr ≤ 4.28, 1.25 ≤ L/D ≤ 5.37 and 69.3 ≤ L ≤ 270 mm.

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Fig. 10. Effect of filling ratio (f) on the mixing dynamics analyzed by the RGB color method for powders of different colors with dr = 1.68, Fr = 10− 4 and x = 50/50.

6. Segregation dynamic model As it is desired to determine mixing and segregation time from a standstill, a second-order with numerator transfer function model is proposed to describe these events: MðsÞ ¼

K ðτs s þ 1Þ s ðτm s þ 1Þ2

ð7Þ

where K, τm and τs are the segregation intensity, characteristic time of mixing and segregation time, respectively. These parameters are strongly dependent on the mixing conditions. Note that the model proposed in the above equation naturally simplifies to our previously published model [28–30] when no segregation occurs (i.e. τs = 0). Applying the inverse Laplace transform, Eq. (7) can be expressed as a function of time:     τ −τ ð−t=τm Þ ð−t=τm Þ MðtÞ ¼K 1−e þt s 2 m e : ð8Þ τm

Fitting Eq. (8) to our binary mixtures of black and red particles of different sizes allowed us to find relationships between K, τm and τs and the mixing conditions as: K = ð0:30 þ 17:5 expð−3:36 dr ÞÞð−3:43−3:26 xs Þ

ð9Þ

ð−4:02 þ 2:55fÞð0:08−1:70FrÞ τm = ð−0:38 þ 0:06dr Þð36:7−21:6 xs Þð−143:4 þ 29:83f Þð0:48 þ 13:23FrÞ

ð10Þ τs = ð−0:42 þ 0:06dr Þð37:25−9:73xs Þð−131:10−37:18f Þð0:59 þ 4:88FrÞ:

ð11Þ The correlations of Eqs. (9)–(11) are valid in the following range: 10− 4 ≤ Fr ≤ 10− 2, 0.5 ≤ xs ≤ 0.7, 0.17 ≤ f ≤ 0.43 and 1.18 ≤ dr ≤ 4.28. In all the correlations developed, i.e. Eqs. (9)–(11), the interactions between each experimental parameter were found to be negligible.

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Fig. 11. Mixing degree as a function of time from the GLCM method for different initial bed compositions with dr = 1.68, f = 20% and Fr = 10− 4. The lines represent fits to Eqs. (8)–(11).

331

Fig. 13. Effect of Froude number on mixing degree as a function of time from the GLCM method for dr = 1.68, f = 20% and x = 50/50. The lines represent fits to Eqs. (8)–(11).

Fig. 12. Effect of initial composition on mixing dynamics from the RGB color analysis for dr = 1.68, f = 20% and Fr = 10− 4.

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Fig. 14. Effect of Froude number on the mixing dynamics from the RGB color analysis for dr = 1.68, f = 20% and x = 50/50.

Finally, one important parameter is the time to achieve maximum homogeneity (topt) before segregation starts. This time can be determined mathematically by solving:

with τs = 0 yields again two solutions, either t = 0 (initial time) or topt → ∞ which is the right solution since the highest mixing index is obtained at steady-state when particles do not segregate.

  d MðtÞ

7. Conclusion

dt

= 0:

ð12Þ

Giving rise to two possible solutions: either t → ∞ which corresponds to the steady-state solution, or to the following expression providing the optimal mixing time before segregation starts: topt =

τs τm : τs − τm

ð13Þ

Introduction of Eqs. (10) and (11) into Eq. (13) gives the value of the optimum mixing time. Also note that computing the optimal mixing time with the proposed model (Eq. (8)) is consistent with our previous model [28–30] when no segregation occurs. Solving Eq. (8)

Mixing components with different physical properties is invariably accompanied by a phenomenon of segregation which represents any space or space-time heterogeneity caused by the movement of the particles. This segregation depends not only on differences in particle size, but also on density, geometry and surface properties of the components. To quantify the dynamic mixing of polymer powders, two image analysis techniques were used to give complementary results. The GLCM texture analysis gives information on homogeneity (dispersion of the particles), while the RGB color analysis gives information about the relative content of each particle. From the data gathered, it was possible to get some information of mixing dynamics and homogeneity stability.

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Fig. 15. Number of bands as a function of different experimental parameters (Fr, xs, f, dr, L/D and L).

First, it was shown that for particles (polymer powders) of equal density and surface properties, negligible segregation was observed when the particle diameter ratio (dr) is between 1 and 1.18. Second, for the case dr N 1.18, a correlation was proposed to determine the evolution of the number of segregation bands formed throughout the cylinder's axis. It was shown that the number of bands decreased with increasing rotational speed or Froude number (Fr), but increased with increasing the concentration of smaller particles (xs) for a given rotational speed. A higher number of bands were also obtained with increasing f, L/D, L and dr. Finally, a second-order dynamic model was proposed to determine the evolution of the mixing degree with time. From this model, it was possible to approximate an optimum mixing time (topt) before segregation starts, thus producing the best mixture (homogeneity) for a specific blend. Acknowledgements Polyethylene samples from WES Industries (Princeville, Quebec, Canada) and financial support from the National Sciences and Engineering Council of Canada (NSERC) were greatly appreciated.

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Glossary D: cylinder diameter, cm dL: large particles diameter, μm dr: particle size diameter ratio ds: small particles diameter, μm f: filling ratio Fr: Froude number GLCM: grey level co-occurrence matrix I: mixing index K: segregation intensity L: cylinder length, cm LMDPE: linear medium density polyethylene M(t): mixing degree R: cylinder radius, cm RGB: red, green and blue t: time, s topt: optimum mixing time, s x: initial concentration xL: initial concentration of large particles xs: initial concentration of small particles τm: characteristic mixing time, s τs: characteristic segregation time, s