Investigation of an intensifier-bar tumble bin scale-up model

    Investigation of an intensifier-bar tumble bin scale-up model Aaron Zettler PII: DOI: Reference:

S0032-5910(16)30648-9 doi:10.1016/j.powtec.2016.09.064 PTEC 11974

To appear in:

Powder Technology

Received date: Revised date: Accepted date:

30 March 2016 13 September 2016 26 September 2016

Please cite this article as: Aaron Zettler, Investigation of an intensifier-bar tumble bin scale-up model, Powder Technology (2016), doi:10.1016/j.powtec.2016.09.064

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Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model

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Aaron Zettler

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1-317-276-3076

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Eli Lilly and Company

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Abstract

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In recent years, more and more powder blending operations have been augmented with the addition of an intensifier bar (I-bar) in a tumble bin. While the tumble bin rotates with rotational speeds of 5-20 RPM, I-bars rotate at 1000-4000 RPM, with tip speeds of ~1419 m/s. I-bars thus impart significant mechanical dispersive energy into the blend, both in terms of shear stress and in terms of shear strain.

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Because I-bars impart so much energy into the blend, it is critically important to devise a good scale-up strategy, thus ensuring that blending conditions that have been established at a small scale can be reliably reproduced at a large scale. In this work, the blending process is described using a first order rate constant, k, to describe the fraction of powder that has been processed by the I-bar. A mathematical model is derived to predict how k changes when scaling to a larger tumble bin with a larger I-bar running at a different tipspeed. The model indicates that the quantity vLD2/V4/3 largely determines the blending rate during scale-up where v, L, D, and V, denote the I-bar tip speed, I-bar length, I-bar diameter, and tumble bin volume, respectively. To keep the extent of blending constant between two scales, we find that the dimensionless number vLD2t/V4/3 should be held constant where t is the blending time.

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Experimental data are summarized and used to assess the validity of the scale-up model.

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A novel characterization method involving tracer particles and X-ray image analysis was

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developed and used to quantify the extent of mixing. Experimental data are provided from 59 blends, covering a range of tumble bin scales from 8 L to 700 L, and producing 296 samples that were analyzed by X-ray imaging. The data show that the process can be reasonably approximated by a first order rate equation, with the rate constant being linearly proportional to vLD2/V4/3.

Keywords: powders; scale-up; Intensifier bar; blending; model; agglomerates

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1 Introduction

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Tumble bin blending has been used extensively in various industries to mix powders (e.g.

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pharmaceuticals) and slurries (e.g. cement) by tumbling materials inside a rotating container or ‘bin’. In the pharmaceutical industry, the bin shape often resembles a

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pyramidal cone stacked on top of a rectangular prism as shown schematically in Figure 1. The tumble bin is typically rotated between 5-20 revolutions per minute (RPM) about an

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axis that is angled to the walls of the bin (e.g. by 60° as shown in Figure 1, Top View). The angled axis is considered to reduce the probability of ‘dead zones’ where powders do

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for example the hopper of a tablet press.

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not mix. The conical section of the bin facilitates emptying of the bin after blending into

The high speed intensifier bar (I-bar), when used, is generally centered along the

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rotational axis of the bin, as represented by the dashed-line cylinder in Figure 1, Oblique View. The coincidence of the I-bar rotational axis with the tumble bin rotational axis allows for the use of a single blender base and mechanical connection to independently operate both the bin and the I-bar. The geometry of the I-bar is illustrated in Figure 2. The I-bar may contain one or more sets of tines (Figure 2 displays a bar with two sets of tines), which rotate with tip speeds as high as ~19 m/s to effectively mix powders and eliminate any agglomerated materials. Thus, I-bar blending can be particularly beneficial when one or more components are highly cohesive, agglomerated and/or exist in a low concentration. The bin and I-bar dimensions called out in Figure 1 and Figure 2 are discussed in later sections.

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The goal of blending is always to produce a spatially random mixture. In process

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development, early evaluations often require material sparing design, and studies are conducted in small mixing vessels. When the process is scaled up, new blending

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parameters must be determined for the larger scale, and having a quantitative scale-up model to achieve a comparable blending endpoint to studies conducted at small scale is

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extremely useful.

Tumble bin blending without an I-bar is well studied and provides a framework for

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scaling of tumble bin blending parameters. Wang et al. [1] describe the various mechanisms occurring during tumble bin mixing and provide calculus for bin speed

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scale-up. The authors describe the importance of maintaining geometric, kinematic and

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dynamic similarity in scale-up. They apply Buckingham’s theorem to derive the Froude Number and other dimensionless numbers as being relevant to tumble bin blending.

