- Email: [email protected]
Solving granular segregation problems using a biaxial rotary mixer
Chemical Engineering and Processing 57–58 (2012) 42–50
Contents lists available at SciVerse ScienceDirect
Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Solving granular segregation problems using a biaxial rotary mixer Janet Cho a , Yunfeng Zhu a , Karol Lewkowicz a , SungHee Lee a , Theodore Bergman b , Bodhisattwa Chaudhuri a,c,∗ a b c
Department of Pharmaceutical Sciences, University of Connecticut, Storrs, CT 06269, United States Department of Mechanical Engineering, University of Connecticut, Storrs, CT 06269, United States Institute of Material Sciences, University of Connecticut, Storrs, CT 06269, United States
a r t i c l e
i n f o
Article history: Received 27 November 2011 Received in revised form 18 March 2012 Accepted 23 April 2012 Available online 28 April 2012 Keywords: Granular mixing Powder flow Rotary mixer Sampling Image analysis
a b s t r a c t Granular mixing is a critical but poorly understood aspect in the manufacture of many industrial products, for example, pharmaceuticals, food, cosmetics, ceramics, fertilizer and polymers. The mixing and segregation phenomenon occur in most systems of granular solids and have a significant influence on the quality and outcome of the final product. The usual approach to mix the powders is by using a tumbling blender which rotates around one axis, where, the radial convection is reported to be faster than axial dispersion transport, hindering the mixing performance. A double cone mixer is fabricated which rotates around two axes, causing axial mixing competitive to its radial counterpart. Samples are collected intrusively using the discrete pocket samplers to quantify the characteristics of mixing for millimeter sized glass beads. Digital video recording and MATLAB based image analysis techniques are used for non-intrusive characterization of mixing in micron sized art sands. A parametric study of the effect of particle size, vessel speeds on the granular mixing is accomplished. Incorporation of dual axis rotation enhances axial mixing by 70–90% in comparison to single axis rotation. Particles of smaller sizes (art sand) tend to mix quicker than the bigger particles (glass beads) due to mild cohesive effects. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The significance of granular mixing to the world economy is paramount as the products from industries spanning from pharmaceuticals, minerals, agriculture and food to chemical and ceramics, all increasingly depend on reliable granular flow and uniform granular mixing. As for instance, the annual cost of inefficient industrial mixing in the US has been estimated to be US$10 billion [1]. The efficiency of all pharmaceutical solid dosage formulations (tablets/capsules) depends on their blend homogeneity; therefore, inconsistency in the mixture can be detrimental for the patients. The routinely used powder mixers can be categorized into two particular types: rotary blenders [2,3] and convective blenders [4,5]. Despite the rotary blenders rely upon the action of gravity to cause the powder to cascade and mix within a rotating vessel, the convective blenders employs an paddle, impeller, blade, or screw which stirs the powder inside a static vessel. Convective blenders show variations in both impeller and vessel geometries, while rotary blenders which rotate around one axis, differ mainly
∗ Corresponding author at: Department of Pharmaceutical Sciences, University of Connecticut, Storrs, CT 06269, United States. Tel.: +1 860 486 4861; fax: +1 860 486 2072. E-mail address: [email protected] (B. Chaudhuri). 0255-2701/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cep.2012.04.002
in the geometry of the vessel. One of the most common batch type rotary mixers in industrial use is double cone mixer, where granular materials are caused to flow by a combination of the action of gravity and the rotating motion of the mixer. The double cone mixer consists of a vertical cylindrical shell with the conical top and bottom. Despite the common usage of the double cone mixer in batch mixing operations, relatively less research on it has been published. In several preliminary studies on standard double cone mixer, experiment based parametric investigations on mixer performance were done for a given set of materials and operating conditions [6–9]. Studies on the mixing of solids in a double cone blender [10,11] investigate axial and radial mixing separately using sampling ports located parallel to the rotation axis for axial mixing and perpendicular to the rotation axis for radial mixing. The effect of particle size and flowability on sampling and quantitative characterizations of mixing performance as a function of the most basic parameters, such as vessel speed or filling level, are also scarce in the literature [12–14]. Experimentally validated modeling of granular flow was first attempted by [1] to analyze robust segregation tendencies persistent in double cone blenders. In most of the rotary mixers, the radial convection is faster than the axial dispersion transport [1,11,15,16]. This slow dispersive process hinders mixing performance. In order to address this mixing problem, previous researcher [9,13,17] performed experiments comparing a standard double cone to one with a baffle attached to the shell of the
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
vessel. The baffle was same as the length of the vessel, and was at an angle with the rotation axis, apparently in an effort to cause axial motion within the system. The presence of the baffle, however, did not always affect the rate of mixing [9]. The reason behind the enormous loss of resources (energy, materials and manpower) [18] is the lack of knowledge and unpredictability of mixing in rotational mixing devices. In a situation where a final product is particularly expensive to produce or sensitive to small fluctuations in the final form, efficient and reproducible mixing carries key importance in the process. With that goal in mind, in a previously published paper [19], we introduced a novel concept of multi-dimensional rotation to the traditional double cone blender and perform experiments with spherical glass beads and particle dynamics based numerical modeling to study granular flow and mixing. While traditional mixers (drum, double cone, bin, V, bohle-bin) rotate about a single axis, the multi-dimensional rotary mixer rotates simultaneously about two perpendicular axes using two separate step motors, mounted on a frame built to support rotation about one axis, while being rotated itself about another. An experimental study with more realistic micron sized powder systems and subsequent characterization using image analysis technique based non-intrusive is presented in this paper. The organization of the article is as follows. The brief descriptions of the experimental method and experimental results are presented in Sections 2 and 3, respectively. Section 4 highlights the major conclusions of the research.
2. Experimental method, sampling and materials A vessel of 3 liters volume is fabricated out of two Pyrex made long stem funnels where the stems are plugged to the outer aluminum made frame (as shown in Fig. 1) to create the appropriate geometry. The photograph of the actual apparatus is illustrated in Fig. 1. The vessel is 5.6 in. in diameter and 12 in. high, with a 3 in. straight side. The glass blower is used to attach external hooks to be used in fastening the two funnels together by rubber bands. The vessel frame, which surrounds the vessel, consists of an aluminum ring (marked C in Fig. 1a) of 14-in. outer diameter and 13-in. inner diameter and 2.25 in. of thickness. Two step motors (Lin Engineering, CA) are used to separately rotate the frame and the vessel tied up to the frame using a flanged ball bearing respectively. The bottom portion of the frame is machined so that the one of the stepper motor (marked A in Fig. 1a) can be mounted. The vessel attaches to the ball bearing and the motor shaft so that it can be rotated about the vertical axis. The base frame is a sheet of 5/8 in. plywood. Steel rods are bolted and supported to build the structure to support the vessel frame. The other stepper motor (marked B in Fig. 1a) is mounted on the outside of one of the steel supports on the base frame to rotate the vessel frame via axels about the horizontal axis. The motors are connected to the respective drivers, which are controlled by a PC. A slip ring is placed outside the frame and across the higher powered motor to connect the driver and the low powered motor, thus removing the possibility of tangled wiring caused by simultaneous rotations by two different motors. To perform the rotation experiments of radial mixing equal volume (and mass) of glass beads of two different colors, but of same size, are loaded up to the fill level of 40%, in a side-by-side (as shown in Fig. 1b) initial configuration, then rotated at definite speeds using computer controlled motors. Experiments with systems homogenous in size but comprising different colors are being performed using two different sizes of spherical glass beads (1 mm and 3 mm; Ceroglass Technologies, TN) and art sand (250 m, Catskill Mountain Industries, NY) of two different colors. A typical run includes 450 ml of each species. A computer program interfacing the drivers of the motors is developed to control the rotation rates, direction of rotation and duration of rotation of the two different step motors.
43
2.1. Intrusive sampling of glass beads After the required number of rotations, the experiment is temporarily stopped to open up the top half of the cone, place the sampling template (shown in Fig. 1c) on the top surface of the granular bed, and then to draw samples using discrete pocket sampler (shown in Fig. 1d, manufacturer: GlobalPharma, NJ) from the same area of the bed through the holes of the sampling template. The holes in the template (ash shown in Fig. 1c) are strategically made to draw samples along the axis of the double cone mixer to quantify mixing in the axial direction. No attempt of sampling in the radial direction is made for quantifying radial mixing as it is known to be very rapid as compared to its axial counterpart [10,11]. The mixing states are quantified in each batch run, by hand counting the number of beads of different colors present in each sample to be a function of space and time. 2.2. Non-intrusive sampling of art sand The main obstacles in the characterization of mixing states for art sands or powder blends for uniform distribution of blend components depend in the collection of representative samples and their accurate analysis. Conventionally, samples are obtained from the blender by inserting the thief sampler or discrete pocket sampler at defined time intervals. Despite the simplicity in operating these sampler, the detrimental effects of intrusive probes such as tendency to disturb the powder bed, withdrawal of non-uniform samples in terms of composition and quantity, has long been recognized [20–22]. Several noninvasive methods have been investigated by other researchers, such as use of Raman spectroscopy [23], radioactive tracers [20], image analysis based on color difference [24], thermal effusivity [25], light induced fluorescence [20,26], fluorescence microscopy [27], and near infrared (NIR) spectroscopy [28–30]. Among these methods, image analysis method is being chosen due to its simplicity and low cost. Image analysis technique allows a full experiment to continue without interruption or disturbance to the granular bed. It also offers the ability to perform multicomponent analysis in a fast, non-destructive manner, requiring little or no sample preparation. The continuous runs of the mixing experiments are digitally recorded using a camcorder at the rate of 40 frames per second for non-intrusive sampling purpose and also to qualitatively validate of numerical simulation. As shown in the Fig. 2a, a frame corresponding to particular time, is acquired from the digitally recorded movie of our mixing experiment with art sands. The movie of the side view of the mixing experiment is captured keeping the digital camcorder outside the apparatus. This image is loaded in to Adobe Photoshop and as all the particles are concentrated in the triangular part of the double cone vessel, that part of the image is zoomed and saved into another image file (as shown in Fig. 2b). The triangular domain is discretized into 8 by 8 matrix rectangular space and a previously developed MATLAB based custom designed pixel-counting program [31,32] is used to determine the number of red and blue pixels in each of the squares. Thereafter, intensity of segregation (I) as a function of time is calculated from the concentration of each of species in each of the discretized squares at the corresponding time instants. The nonintrusive characterization of mixing is also accomplished by same digital image analysis approach (as depicted in Fig. 3a–c) to the top surface of the granular bed by analyzing the top view image. The horizontal and vertical axes of the double cone are named X and Y axes for convenience, throughout the rest of the paper. In our study we have checked the effect of initial loading (front–back, side–side), fill level, rotational speeds at orthogonal directions (about X and Y) on the mixing of initially segregated granular systems. The evolution of mixing is quantified by estimating variation of concentration and intensity of segregation (I) as a function of time for all batch
44
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
Fig. 1. (a) The double cone is set inside the aluminum made frame (C). The frame is rotated around horizontal axis by motor (B) and the vessel is rotated around its vertical axis by another motor (A). (b) Top view of the double cone showing the initial configuration of side-by-side loading of same material but of two different colors to check axial loading. A divider is used to load the beads. (c) The template with four holes to ensure sampling from same space of the granular bed. (d) A discrete pocket sampler used to collect a mixture of red and blue glass beads. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. (a) A snapshot (side view) of the mixer from the digitally recorded movie. (b) A zoomed view of the mixer containing the mixture of powders. (c) The area of the image is discretized into a 8 by 8 square grid for image analysis purpose.
runs. The fill ratio for all the experiments with glass beads and art sand was maintained to be 40%. 3. Results and discussion 3.1. Effect of vessel speed An important feature of a double cone blender is that the cross sectional area available for powder flow varies with time as the vessel rotates. The change in cross sectional area creates axial flow
within each half of the blender [13], creating convective flow on each side of the plane of symmetry, but not across the centerline of the vessel in uniaxial rotation (around the horizontal line of symmetry of the vessel). A simultaneous secondary rotation around the vertical axis is incorporated along with the usual rotary motion around the horizontal axis. The effect of vessel speeds on the mixing patterns is studied experimentally. The effect is studied separately with glass beads of two sizes: 1 mm diameter and 3 mm diameter and with art sand of size of 250 . Red and white colored glass beads of 3 mm size are used for experiments using
Fig. 3. (a) A snapshot (top view) of the mixer. (b) A zoomed view of the mixer containing the mixture of powders. (c) The area of the image is discretized into a 8 by 8 square grid for image analysis purpose.
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
the larger size in glass beads. In the trial with the smaller size in glass beads, red and blue colored glass beads are used. The red and blue colored art sand of 250 size are used for mixing experiments. A fill level of 40% and side–side initial loading is used for all the experiments. This side–side initial loading is chosen due to the well-known segregation problem for this particular loading [11,16]. Twelve different experiments (X = 10, 20, and 30 rpm and Y = 0, 10, 20, and 30 rpm) for all combinations of orthogonal rotation speeds are being performed separately with smaller, bigger beads and art sands. Digital video recording of the experiments is done for the qualitative analysis. In each of the experiments with all sizes of glass beads, to ascertain the temporal and spatial concentration of each of the species, a discrete pocket sampler is used to intrusively draw samples at definite time intervals by stopping the experiments. Non-intrusive characterization of mixing is done for art sand, using image analysis techniques to the time based snapshots of the digital movies (and photos) recorded from different view points (side and top views). Fig. 4a and b shows the time sequence of experimental snapshots with smaller beads (blue and red) rotated at X = 10 rpm; Y = 0 rpm and X = 10 rpm; Y = 30 rpm respectively. The time sequences of mixing states of bigger particles (white and red glass beads) under similar experimental conditions are depicted in Fig. 4c and d. Fig. 4a and c corresponds to single axis rotation and in both cases very nominal mixing is observed, in the course of time. However, with the addition of second rotation around the vertical (Y) axis, the mixing is quickly achieved as evident in Fig. 4b and d for smaller and bigger beads respectively. The mixing states from experiments using different sizes of beads but under same rotational conditions look very similar to each other. Thus, no prominent effect can be attributable to the size of the beads and further experimentation is done with the micron sized art sands. In Fig. 5 the time series of snapshots gathered from the experiments with art sand are illustrated. The time series of experimental snapshots are presented for the cases where the blender is rotated at 10 rpm around X axis and the Y axis rotation speed is set at: 0 rpm, 10 rpm and 30 rpm (shown in Fig. 5a–c respectively). Similar to the experiments with the glass beads, a sluggish axial mixing is observed in Fig. 5a, corresponding to the single axis rotation. From the snapshots in Fig. 5b and c, it is evident that rotating the blender around two axes manifests quicker mixing conditions. The second rotation (about Y axis) promotes axial transport of the particles along X axis, causing particles to change sides from one longitudinal half of the blender to the other half. After qualitative observation of the importance of dual rotation to granular mixing, mixing pattern is quantified using the experimental sampling technique and image analysis for glass beads and art sands respectively, as mentioned in Section 2. The double cone is rotated at a set speed (s) till the mixed state is achieved. In the intrusive characterization of mixing of glass beads, the vessel is stopped during the experiment and samples are collected at each of the four sampling locations of the template. The sample size drawn by only one pocket of the discrete pocket sampler is 20 ml comprising almost 100 beads. For each sampling location, the number of beads of each color was recorded. The beads are then placed back into the original sampling location and the rotation of the vessel is resumed. The concentration of red beads for four of the locations (in the sampling template) of the granular bed is estimated as a function of time for mixing experiment where the vessel is rotated around horizontal axis (X) at 10 rpm with no Y axis rotation (0 rpm). The evolution of mixing is also quantified using I, defined as Eq. (1). The intensity of segregation, I was calculated using the formula [4]: I=
2 02
(1)
45
where 2 was the variances of the concentration of red particle calculated at any time instant and at time = 0 s for the numerator and denominator of I. Variance ( 2 ) is calculated using the following formula:
2 =
¯ (Ci − C) N
2
(2)
where Ci is the concentration of red beads at point i (‘i’ corresponds to the sample points, i = 1, 2, 3, 4), C¯ the average concentration of red beads, N is the number of sample points (N = 4). The intensity of segregation is estimated for sampling data collected at every time interval of stoppage during the experiments. Fig. 6a illustrates the temporal variations of intensity of segregation (measured of the concentration of red beads of big red/white bead system) corresponding to three rotary systems ((i) X rotational speed: 10 rpm; (ii) X rotational speed: 10 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 10 rpm, Y rotational speed: 30 rpm). In all the cases, the granular bed becomes less segregated as time proceeds. Mixing rate is determined by the slope of the intensity of segregation plots. The curve reaching the asymptotic state earliest compared to other curves is considered to be mixing in the quickest rate. Though the uniaxially rotating case (X rotation = 10 rpm) decreases steadily but the dual axes rotating cases (X rotation = 10 rpm, Y rotations = 10 rpm, 30 rpm) have a higher slope of decline. Moreover, the case with highest rotational speed around Y axis (X rotation = 10 rpm, Y rotation = 30 rpm) reaches asymptotic value of intensity at around 50 s, whereas uniaxial rotating case is yet to reach the asymptote even at 300 s. The reduction in segregation (increase in mixing) occurs faster with increase in the Y rotational speed. The value of intensity of segregation (Ln(I) = −3) reached in 300 s by the case of X rotation = 10 rpm and Y rotation = 0 rpm is achieved in less than 30 s by the case with X rotation = 10 rpm, Y rotation = 30 rpm. Incorporation of dual axis rotation enhances the time of mixing by almost 90% in comparison to single axis rotation. Fig. 6b depicts the temporal variations of intensity of segregation corresponding to three rotary systems ((i) X rotational speed: 20 rpm; (ii) X rotational speed: 20 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 20 rpm, Y rotational speed: 30 rpm). Similar to the series of X rotation = 10 rpm, in the series of X rotation of 20 rpm, the reduction in segregation occurs faster with increase in the Y rotational speed and the mixing is quickest for X rotation = 20 rpm and Y rotation = 30 rpm. However, the mixing patterns for X rotation = 30 rpm series show distinct difference than the counterparts of X = 10 and X = 20 series. In Fig. 6c, it is observed that with the introduction of Y axis rotation, the mixing is achieved quicker, but mixing with Y rotational speed = 10 rpm is quicker in comparison to counterpart with Y rotational speed = 30 rpm. Moreover, the case showing quickest mixing (X rotation = 30 rpm, Y rotation = 10 rpm) reaches asymptotic value of intensity at around 25 s, whereas uniaxial rotating case is yet to reach the asymptote even at 200 s. Thus the incorporation of dual axis rotation enhances the time of mixing by almost 88% in comparison to single axis rotation. The mixing pattern in the art sand is non-intrusively estimated by analyzing several snapshot images (frames) of various time instants, from the digitally recorded movies of the continuous runs of the mixing experiments. As described in the Section 2, the image is discretized into small square areas and MATLAB is used to estimate the number of red and blue pixels present in each of the squares. Colors can be always described as vectors belonging to a 3D space, where each color can be defined by three co-ordinates. Colors images are categorically digitized as 24 bit RGB files by MATLAB, where 8 bits for each red, green and blue are used. The concentration of red particles in each of the square area is ascertained by calculating the ratio of red pixels to total number of pixel present in the space. The average concentration of red particles is then
46
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
Fig. 4. Snapshots from the experiment with glass beads of different sizes for single and dual axes rotations. (a) 1 mm glass beads: corresponds to X rotational speed = 10 rpm; no rotation about the Y axis (i.e. 0 rpm); (b) 1 mm glass beads: corresponds to X rotational speed = 10 rpm; the Y rotational speed = 10 rpm; (c) 3 mm glass beads: corresponds to X rotational speed = 10 rpm; no rotation about the Y axis (i.e. 0 rpm); and (d) 3 mm glass beads: corresponds to X rotational speed = 10 rpm; the Y axis rotational speed = 30 rpm. Dual rotation enhances mixing. (For interpretation of the references to colour in this text, the reader is referred to the web version of this article.)