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However, the analysis is limited to tumble bin systems without I-bar agitation. Bridgwater [2] expands on this and covers the various powder mixing mechanisms of diffusion, convection and shear. This reference provides insight in design consideration and mixing equipment selection as it relates to scaling. Muzzio et al. [3], provide general guidance as it relates to blending scale-up strategies depending on powder flow characteristics. Heuristic approaches are provided with respect to free-flowing, cohesive and agglomerated mixtures. A more in-depth analysis of cohesive effects is conducted by Chaudhuri et al. [4] using computational modeling of a binary system to demonstrate that more cohesive mixtures benefit from the increased energy of higher rotational speeds. Each of these resources provides insight into various blending and scale-up strategies; however provide no guidance for scaling of an I-bar system.

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Some authors have considered the impact of powder fill level on blending endpoint.

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Sudah et al. [5] use a first-order mixing model to evaluate the effect of bin fill level as

well as various baffle configurations to characterize relative blending homogeneity and

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identify an optimum bin fill level for diffusive blending. Additionally the impact of fill level for diffusive blending as it relates to lubrication is also supported in the work of

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Kushner et al. [6]. These resources provide insight into importance of blending vessel powder fill level; however provide no guidance for scaling of an I-bar system.

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Computational modeling could be considered in modeling an I-bar system. Sato et al. [7] conduct numerical simulations using three-dimensional discrete element method (DEM).

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The studies provide insight in particle behavior in a granulator, but the DEM approach

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requires advanced computational analysis in order to model that behavior, and the selection of appropriate inter-particle forces is a challenge. For I-bar modeling a different

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approach will need to be applied.

Given that I-bar agitation incorporates a higher energy mix than diffusion alone, studying other higher energy blending processes may provide insight. Chirkot [8] develops a scaling model using similar I-bar equipment within a V-blender and emphasizes the relevance of I-bar swept area in scaling. However, the scope was low shear wet granulation which provides limited insight to high speed, dry powder blending. Other high energy systems have been modeled using a dimensionless power number correlation [9, 10, 11, 12, 13]. However, in each of these cases, the blending system consisted of a stationary container which was considerably different from that of the I-bar equipped tumble bin.

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In line with this approach, Patterson-Kelley (PK), a forerunner in I-bar technology

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development, has provided a scaling model [14] based on the normalized power

consumption at the two scales, based on the specific configurations of the equipment

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being used. The PK model has been successfully used for scaling, however is a minimally studied heuristic model and is limited to scaling of two systems with equal powder fill

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levels and I-bar tip speeds.

Michaels [15] discusses the differences between approaches for powders and fluids, and

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suggests bridging the gap. Michaels also makes comparisons to various chemical reactors, and suggests potential application of the continuous ideal stirred tank reactor

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(CISTR) model to powder systems. In this work, the basic assumptions of the CISTR

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model are successfully used to describe the kinetics of I-bar tumble bin blending. The objectives of this study are to document a mathematical model that has been

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developed to estimate both blending kinetics and scaling relations for I-bar blending processes. The model is expected to apply generally to powder blenders containing a high-speed agitator within a rotating bin operated under such a condition that the agitator imparts a large majority of mixing energy into the system. The model is demonstrated to apply across a range of powder compositions and blending scales, for the tumble bin and I-bar geometries described in Figures 1 and 2.

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2.1 Preliminary Observations

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2 Methods and Materials

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The dispersion behavior of the powdered colorant Red Iron Oxide (RIO) was studied visually during the course of development of a low-dose pharmaceutical compound.

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SEM images of the RIO are shown in Figure 3. The figure shows that the RIO powder contained large agglomerates, several hundred microns in size. The agglomerates were composed of many small (sub-micron sized) primary particles of Fe2O3. Particle size

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analysis was also performed on two different lots of RIO and at various dispersion

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pressures using a Malvern Mastersizer 2000 with Srirocco dry dispersion accessory. Results are shown in Table 1. The data show that at low pressures, the d90 values (the

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90th percentile of particle diameters) correspond approximately to the size of the agglomerates, but at high pressures, the d90’s are substantially smaller than the agglomerates. These results suggest that the agglomerates are broken or dispersed at higher pressures before reaching the detector of the particle size analyzer. The RIO dispersion behavior was also examined by adding RIO to a powder and blending. Example images are shown in Figure 3. The RIO shown at the top of Figure 3 was added at a low level (1 wt%) to a starch-based formulation and initially tumbled without engaing the I-bar. After 1 minute of tumbling (I-bar turned off), RIO agglomerates were visually observed in the blend, and the bulk of the powder remained substantially white in appearance. In similar experiments the bin was tumbled for as long as 15 minutes with similar results (white powder, visible agglomerates). However, after Page 7 of 76

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turning on the I-bar and tumbling for only 3 minutes, the bulk powder became red in

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color and agglomerates were no longer visible, as shown at the bottom of Figure 3. The results in Figure 3 suggested that the I-bar was effective in breaking the RIO

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agglomerates down to smaller (e.g. primary) particles, while tumbling alone did not. The combined actions of the tumble bin and I-bar simultaneously broke agglomerates and

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dispersed RIO throughout the blend to create a uniformly red powder.