calculated using Eq. (3) and thereafter calculates the variance (shown in Eq. (4)) of the pertinent triangular space of the image of the mixer.
where Cpi is the concentration of red particles in the i-th square; Np is the total number of squares which fully or partially contains the mixture of materials.
p2
C¯ i =
Cpi
Np
(3)
=
(Cpi − C¯ i ) N
2
(4)
Fig. 7a illustrates the temporal variations of intensity of segregation (of red art sand particles) corresponding to three rotary systems ((i) X rotational speed: 10 rpm; (ii) X rotational speed:
Fig. 5. Variation of intensity of segregation (for art sands) with time for the cases with (i) X rotational speed 10 rpm; (ii) X rotational speed: 10 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 10 rpm, Y rotational speed: 30 rpm. For higher Y rotation speeds, the beads quickly become less segregated with time. Quickest mixing at Y rotation speed = 30 rpm.
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
47
Fig. 6. Variation of intensity of segregation (with glass beads) with time for the cases with (a) X rotational speed 10 rpm, Y rotation = 0, 10, 30 rpm; (b) X rotational speed: 20 rpm; Y rotational speed: 0, 10, 30 rpm; (c) X rotational speed: 30 rpm; Y rotational speed: 0, 10, 30 rpm. For higher Y rotation speeds, the beads quickly become less segregated with time.
10 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 10 rpm, Y rotational speed: 30 rpm), all measured from the images gathered from the side view of the mixer. The same experiments with art sands are repeated to gather the digital images of the evolution of mixing in the granular bed from the top view. Images pertinent to specific time intervals are acquired by stopping the experiment. The images from the viewpoint at the top look similar to image shown in Fig. 3a. The discretization technique described in Section 2 is used to estimate the intensity of segregation of all the three cases of series X rotation = 10 rpm (shown in Fig. 7b). In all the cases, the granular bed becomes less segregated as time proceeds. Though the uniaxially rotating case (X rotation = 10 rpm) decreases steadily but the dual axes rotating cases (X rotation = 10 rpm, Y rotations = 10 rpm, 30 rpm) have a higher slope of decline. Moreover, the case with highest rotational speed around Y axis (X rotation = 10 rpm, Y rotation = 30 rpm) reaches its lower values of intensity (mixed state) at around 22 s, whereas, uniaxially rotating case is yet to reach the asymptote even at 90 s in Fig. 7a. Thus the incorporation of dual
axis rotation enhances the time of mixing in art sands by almost 75% in comparison to single axis rotation. The intensity of segregation plot shown for the similar cases, made from the top view of the experiments, show essentially the same trend as observed for side view results (Fig. 7a). The intensity of segregation curves in Fig. 7b shows some fluctuations (unlike the corresponding ones in Fig. 7a) and the time of mixing vary from the side view results. The intrusive techniques reveal the evolution of mixing on the surfaces of the granular bed and the mixing on the top surface (top view) exhibits slower progress in mixing in contrast to the slant longitudinal surfaces (side view). The characterization of mixing using image analysis technique of images acquired from different viewpoints (side and top) reveals almost the same trend and thus results estimated from the side view will be presented in the rest of the paper. The image analysis work performed on the side views of the mixer is also preferred as it can be done without stopping (and restarting) the experiments at different time intervals necessary for procuring the top view images. The reduction in segregation (increase in
Fig. 7. Variation of intensity of segregation (with art sand) with time for the cases with (a) side view: X rotational speed 10 rpm, Y rotation = 0, 10, 30 rpm; (b) top view: X rotational speed: 10 rpm, Y rotational speed: 0, 10, 30 rpm.
48
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
Fig. 8. The time series of snapshots from the experiments (with art sands) for single and dual axes rotations. (a) corresponds to X rotational speed = 30 rpm, no rotation about the Y axis (i.e. 0 rpm); (b) corresponds to X rotational speed = 30 rpm, the Y rotational speed = 10 rpm; and (c) corresponds to X rotational speed = 30 rpm; the Y axis rotational speed = 30 rpm.
mixing) occurs faster with increase in the Y rotational speed for art sand, similar to what is been observed for binary systems of glass beads. Thereafter, in Fig. 8 the time series of snapshots gathered from the experiments with art sand are illustrated, where the blender is rotated at 30 rpm around X axis and the Y axis rotation speed is set at: 0 rpm, 10 rpm and 30 rpm (shown in Fig. 8a–c respectively). Similar to the experiments with glass beads, sluggish axial mixing is observed in Fig. 8a, corresponding to the case with only one axis rotation. From the snapshots in Fig. 8b and c, it is evident that rotating the blender around two axes manifests quicker mixing conditions but mixing is quicker for Y rotation = 10 rpm as compared to Y rotation = 30 rpm. This observation is similar to what observed with glass beads. Irrespective of the materials used, quicker mixing is always achieved when there is phase lag between the rotations around two orthogonal axes (X and Y). The phase lag between the rotational speeds is responsible to break the symmetry of movement of the granular bed, leading to better mixing. Better mixing is evident in the cases of X = 10 rpm, and Y = 30 rpm, as compared to X = 10 rpm, and Y = 10 rpm in the series of X = 10 rpm; and in the cases of X = 30 rpm, and Y = 10 rpm, as compared to X = 30 rpm, and Y = 30 rpm in the series of X = 30 rpm. Moreover, the high rotational speed (30 rpm) creates more centrifugal force to the particles causing them to stick to the wall, manifesting lack of axial flow. This is again reinforced with the intensity of segregation plots shown in Fig. 9, estimated from the side view images of the experiments elucidated in Fig. 8. The mixing is fastest in dual axis rotation with the secondary rotational speed around Y = 10 rpm, while the rotational speed around X = 30 rpm.
As a general observation, we see that when the blender is rotated only around the horizontal axis (X), i.e. for no vertical rotation, mixing is faster for higher speeds. Mixing is also faster for dual rotations in the systems of glass beads or art sands, with any combination of vertical and horizontal rotational speeds, if compared with the same undergoing single axis rotation.
Fig. 9. Variation of intensity of segregation (for art sands) with time for the cases with (i) X rotational speed 30 rpm; (ii) X rotational speed: 30 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 30 rpm, Y rotational speed: 30 rpm. For higher Y rotation speeds, the beads quickly become less segregated with time. Quickest mixing at Y rotation speed = 10 rpm.
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
49
Fig. 10. The effect of size of the particles on mixing. The time series of snapshots from the experiments with dual axes rotations (X rotational speed = 10 rpm; rotation about the Y axis = 30 rpm). (a) corresponds to experiments with 3 mm sized glass beads, (b) corresponds to experiments with 1 mm sized glassbeads, (c) corresponds to experiments with 250 art sands. Art sands mix faster than the glass beads.