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The observed behavior in Figure 4 provided a mechanism to measure the extent of blending by monitoring the disappearance of RIO agglomerates within the blend. Theoretically once all of the powders have passed through the I-bar, no agglomerates

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the disappearance of RIO agglomerates.

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should remain. X-ray Micro-Computed Tomography (XMCT) was employed to monitor

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2.2 X-Ray Micro Computed Tomography

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The mathematical model and experiments described in this study extensively leverage Xray micro computed tomography (XMCT) analysis methods and agglomerated red iron

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oxide (RIO) tracer particles incorporated in powder blends.

XMCT is a 3D imaging technique in which many X-ray images of a sample are captured

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with the sample being rotated a small amount (e.g. ~1 degree) between each image. A computer algorithm is then executed to infer a 3D structure that would result in the

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captured images. XMCT has many possible uses and has been used recently, for example,

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by Crean et al. [16] to explore the grain structure of pharmaceutical granules. A critical feature of RIO in this study is that it contains iron (Fe). Fe has a high atomic

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number and associated high X-ray absorption coefficient in comparison with most pharmaceutical powders which are composed largely of C, O, and N. This provides high contrast in X-ray images of RIO agglomerates in pharmaceutical powder blends. The high-contrast images permit reconstruction of 3D XMCT models as shown in Figure 5. The figure shows large (white) RIO agglomerates dispersed within a ~10 g sample of starch-based placebo powder. The image resolution is ~5 microns. RIO particles smaller than 5 microns contribute to the background X-ray absorption of the blend, but they do not otherwise appear in the image. Only large agglomerates are visible. An advantage of the XMCT modeling software is that it can be used to categorize the grayscale image voxels (3D pixels) in Figure 5 as being either ‘RIO’ or ‘Not RIO’ based on their grayscale level above an assigned threshold value. Once RIO voxels are Page 9 of 76

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categorized, the software can both integrate the agglomerate volumes and count the

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number of agglomerates within a sample. An edge effect occurs in the analysis for voxels at the surface of an agglomerate. These voxels contain both RIO and placebo powders

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and produce an intermediate grayscale level that is difficult to categorize reliably.

An analyzed data set is provided in Figure 6. Agglomerate sizes are expressed by their

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volume-equivalent spherical radius (i.e. radius of a sphere that would have the same volume). Agglomerate counts were divided by the sample volume to determine

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agglomerate concentrations (particles per gram). Four samples were collected from the tumble bin and analyzed to produce the chart in Figure 6. Samples were analyzed after 5,

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10, 15 and 20 tumble bin rotations with the I-bar engaged. The data show a reduction of

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RIO agglomerates with additional I-bar blending. The data thus indicate that the I-bar is effective in disintegrating agglomerates into smaller particles. Agglomerates smaller than

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50 microns were not analyzed in order to minimize the impact edge effects. The data in Figure 6 suggest a physical interpretation of the blending process as illustrated in Figure 7. As the tumble bin rotates (large circular arrow), a portion of powder falls into contact with the I-bar. The I-bar, having tip speeds of ~14 m/s or higher, impacts the RIO agglomerates causing mechanical disintegration. The disintegrated RIO, along with other excipient powders is propelled into the headspace of the tumble bin and then falls onto the cascading surface of the mixing layer (Figure 7). It is at this interface where the agglomerate-free powders are reincorporated into the blend as the tumble bin continues to rotate. Since the RIO exists at a low concentration, once the agglomerates are dispersed they do not re-form. The process can be modeled as an ideal mixing model where agglomerate-free powders would ideally be distributed Page 10 of 76

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instantly and uniformly throughout the entire blend (i.e. not just within the mixing layer),

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thus serving to reduce the overall agglomerate concentration in the bin.