3.2. Effect of size of the particle
4. Conclusions
The effect of size of particles on the granular mixing patterns is also studied in the multi axis mixer. The effect is studied separately with glass beads of two sizes: 1 mm diameter and 3 mm diameter and 250 sized art sands. As mentioned in the Section 2, red and blue art sand are used for mixing experiments. In the trial with the smaller sized glass beads, red and blue colored beads are used. Red and white colored glass beads are used for experiments using the larger size. A fill level of 40% and side–side initial loading is used for all the experiments. Fig. 10a–c shows the time sequence of experimental snapshots with bigger beads (white and red), smaller beads (blue and red) and art sands (red and blue) respectively, all rotated at X = 10 rpm; and Y = 30 rpm. The three different time points (0, 15, 30 s) show the progression of mixing and it appear qualitatively different where art sand has quickest mixing rate and nearly complete mixing at t = 30 s. The end times of complete mixing for all three different materials are ascertained from the intensity of segregation graphs and also qualitatively from experimental movies. Though there is not much difference in the time of mixing for glass beads of 1 mm and 3 mm sizes but significant difference is observed between the beads and art sand. Micron sized art sand particles may have experienced mild cohesive effects due to electrostatics and Van der Waals forces causing rapid mixing compared to the free flowing (non cohesive) glass bead materials, a phenomena previously observed by Shinbrot [33] and Chaudhuri [34]. The rotating wall imparts shear or frictional force on the particles processed in the tumbling blender dictating the shear rate and the linear response of the particles participating in the 2-D flow in the cascading layer situated at the top surface of the granular bed. During the biaxial motion, the resultant axis of rotation of the vessel changes with time, also changing the direction of normal vector of the cascading layer surface. The particles at the surface in contact with the moving walls thus acquired time-dependent variation in linear velocity to produce a chaotic convective mixing in the cascading layer and eventually the whole granular bed.
A multi-dimensional rotary mixer is fabricated to successfully resolve the conventional segregation problem of axial mixing in rotary double cone blender. The effect of rotational vessel speed and particle size on mixing performance is evaluated by experiments and numerical modeling. The time of axial mixing is reduced in dual axis rotation as compared to single axis rotation. Incorporation of dual axis rotation enhances the time of mixing by 70–90% in comparison to single axis rotation. Higher rotational speed (30 rpm) around both the axes results in sluggish mixing. Micron sized art sand particles mix significantly quicker than the bigger glass beads of size 1–3 mm due to the mild cohesive behavior in art sands. Irrespective of the materials used, quicker mixing is always achieved when there is phase lag between the rotations around two orthogonal axes. Mixing of very fine particles is a challenge due to cohesion and van der waals forces. Though the mixer was successful to efficiently mix glass beads and art sands, but a proof of concept of mixing the real pharmaceutical drug powder and excipients is warranted as future work to bolster the applicability of the blender in reality. Intrusive analytical technique with discrete pocket sampler was used when mixing was quantified by drawing samples from four fixed areas of bed through the holes of the card board template. Sample size of 10 ml was drawn from regions of layer thickness 10–15 particle size diameters (for the bed with 3 mm size). On the contrary, image analysis based non-intrusive technique was used for smaller particles (art sand) where the mixing was only characterized on the outer surface of the granular bed. Acknowledgments We thank the University of Connecticut Research Foundation for supporting the work, and the undergraduate students Melissa Kuhn, Roshan Shah, Mi Hye Kim, Varunkumar Bhattaram, Michael Saito, Sweta Vachani, Rayhan Saikh, Jason Tomei, Seetha Manickam, and Eesha Desai for helping in the experiments. We are grateful to Dr. Robin Bogner and Dr. Michael Pikal for their support in pursuing Mechanical Engineering Senior Design Project.
50
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
References [1] M. Moakher, T. Shinbrot, F.J. Muzzio, Experimentally validated computations of flow, mixing, segration of noncohesive grains in 3D tumbling blenders, Powder Technology 109 (2000) 58–71. [2] L. Fan, Y. Chan, F. Lai, Recent developments in solids mixing, Powder Technology 61 (1991) 255–287. [3] A. Alexandar, A.T. Shinbrot, F. Muzzio, Scaling surface velocities in rotating cylinders as a function of vessel radius, rotation rate, and particle size, Powder Technology 126 (2002) 174–190. [4] M. Poux, P. Fayolle, J. Bertrand, D. Bridoux, J. Bousquet, Powder mixing: some practical applied to agitated systems, Powder Technology 68 (1991) 213–234. [5] P. Portillo, M. Ierapetritou, F. Muzzio, Characterization of continuous convective powder mixing processes, Powder Technology 182 (2008) 368–378. [6] M. Ashton, F.H.H. Valentin, The mixing of powders and particles in industrial mixers, Transactions of the Institution of Chemical Engineers 44 (1966) T166. [7] J. Gray, Performance of dry solids mixing equipment, Chemical Engineering Progress 53 (1957) 25. [8] K. Carley-Macauly, M. Donald, The mixing of solids in tumbling mixers—I, Chemical Engineering Science 17 (1962) 493–506. [9] K. Carley-Macauly, M. Donald, The mixing of solids in tumbling mixers—II, Chemical Engineering Science 19 (1964) 191–199. [10] T. Ramanujam, S. Davies, D. Venketaswarlu, Studies on the mixing of solids in a double cone blender, Indian Journal of Technology 7 (1969) 218. [11] A. Alexander, T. Shinbrot, F.J. Muzzio, Granular segregation in the double cone blender: transitions and mechanism, Physics of Fluids 13 (2001) 578–587. [12] A. Chester, J. Kowalski, M. Coles, E. Muegge, F. Muzzio, D. Brone, Mixing dynamics in catalyst impregnation in double cone blenders, Powder Technology 102 (1999) 85–94. [13] D. Brone, F. Muzzio, Enhanced mixing in double cone blenders, Powder Technology 110 (1998) 179–189. [14] R. Chang, J. Shukla, J. Buehler, An evaluation of a unit dose compacting sample thief and a discussion of content uniformity testing and blending validation issues, Drug Development and Industrial Pharmacy 22 (1996) 1031–1035. [15] A. Alexander, T. Shinbrot, F.J. Muzzio, Segregation patterns in V-blenders, Chemical Engineering Science 58 (2003) 487–496. [16] K. Hill, J. Kakalios, Reversible axial segregation of rotating granular media, Physics Review E 52 (1995) 4393. [17] D. Brone, C. Wightman, K. Connor, A. Alexander, F. Muzzio, P. Robinson, Using flow perturbations to enhance mixing of dry powders in V-blenders, Powder Technology 91 (3) (1997) 165–172. [18] J. Vernon, W. Hugen, A. Trujillo, Pharmaceutical manufacturing efficiency, drug prices and public health: examining the casual links, Drug Information Journal (2007).
[19] S. Manickam, R. Shah, J. Tomei, T. Bergman, B. Chaudhuri, Investigating mixing in a multi-dimensional rotary mixer: experiments and simulations, Powder Technology 201 (2009) 83–92. [20] C. Harwood, Powder segregation due to vibration, Powder Technology 16 (1977) 51–57. [21] R. Chang, S. Badway, M. Hussain, J. Beuler, A comparison of free flowing, segregating and non-free-flowing, cohesive mixing systems in assembling the performance of a modified v-shaped solid mixer, Drug Development and Industrial Pharmacy 21 (1995) 361–368. [22] F. Muzzio, M. Roddy, D. Brone, A. Alexander, O. Sudah, An improved powder sampling tool, Pharmaceutical Technology (1999) 92–110. [23] G. Vergote, T. De Beer, C. Vervaet, J. Remon, W. Baeyens, N. Diericx, F. Verpoort, In-line monitoring of a pharmaceutical blending process using FT-Raman spectroscopy, European Journal of Pharmaceutical Sciences 21 (2004) 479–485. [24] K. Lim, V. Gururajan, P. Agarwal, Mixing of homogeneous solids in bubbling fluidized beds: theoretical modelling and experimental investigation using digital image analysis, Chemical Engineering Science 48 (1993) 2251–2265. [25] G. Leonard, F. Bertrand, J. Chaouki, P. Gosselin, An experimental investigation of effusivity as an indicator of powder blend uniformity, Powder Technology 181 (2008) 149–159. [26] C. Lai, D. Holt, J. Leung, C. Cooney, G. Raju, P. Hansen, Real time and noninvasive monitoring of dry powder blend homogeneity, AIChE Journal 47 (2001) 2618–2622. [27] J. Staniforth, S. Iveson, An investigation of the use of UV fluorescence microscopy as a method for quantifying the homogeneity of powder mixes, International Journal of Pharmaceutics 31 (1986) 145–150. [28] S. Sekulic, J. Wakeman, P. Doherty, P. Hailey, Automated system for the on-line monitoring of powder blending processes using near-infrared spectroscopy. Part II. Qualitative approaches to blend evaluation, Journal of Pharmaceutical and Biomedical Analysis 17 (1998) 1285–1309. [29] A. Patel, P. Luner, M. Kemper, Quantitative analysis of polymorphs in binary and multi-component powder mixtures by near-infrared reflectance spectroscopy, International Journal of Pharmaceutics 206 (2000) 63–74. [30] C. Ufret, K. Morris, Modeling of powder blending using on-line nearinfrared measurements, Drug Development and Industrial Pharmacy 27 (2001) 719–721. [31] B. Chaudhuri, A. Alexander, A. Faqih, F. Muzzio, C. Davies, M. Tomassone, Avalanching flow of cohesive powders, Powder Technology 164 (2006) 13–21. [32] A. Faqih, B. Chaudhuri, A. Alexander, S. Hammond, F. Muzzio, M. Tomassone, Dilation effects of cohesive granular material in a rotating drum: experiments and simulations, AICHE Journal 52 (2006) 4124–4132. [33] T. Shinbrot, A. Alexander, F. Muzzio, Spontaneous chaotic granular mixing, Nature 397 (1999) 675–678. [34] B. Chaudhuri, A. Mehrotra, F. Muzzio, M. Tomassone, Cohesive effects in powder mixing in a tumbling blender, Powder Technology 165 (2006) 105–114.
Contents lists available at SciVerse ScienceDirect
Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Solving granular segregation problems using a biaxial rotary mixer Janet Cho a , Yunfeng Zhu a , Karol Lewkowicz a , SungHee Lee a , Theodore Bergman b , Bodhisattwa Chaudhuri a,c,∗ a b c
Department of Pharmaceutical Sciences, University of Connecticut, Storrs, CT 06269, United States Department of Mechanical Engineering, University of Connecticut, Storrs, CT 06269, United States Institute of Material Sciences, University of Connecticut, Storrs, CT 06269, United States
a r t i c l e
i n f o
Article history: Received 27 November 2011 Received in revised form 18 March 2012 Accepted 23 April 2012 Available online 28 April 2012 Keywords: Granular mixing Powder flow Rotary mixer Sampling Image analysis
a b s t r a c t Granular mixing is a critical but poorly understood aspect in the manufacture of many industrial products, for example, pharmaceuticals, food, cosmetics, ceramics, fertilizer and polymers. The mixing and segregation phenomenon occur in most systems of granular solids and have a significant influence on the quality and outcome of the final product. The usual approach to mix the powders is by using a tumbling blender which rotates around one axis, where, the radial convection is reported to be faster than axial dispersion transport, hindering the mixing performance. A double cone mixer is fabricated which rotates around two axes, causing axial mixing competitive to its radial counterpart. Samples are collected intrusively using the discrete pocket samplers to quantify the characteristics of mixing for millimeter sized glass beads. Digital video recording and MATLAB based image analysis techniques are used for non-intrusive characterization of mixing in micron sized art sands. A parametric study of the effect of particle size, vessel speeds on the granular mixing is accomplished. Incorporation of dual axis rotation enhances axial mixing by 70–90% in comparison to single axis rotation. Particles of smaller sizes (art sand) tend to mix quicker than the bigger particles (glass beads) due to mild cohesive effects. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The significance of granular mixing to the world economy is paramount as the products from industries spanning from pharmaceuticals, minerals, agriculture and food to chemical and ceramics, all increasingly depend on reliable granular flow and uniform granular mixing. As for instance, the annual cost of inefficient industrial mixing in the US has been estimated to be US$10 billion [1]. The efficiency of all pharmaceutical solid dosage formulations (tablets/capsules) depends on their blend homogeneity; therefore, inconsistency in the mixture can be detrimental for the patients. The routinely used powder mixers can be categorized into two particular types: rotary blenders [2,3] and convective blenders [4,5]. Despite the rotary blenders rely upon the action of gravity to cause the powder to cascade and mix within a rotating vessel, the convective blenders employs an paddle, impeller, blade, or screw which stirs the powder inside a static vessel. Convective blenders show variations in both impeller and vessel geometries, while rotary blenders which rotate around one axis, differ mainly
∗ Corresponding author at: Department of Pharmaceutical Sciences, University of Connecticut, Storrs, CT 06269, United States. Tel.: +1 860 486 4861; fax: +1 860 486 2072. E-mail address: [email protected] (B. Chaudhuri). 0255-2701/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cep.2012.04.002
in the geometry of the vessel. One of the most common batch type rotary mixers in industrial use is double cone mixer, where granular materials are caused to flow by a combination of the action of gravity and the rotating motion of the mixer. The double cone mixer consists of a vertical cylindrical shell with the conical top and bottom. Despite the common usage of the double cone mixer in batch mixing operations, relatively less research on it has been published. In several preliminary studies on standard double cone mixer, experiment based parametric investigations on mixer performance were done for a given set of materials and operating conditions [6–9]. Studies on the mixing of solids in a double cone blender [10,11] investigate axial and radial mixing separately using sampling ports located parallel to the rotation axis for axial mixing and perpendicular to the rotation axis for radial mixing. The effect of particle size and flowability on sampling and quantitative characterizations of mixing performance as a function of the most basic parameters, such as vessel speed or filling level, are also scarce in the literature [12–14]. Experimentally validated modeling of granular flow was first attempted by [1] to analyze robust segregation tendencies persistent in double cone blenders. In most of the rotary mixers, the radial convection is faster than the axial dispersion transport [1,11,15,16]. This slow dispersive process hinders mixing performance. In order to address this mixing problem, previous researcher [9,13,17] performed experiments comparing a standard double cone to one with a baffle attached to the shell of the
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
vessel. The baffle was same as the length of the vessel, and was at an angle with the rotation axis, apparently in an effort to cause axial motion within the system. The presence of the baffle, however, did not always affect the rate of mixing [9]. The reason behind the enormous loss of resources (energy, materials and manpower) [18] is the lack of knowledge and unpredictability of mixing in rotational mixing devices. In a situation where a final product is particularly expensive to produce or sensitive to small fluctuations in the final form, efficient and reproducible mixing carries key importance in the process. With that goal in mind, in a previously published paper [19], we introduced a novel concept of multi-dimensional rotation to the traditional double cone blender and perform experiments with spherical glass beads and particle dynamics based numerical modeling to study granular flow and mixing. While traditional mixers (drum, double cone, bin, V, bohle-bin) rotate about a single axis, the multi-dimensional rotary mixer rotates simultaneously about two perpendicular axes using two separate step motors, mounted on a frame built to support rotation about one axis, while being rotated itself about another. An experimental study with more realistic micron sized powder systems and subsequent characterization using image analysis technique based non-intrusive is presented in this paper. The organization of the article is as follows. The brief descriptions of the experimental method and experimental results are presented in Sections 2 and 3, respectively. Section 4 highlights the major conclusions of the research.
2. Experimental method, sampling and materials A vessel of 3 liters volume is fabricated out of two Pyrex made long stem funnels where the stems are plugged to the outer aluminum made frame (as shown in Fig. 1) to create the appropriate geometry. The photograph of the actual apparatus is illustrated in Fig. 1. The vessel is 5.6 in. in diameter and 12 in. high, with a 3 in. straight side. The glass blower is used to attach external hooks to be used in fastening the two funnels together by rubber bands. The vessel frame, which surrounds the vessel, consists of an aluminum ring (marked C in Fig. 1a) of 14-in. outer diameter and 13-in. inner diameter and 2.25 in. of thickness. Two step motors (Lin Engineering, CA) are used to separately rotate the frame and the vessel tied up to the frame using a flanged ball bearing respectively. The bottom portion of the frame is machined so that the one of the stepper motor (marked A in Fig. 1a) can be mounted. The vessel attaches to the ball bearing and the motor shaft so that it can be rotated about the vertical axis. The base frame is a sheet of 5/8 in. plywood. Steel rods are bolted and supported to build the structure to support the vessel frame. The other stepper motor (marked B in Fig. 1a) is mounted on the outside of one of the steel supports on the base frame to rotate the vessel frame via axels about the horizontal axis. The motors are connected to the respective drivers, which are controlled by a PC. A slip ring is placed outside the frame and across the higher powered motor to connect the driver and the low powered motor, thus removing the possibility of tangled wiring caused by simultaneous rotations by two different motors. To perform the rotation experiments of radial mixing equal volume (and mass) of glass beads of two different colors, but of same size, are loaded up to the fill level of 40%, in a side-by-side (as shown in Fig. 1b) initial configuration, then rotated at definite speeds using computer controlled motors. Experiments with systems homogenous in size but comprising different colors are being performed using two different sizes of spherical glass beads (1 mm and 3 mm; Ceroglass Technologies, TN) and art sand (250 m, Catskill Mountain Industries, NY) of two different colors. A typical run includes 450 ml of each species. A computer program interfacing the drivers of the motors is developed to control the rotation rates, direction of rotation and duration of rotation of the two different step motors.
43
2.1. Intrusive sampling of glass beads After the required number of rotations, the experiment is temporarily stopped to open up the top half of the cone, place the sampling template (shown in Fig. 1c) on the top surface of the granular bed, and then to draw samples using discrete pocket sampler (shown in Fig. 1d, manufacturer: GlobalPharma, NJ) from the same area of the bed through the holes of the sampling template. The holes in the template (ash shown in Fig. 1c) are strategically made to draw samples along the axis of the double cone mixer to quantify mixing in the axial direction. No attempt of sampling in the radial direction is made for quantifying radial mixing as it is known to be very rapid as compared to its axial counterpart [10,11]. The mixing states are quantified in each batch run, by hand counting the number of beads of different colors present in each sample to be a function of space and time. 2.2. Non-intrusive sampling of art sand The main obstacles in the characterization of mixing states for art sands or powder blends for uniform distribution of blend components depend in the collection of representative samples and their accurate analysis. Conventionally, samples are obtained from the blender by inserting the thief sampler or discrete pocket sampler at defined time intervals. Despite the simplicity in operating these sampler, the detrimental effects of intrusive probes such as tendency to disturb the powder bed, withdrawal of non-uniform samples in terms of composition and quantity, has long been recognized [20–22]. Several noninvasive methods have been investigated by other researchers, such as use of Raman spectroscopy [23], radioactive tracers [20], image analysis based on color difference [24], thermal effusivity [25], light induced fluorescence [20,26], fluorescence microscopy [27], and near infrared (NIR) spectroscopy [28–30]. Among these methods, image analysis method is being chosen due to its simplicity and low cost. Image analysis technique allows a full experiment to continue without interruption or disturbance to the granular bed. It also offers the ability to perform multicomponent analysis in a fast, non-destructive manner, requiring little or no sample preparation. The continuous runs of the mixing experiments are digitally recorded using a camcorder at the rate of 40 frames per second for non-intrusive sampling purpose and also to qualitatively validate of numerical simulation. As shown in the Fig. 2a, a frame corresponding to particular time, is acquired from the digitally recorded movie of our mixing experiment with art sands. The movie of the side view of the mixing experiment is captured keeping the digital camcorder outside the apparatus. This image is loaded in to Adobe Photoshop and as all the particles are concentrated in the triangular part of the double cone vessel, that part of the image is zoomed and saved into another image file (as shown in Fig. 2b). The triangular domain is discretized into 8 by 8 matrix rectangular space and a previously developed MATLAB based custom designed pixel-counting program [31,32] is used to determine the number of red and blue pixels in each of the squares. Thereafter, intensity of segregation (I) as a function of time is calculated from the concentration of each of species in each of the discretized squares at the corresponding time instants. The nonintrusive characterization of mixing is also accomplished by same digital image analysis approach (as depicted in Fig. 3a–c) to the top surface of the granular bed by analyzing the top view image. The horizontal and vertical axes of the double cone are named X and Y axes for convenience, throughout the rest of the paper. In our study we have checked the effect of initial loading (front–back, side–side), fill level, rotational speeds at orthogonal directions (about X and Y) on the mixing of initially segregated granular systems. The evolution of mixing is quantified by estimating variation of concentration and intensity of segregation (I) as a function of time for all batch
44
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
Fig. 1. (a) The double cone is set inside the aluminum made frame (C). The frame is rotated around horizontal axis by motor (B) and the vessel is rotated around its vertical axis by another motor (A). (b) Top view of the double cone showing the initial configuration of side-by-side loading of same material but of two different colors to check axial loading. A divider is used to load the beads. (c) The template with four holes to ensure sampling from same space of the granular bed. (d) A discrete pocket sampler used to collect a mixture of red and blue glass beads. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. (a) A snapshot (side view) of the mixer from the digitally recorded movie. (b) A zoomed view of the mixer containing the mixture of powders. (c) The area of the image is discretized into a 8 by 8 square grid for image analysis purpose.
runs. The fill ratio for all the experiments with glass beads and art sand was maintained to be 40%. 3. Results and discussion 3.1. Effect of vessel speed An important feature of a double cone blender is that the cross sectional area available for powder flow varies with time as the vessel rotates. The change in cross sectional area creates axial flow
within each half of the blender [13], creating convective flow on each side of the plane of symmetry, but not across the centerline of the vessel in uniaxial rotation (around the horizontal line of symmetry of the vessel). A simultaneous secondary rotation around the vertical axis is incorporated along with the usual rotary motion around the horizontal axis. The effect of vessel speeds on the mixing patterns is studied experimentally. The effect is studied separately with glass beads of two sizes: 1 mm diameter and 3 mm diameter and with art sand of size of 250 . Red and white colored glass beads of 3 mm size are used for experiments using
Fig. 3. (a) A snapshot (top view) of the mixer. (b) A zoomed view of the mixer containing the mixture of powders. (c) The area of the image is discretized into a 8 by 8 square grid for image analysis purpose.
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
the larger size in glass beads. In the trial with the smaller size in glass beads, red and blue colored glass beads are used. The red and blue colored art sand of 250 size are used for mixing experiments. A fill level of 40% and side–side initial loading is used for all the experiments. This side–side initial loading is chosen due to the well-known segregation problem for this particular loading [11,16]. Twelve different experiments (X = 10, 20, and 30 rpm and Y = 0, 10, 20, and 30 rpm) for all combinations of orthogonal rotation speeds are being performed separately with smaller, bigger beads and art sands. Digital video recording of the experiments is done for the qualitative analysis. In each of the experiments with all sizes of glass beads, to ascertain the temporal and spatial concentration of each of the species, a discrete pocket sampler is used to intrusively draw samples at definite time intervals by stopping the experiments. Non-intrusive characterization of mixing is done for art sand, using image analysis techniques to the time based snapshots of the digital movies (and photos) recorded from different view points (side and top views). Fig. 4a and b shows the time sequence of experimental snapshots with smaller beads (blue and red) rotated at X = 10 rpm; Y = 0 rpm and X = 10 rpm; Y = 30 rpm respectively. The time sequences of mixing states of bigger particles (white and red glass beads) under similar experimental conditions are depicted in Fig. 4c and d. Fig. 4a and c corresponds to single axis rotation and in both cases very nominal mixing is observed, in the course of time. However, with the addition of second rotation around the vertical (Y) axis, the mixing is quickly achieved as evident in Fig. 4b and d for smaller and bigger beads respectively. The mixing states from experiments using different sizes of beads but under same rotational conditions look very similar to each other. Thus, no prominent effect can be attributable to the size of the beads and further experimentation is done with the micron sized art sands. In Fig. 5 the time series of snapshots gathered from the experiments with art sand are illustrated. The time series of experimental snapshots are presented for the cases where the blender is rotated at 10 rpm around X axis and the Y axis rotation speed is set at: 0 rpm, 10 rpm and 30 rpm (shown in Fig. 5a–c respectively). Similar to the experiments with the glass beads, a sluggish axial mixing is observed in Fig. 5a, corresponding to the single axis rotation. From the snapshots in Fig. 5b and c, it is evident that rotating the blender around two axes manifests quicker mixing conditions. The second rotation (about Y axis) promotes axial transport of the particles along X axis, causing particles to change sides from one longitudinal half of the blender to the other half. After qualitative observation of the importance of dual rotation to granular mixing, mixing pattern is quantified using the experimental sampling technique and image analysis for glass beads and art sands respectively, as mentioned in Section 2. The double cone is rotated at a set speed (s) till the mixed state is achieved. In the intrusive characterization of mixing of glass beads, the vessel is stopped during the experiment and samples are collected at each of the four sampling locations of the template. The sample size drawn by only one pocket of the discrete pocket sampler is 20 ml comprising almost 100 beads. For each sampling location, the number of beads of each color was recorded. The beads are then placed back into the original sampling location and the rotation of the vessel is resumed. The concentration of red beads for four of the locations (in the sampling template) of the granular bed is estimated as a function of time for mixing experiment where the vessel is rotated around horizontal axis (X) at 10 rpm with no Y axis rotation (0 rpm). The evolution of mixing is also quantified using I, defined as Eq. (1). The intensity of segregation, I was calculated using the formula [4]: I=
2 02
(1)
45
where 2 was the variances of the concentration of red particle calculated at any time instant and at time = 0 s for the numerator and denominator of I. Variance ( 2 ) is calculated using the following formula:
2 =
¯ (Ci − C) N
2
(2)
where Ci is the concentration of red beads at point i (‘i’ corresponds to the sample points, i = 1, 2, 3, 4), C¯ the average concentration of red beads, N is the number of sample points (N = 4). The intensity of segregation is estimated for sampling data collected at every time interval of stoppage during the experiments. Fig. 6a illustrates the temporal variations of intensity of segregation (measured of the concentration of red beads of big red/white bead system) corresponding to three rotary systems ((i) X rotational speed: 10 rpm; (ii) X rotational speed: 10 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 10 rpm, Y rotational speed: 30 rpm). In all the cases, the granular bed becomes less segregated as time proceeds. Mixing rate is determined by the slope of the intensity of segregation plots. The curve reaching the asymptotic state earliest compared to other curves is considered to be mixing in the quickest rate. Though the uniaxially rotating case (X rotation = 10 rpm) decreases steadily but the dual axes rotating cases (X rotation = 10 rpm, Y rotations = 10 rpm, 30 rpm) have a higher slope of decline. Moreover, the case with highest rotational speed around Y axis (X rotation = 10 rpm, Y rotation = 30 rpm) reaches asymptotic value of intensity at around 50 s, whereas uniaxial rotating case is yet to reach the asymptote even at 300 s. The reduction in segregation (increase in mixing) occurs faster with increase in the Y rotational speed. The value of intensity of segregation (Ln(I) = −3) reached in 300 s by the case of X rotation = 10 rpm and Y rotation = 0 rpm is achieved in less than 30 s by the case with X rotation = 10 rpm, Y rotation = 30 rpm. Incorporation of dual axis rotation enhances the time of mixing by almost 90% in comparison to single axis rotation. Fig. 6b depicts the temporal variations of intensity of segregation corresponding to three rotary systems ((i) X rotational speed: 20 rpm; (ii) X rotational speed: 20 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 20 rpm, Y rotational speed: 30 rpm). Similar to the series of X rotation = 10 rpm, in the series of X rotation of 20 rpm, the reduction in segregation occurs faster with increase in the Y rotational speed and the mixing is quickest for X rotation = 20 rpm and Y rotation = 30 rpm. However, the mixing patterns for X rotation = 30 rpm series show distinct difference than the counterparts of X = 10 and X = 20 series. In Fig. 6c, it is observed that with the introduction of Y axis rotation, the mixing is achieved quicker, but mixing with Y rotational speed = 10 rpm is quicker in comparison to counterpart with Y rotational speed = 30 rpm. Moreover, the case showing quickest mixing (X rotation = 30 rpm, Y rotation = 10 rpm) reaches asymptotic value of intensity at around 25 s, whereas uniaxial rotating case is yet to reach the asymptote even at 200 s. Thus the incorporation of dual axis rotation enhances the time of mixing by almost 88% in comparison to single axis rotation. The mixing pattern in the art sand is non-intrusively estimated by analyzing several snapshot images (frames) of various time instants, from the digitally recorded movies of the continuous runs of the mixing experiments. As described in the Section 2, the image is discretized into small square areas and MATLAB is used to estimate the number of red and blue pixels present in each of the squares. Colors can be always described as vectors belonging to a 3D space, where each color can be defined by three co-ordinates. Colors images are categorically digitized as 24 bit RGB files by MATLAB, where 8 bits for each red, green and blue are used. The concentration of red particles in each of the square area is ascertained by calculating the ratio of red pixels to total number of pixel present in the space. The average concentration of red particles is then
46
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
Fig. 4. Snapshots from the experiment with glass beads of different sizes for single and dual axes rotations. (a) 1 mm glass beads: corresponds to X rotational speed = 10 rpm; no rotation about the Y axis (i.e. 0 rpm); (b) 1 mm glass beads: corresponds to X rotational speed = 10 rpm; the Y rotational speed = 10 rpm; (c) 3 mm glass beads: corresponds to X rotational speed = 10 rpm; no rotation about the Y axis (i.e. 0 rpm); and (d) 3 mm glass beads: corresponds to X rotational speed = 10 rpm; the Y axis rotational speed = 30 rpm. Dual rotation enhances mixing. (For interpretation of the references to colour in this text, the reader is referred to the web version of this article.)
calculated using Eq. (3) and thereafter calculates the variance (shown in Eq. (4)) of the pertinent triangular space of the image of the mixer.
where Cpi is the concentration of red particles in the i-th square; Np is the total number of squares which fully or partially contains the mixture of materials.
p2
C¯ i =
Cpi
Np
(3)
=
(Cpi − C¯ i ) N
2
(4)
Fig. 7a illustrates the temporal variations of intensity of segregation (of red art sand particles) corresponding to three rotary systems ((i) X rotational speed: 10 rpm; (ii) X rotational speed:
Fig. 5. Variation of intensity of segregation (for art sands) with time for the cases with (i) X rotational speed 10 rpm; (ii) X rotational speed: 10 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 10 rpm, Y rotational speed: 30 rpm. For higher Y rotation speeds, the beads quickly become less segregated with time. Quickest mixing at Y rotation speed = 30 rpm.
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
47
Fig. 6. Variation of intensity of segregation (with glass beads) with time for the cases with (a) X rotational speed 10 rpm, Y rotation = 0, 10, 30 rpm; (b) X rotational speed: 20 rpm; Y rotational speed: 0, 10, 30 rpm; (c) X rotational speed: 30 rpm; Y rotational speed: 0, 10, 30 rpm. For higher Y rotation speeds, the beads quickly become less segregated with time.
10 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 10 rpm, Y rotational speed: 30 rpm), all measured from the images gathered from the side view of the mixer. The same experiments with art sands are repeated to gather the digital images of the evolution of mixing in the granular bed from the top view. Images pertinent to specific time intervals are acquired by stopping the experiment. The images from the viewpoint at the top look similar to image shown in Fig. 3a. The discretization technique described in Section 2 is used to estimate the intensity of segregation of all the three cases of series X rotation = 10 rpm (shown in Fig. 7b). In all the cases, the granular bed becomes less segregated as time proceeds. Though the uniaxially rotating case (X rotation = 10 rpm) decreases steadily but the dual axes rotating cases (X rotation = 10 rpm, Y rotations = 10 rpm, 30 rpm) have a higher slope of decline. Moreover, the case with highest rotational speed around Y axis (X rotation = 10 rpm, Y rotation = 30 rpm) reaches its lower values of intensity (mixed state) at around 22 s, whereas, uniaxially rotating case is yet to reach the asymptote even at 90 s in Fig. 7a. Thus the incorporation of dual
axis rotation enhances the time of mixing in art sands by almost 75% in comparison to single axis rotation. The intensity of segregation plot shown for the similar cases, made from the top view of the experiments, show essentially the same trend as observed for side view results (Fig. 7a). The intensity of segregation curves in Fig. 7b shows some fluctuations (unlike the corresponding ones in Fig. 7a) and the time of mixing vary from the side view results. The intrusive techniques reveal the evolution of mixing on the surfaces of the granular bed and the mixing on the top surface (top view) exhibits slower progress in mixing in contrast to the slant longitudinal surfaces (side view). The characterization of mixing using image analysis technique of images acquired from different viewpoints (side and top) reveals almost the same trend and thus results estimated from the side view will be presented in the rest of the paper. The image analysis work performed on the side views of the mixer is also preferred as it can be done without stopping (and restarting) the experiments at different time intervals necessary for procuring the top view images. The reduction in segregation (increase in
Fig. 7. Variation of intensity of segregation (with art sand) with time for the cases with (a) side view: X rotational speed 10 rpm, Y rotation = 0, 10, 30 rpm; (b) top view: X rotational speed: 10 rpm, Y rotational speed: 0, 10, 30 rpm.
48
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
Fig. 8. The time series of snapshots from the experiments (with art sands) for single and dual axes rotations. (a) corresponds to X rotational speed = 30 rpm, no rotation about the Y axis (i.e. 0 rpm); (b) corresponds to X rotational speed = 30 rpm, the Y rotational speed = 10 rpm; and (c) corresponds to X rotational speed = 30 rpm; the Y axis rotational speed = 30 rpm.
mixing) occurs faster with increase in the Y rotational speed for art sand, similar to what is been observed for binary systems of glass beads. Thereafter, in Fig. 8 the time series of snapshots gathered from the experiments with art sand are illustrated, where the blender is rotated at 30 rpm around X axis and the Y axis rotation speed is set at: 0 rpm, 10 rpm and 30 rpm (shown in Fig. 8a–c respectively). Similar to the experiments with glass beads, sluggish axial mixing is observed in Fig. 8a, corresponding to the case with only one axis rotation. From the snapshots in Fig. 8b and c, it is evident that rotating the blender around two axes manifests quicker mixing conditions but mixing is quicker for Y rotation = 10 rpm as compared to Y rotation = 30 rpm. This observation is similar to what observed with glass beads. Irrespective of the materials used, quicker mixing is always achieved when there is phase lag between the rotations around two orthogonal axes (X and Y). The phase lag between the rotational speeds is responsible to break the symmetry of movement of the granular bed, leading to better mixing. Better mixing is evident in the cases of X = 10 rpm, and Y = 30 rpm, as compared to X = 10 rpm, and Y = 10 rpm in the series of X = 10 rpm; and in the cases of X = 30 rpm, and Y = 10 rpm, as compared to X = 30 rpm, and Y = 30 rpm in the series of X = 30 rpm. Moreover, the high rotational speed (30 rpm) creates more centrifugal force to the particles causing them to stick to the wall, manifesting lack of axial flow. This is again reinforced with the intensity of segregation plots shown in Fig. 9, estimated from the side view images of the experiments elucidated in Fig. 8. The mixing is fastest in dual axis rotation with the secondary rotational speed around Y = 10 rpm, while the rotational speed around X = 30 rpm.
As a general observation, we see that when the blender is rotated only around the horizontal axis (X), i.e. for no vertical rotation, mixing is faster for higher speeds. Mixing is also faster for dual rotations in the systems of glass beads or art sands, with any combination of vertical and horizontal rotational speeds, if compared with the same undergoing single axis rotation.
Fig. 9. Variation of intensity of segregation (for art sands) with time for the cases with (i) X rotational speed 30 rpm; (ii) X rotational speed: 30 rpm, Y rotational speed: 10 rpm; (iii) X rotational speed: 30 rpm, Y rotational speed: 30 rpm. For higher Y rotation speeds, the beads quickly become less segregated with time. Quickest mixing at Y rotation speed = 10 rpm.
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
49
Fig. 10. The effect of size of the particles on mixing. The time series of snapshots from the experiments with dual axes rotations (X rotational speed = 10 rpm; rotation about the Y axis = 30 rpm). (a) corresponds to experiments with 3 mm sized glass beads, (b) corresponds to experiments with 1 mm sized glassbeads, (c) corresponds to experiments with 250 art sands. Art sands mix faster than the glass beads.
3.2. Effect of size of the particle
4. Conclusions
The effect of size of particles on the granular mixing patterns is also studied in the multi axis mixer. The effect is studied separately with glass beads of two sizes: 1 mm diameter and 3 mm diameter and 250 sized art sands. As mentioned in the Section 2, red and blue art sand are used for mixing experiments. In the trial with the smaller sized glass beads, red and blue colored beads are used. Red and white colored glass beads are used for experiments using the larger size. A fill level of 40% and side–side initial loading is used for all the experiments. Fig. 10a–c shows the time sequence of experimental snapshots with bigger beads (white and red), smaller beads (blue and red) and art sands (red and blue) respectively, all rotated at X = 10 rpm; and Y = 30 rpm. The three different time points (0, 15, 30 s) show the progression of mixing and it appear qualitatively different where art sand has quickest mixing rate and nearly complete mixing at t = 30 s. The end times of complete mixing for all three different materials are ascertained from the intensity of segregation graphs and also qualitatively from experimental movies. Though there is not much difference in the time of mixing for glass beads of 1 mm and 3 mm sizes but significant difference is observed between the beads and art sand. Micron sized art sand particles may have experienced mild cohesive effects due to electrostatics and Van der Waals forces causing rapid mixing compared to the free flowing (non cohesive) glass bead materials, a phenomena previously observed by Shinbrot [33] and Chaudhuri [34]. The rotating wall imparts shear or frictional force on the particles processed in the tumbling blender dictating the shear rate and the linear response of the particles participating in the 2-D flow in the cascading layer situated at the top surface of the granular bed. During the biaxial motion, the resultant axis of rotation of the vessel changes with time, also changing the direction of normal vector of the cascading layer surface. The particles at the surface in contact with the moving walls thus acquired time-dependent variation in linear velocity to produce a chaotic convective mixing in the cascading layer and eventually the whole granular bed.
A multi-dimensional rotary mixer is fabricated to successfully resolve the conventional segregation problem of axial mixing in rotary double cone blender. The effect of rotational vessel speed and particle size on mixing performance is evaluated by experiments and numerical modeling. The time of axial mixing is reduced in dual axis rotation as compared to single axis rotation. Incorporation of dual axis rotation enhances the time of mixing by 70–90% in comparison to single axis rotation. Higher rotational speed (30 rpm) around both the axes results in sluggish mixing. Micron sized art sand particles mix significantly quicker than the bigger glass beads of size 1–3 mm due to the mild cohesive behavior in art sands. Irrespective of the materials used, quicker mixing is always achieved when there is phase lag between the rotations around two orthogonal axes. Mixing of very fine particles is a challenge due to cohesion and van der waals forces. Though the mixer was successful to efficiently mix glass beads and art sands, but a proof of concept of mixing the real pharmaceutical drug powder and excipients is warranted as future work to bolster the applicability of the blender in reality. Intrusive analytical technique with discrete pocket sampler was used when mixing was quantified by drawing samples from four fixed areas of bed through the holes of the card board template. Sample size of 10 ml was drawn from regions of layer thickness 10–15 particle size diameters (for the bed with 3 mm size). On the contrary, image analysis based non-intrusive technique was used for smaller particles (art sand) where the mixing was only characterized on the outer surface of the granular bed. Acknowledgments We thank the University of Connecticut Research Foundation for supporting the work, and the undergraduate students Melissa Kuhn, Roshan Shah, Mi Hye Kim, Varunkumar Bhattaram, Michael Saito, Sweta Vachani, Rayhan Saikh, Jason Tomei, Seetha Manickam, and Eesha Desai for helping in the experiments. We are grateful to Dr. Robin Bogner and Dr. Michael Pikal for their support in pursuing Mechanical Engineering Senior Design Project.
50
J. Cho et al. / Chemical Engineering and Processing 57–58 (2012) 42–50
References [1] M. Moakher, T. Shinbrot, F.J. Muzzio, Experimentally validated computations of flow, mixing, segration of noncohesive grains in 3D tumbling blenders, Powder Technology 109 (2000) 58–71. [2] L. Fan, Y. Chan, F. Lai, Recent developments in solids mixing, Powder Technology 61 (1991) 255–287. [3] A. Alexandar, A.T. Shinbrot, F. Muzzio, Scaling surface velocities in rotating cylinders as a function of vessel radius, rotation rate, and particle size, Powder Technology 126 (2002) 174–190. [4] M. Poux, P. Fayolle, J. Bertrand, D. Bridoux, J. Bousquet, Powder mixing: some practical applied to agitated systems, Powder Technology 68 (1991) 213–234. [5] P. Portillo, M. Ierapetritou, F. Muzzio, Characterization of continuous convective powder mixing processes, Powder Technology 182 (2008) 368–378. [6] M. Ashton, F.H.H. Valentin, The mixing of powders and particles in industrial mixers, Transactions of the Institution of Chemical Engineers 44 (1966) T166. [7] J. Gray, Performance of dry solids mixing equipment, Chemical Engineering Progress 53 (1957) 25. [8] K. Carley-Macauly, M. Donald, The mixing of solids in tumbling mixers—I, Chemical Engineering Science 17 (1962) 493–506. [9] K. Carley-Macauly, M. Donald, The mixing of solids in tumbling mixers—II, Chemical Engineering Science 19 (1964) 191–199. [10] T. Ramanujam, S. Davies, D. Venketaswarlu, Studies on the mixing of solids in a double cone blender, Indian Journal of Technology 7 (1969) 218. [11] A. Alexander, T. Shinbrot, F.J. Muzzio, Granular segregation in the double cone blender: transitions and mechanism, Physics of Fluids 13 (2001) 578–587. [12] A. Chester, J. Kowalski, M. Coles, E. Muegge, F. Muzzio, D. Brone, Mixing dynamics in catalyst impregnation in double cone blenders, Powder Technology 102 (1999) 85–94. [13] D. Brone, F. Muzzio, Enhanced mixing in double cone blenders, Powder Technology 110 (1998) 179–189. [14] R. Chang, J. Shukla, J. Buehler, An evaluation of a unit dose compacting sample thief and a discussion of content uniformity testing and blending validation issues, Drug Development and Industrial Pharmacy 22 (1996) 1031–1035. [15] A. Alexander, T. Shinbrot, F.J. Muzzio, Segregation patterns in V-blenders, Chemical Engineering Science 58 (2003) 487–496. [16] K. Hill, J. Kakalios, Reversible axial segregation of rotating granular media, Physics Review E 52 (1995) 4393. [17] D. Brone, C. Wightman, K. Connor, A. Alexander, F. Muzzio, P. Robinson, Using flow perturbations to enhance mixing of dry powders in V-blenders, Powder Technology 91 (3) (1997) 165–172. [18] J. Vernon, W. Hugen, A. Trujillo, Pharmaceutical manufacturing efficiency, drug prices and public health: examining the casual links, Drug Information Journal (2007).
[19] S. Manickam, R. Shah, J. Tomei, T. Bergman, B. Chaudhuri, Investigating mixing in a multi-dimensional rotary mixer: experiments and simulations, Powder Technology 201 (2009) 83–92. [20] C. Harwood, Powder segregation due to vibration, Powder Technology 16 (1977) 51–57. [21] R. Chang, S. Badway, M. Hussain, J. Beuler, A comparison of free flowing, segregating and non-free-flowing, cohesive mixing systems in assembling the performance of a modified v-shaped solid mixer, Drug Development and Industrial Pharmacy 21 (1995) 361–368. [22] F. Muzzio, M. Roddy, D. Brone, A. Alexander, O. Sudah, An improved powder sampling tool, Pharmaceutical Technology (1999) 92–110. [23] G. Vergote, T. De Beer, C. Vervaet, J. Remon, W. Baeyens, N. Diericx, F. Verpoort, In-line monitoring of a pharmaceutical blending process using FT-Raman spectroscopy, European Journal of Pharmaceutical Sciences 21 (2004) 479–485. [24] K. Lim, V. Gururajan, P. Agarwal, Mixing of homogeneous solids in bubbling fluidized beds: theoretical modelling and experimental investigation using digital image analysis, Chemical Engineering Science 48 (1993) 2251–2265. [25] G. Leonard, F. Bertrand, J. Chaouki, P. Gosselin, An experimental investigation of effusivity as an indicator of powder blend uniformity, Powder Technology 181 (2008) 149–159. [26] C. Lai, D. Holt, J. Leung, C. Cooney, G. Raju, P. Hansen, Real time and noninvasive monitoring of dry powder blend homogeneity, AIChE Journal 47 (2001) 2618–2622. [27] J. Staniforth, S. Iveson, An investigation of the use of UV fluorescence microscopy as a method for quantifying the homogeneity of powder mixes, International Journal of Pharmaceutics 31 (1986) 145–150. [28] S. Sekulic, J. Wakeman, P. Doherty, P. Hailey, Automated system for the on-line monitoring of powder blending processes using near-infrared spectroscopy. Part II. Qualitative approaches to blend evaluation, Journal of Pharmaceutical and Biomedical Analysis 17 (1998) 1285–1309. [29] A. Patel, P. Luner, M. Kemper, Quantitative analysis of polymorphs in binary and multi-component powder mixtures by near-infrared reflectance spectroscopy, International Journal of Pharmaceutics 206 (2000) 63–74. [30] C. Ufret, K. Morris, Modeling of powder blending using on-line nearinfrared measurements, Drug Development and Industrial Pharmacy 27 (2001) 719–721. [31] B. Chaudhuri, A. Alexander, A. Faqih, F. Muzzio, C. Davies, M. Tomassone, Avalanching flow of cohesive powders, Powder Technology 164 (2006) 13–21. [32] A. Faqih, B. Chaudhuri, A. Alexander, S. Hammond, F. Muzzio, M. Tomassone, Dilation effects of cohesive granular material in a rotating drum: experiments and simulations, AICHE Journal 52 (2006) 4124–4132. [33] T. Shinbrot, A. Alexander, F. Muzzio, Spontaneous chaotic granular mixing, Nature 397 (1999) 675–678. [34] B. Chaudhuri, A. Mehrotra, F. Muzzio, M. Tomassone, Cohesive effects in powder mixing in a tumbling blender, Powder Technology 165 (2006) 105–114.