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2.3 The Ideal Mixing Model

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Ideal mixing processes are well understood and are easily modeled mathematically. The

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fundamental tenet of ideal mixing as applied to I-bar blending is that the rate of

agglomerate disintegration (dc/dt) is proportional to the concentration, c, of RIO

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agglomerates being fed into the I-bar. Mathematically, this may be expressed as

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Equation 1: dc = − kc dt

where c denotes agglomerate concentration (particles per gram, Figure 6), t denotes time, and k denotes a mixing rate constant. The minus sign is included to indicate that

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agglomerates are reduced over time when k is a positive constant. Larger rate constants

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Equation 2: c ln = − kt co

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thus indicate faster de-agglomeration. Integration of Equation 1 yields:

where co, denotes the initial agglomerate concentration before the I-bar is engaged. The validity of Equation 2 can be probed experimentally by measuring the concentration of agglomerates as a function of time and then constructing a plot of ln(c/co) versus t and assessing linearity.

Preliminary experiments were conducted to determine the validity of Equation 2 at two different I-bar speeds. Results are shown in Figure 8 for both high speed (circles, 3477 rpm) and low speed (squares, 2000 rpm) conditions. The value of co was determined by initially diffusive blending RIO agglomerates into the blend with the I-bar turned off for a fixed duration. This provided a uniform dispersion of agglomerates to be considered as

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time point 0. The blend was then sampled and evaluated by XMCT. In relation to Figure

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6, agglomerates were counted if they were larger than 200 microns. The 200 micron limit was imposed because agglomerates larger than 200 microns could be measured both by

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the XMCT system and by a larger-scale X-ray radiography apparatus, providing analysis of much larger sample sizes (~1 kg) and correspondingly low agglomerate concentrations

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as indicated by the red data point in Figure 8. The use of tracer particles and radiography thus allowed accurate assessment of agglomerate concentrations over 8 natural log units

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(nearly 4 orders of magnitude). This novel technique was enormously beneficial over other analytical techniques such as near-infrared spectroscopy, colorimetry, etc. in which

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concentrations may only be possible over 1-2 orders of magnitude.

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Two critical conclusions can be drawn from Figure 8. First, the data are highly linear on a logarithmic scale. This linearity supports the application of the ideal mixing model to the

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case of I-bar blending. A plug-flow type model for example, would be non-linear in Figure 8. Second, the I-bar speed (predictably) affects the blending rate constant, which is determined from the negative of the slope. Faster I-bar speeds provided faster mixing (k = 3.32 min-1) in relation to slower I-bar speeds (k = 0.73 min-1).

2.4 Scale-up of Mixing Kinetics 2.4.1 The Scale-Up Model The data in Figure 8 indicate that I-bar speed affects k, the mixing rate constant. Higher speeds provide faster mixing as indicated by the steeper blue curve. In addition to the speed effect, a larger I-bar is expected to process the powders faster, resulting in a higher Page 13 of 76

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rate constant. Inversely, a larger blend volume would require more time to process,

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resulting in a lower rate constant. With these scaling relations in mind, a scale-up model was considered in the form: vLD V

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k∝

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where v, L, D, and V denote the I-bar tip speed, I-bar length (length of the cylindrical volume swept by the I-bar), I-bar diameter (tine tip-to-tip), and bin volume, respectively.

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L and D are defined in Figure 2(note that L includes the total length of both sets of I-bar

tines). The scale-up model is derived in the next section.

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2.4.2 Derivation

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The ideal mixing model of Equation 2 describes a conceptual process where the I-bar acts as a pump, pulling in powder and distributing it throughout the blend. The rate constant,

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k, is proportional to the volumetric throughput of the ‘pump’. In this work we provide an

estimate of the volumetric flow rate imposed by the I-bar. The model is based on the schematic image in Figure 9.

According to the schematic, the volumetric flow rate of powder through the I-bar is given by: Equation 3: &

Vej = vLu where Vej denotes the volumetric flow rate associated with the indicated path (Figure 9) of ejected powder, v denotes the I-bar tip speed and other dimensions are as shown. The thickness, u, defines an I-bar “interaction zone”, where powder is close enough to the Ibar tine tips to be effectively blended (agglomerates disintegrated). While an exact value Page 14 of 76

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of u is not estimated, it is thought that u may relate to powder flow properties and would

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be constant for a fixed powder composition.

Equation 3 estimates the powder ejection rate associated with a point along the circular

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path of the I-bar tines. Powder would similarly be ejected along all points of interaction along the circumference of the cylindrical volume. As a result, the integrated volume

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ejection rate is proportional to the circumference, and hence to D as follows: Equation 4: &

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V total ∝ vLD

Note that the constant, u, has been removed and the equals sign has been converted to a

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proportionality sign. Equation 4 gives an estimate of the volumetric flow rate of the I-bar

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when considered as a pump. Since the rate constant, k, is expressed in relation to a powder concentration or number of agglomerates per gram, the total volumetric flow rate

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must also be normalized to the volume of powder in the tumble bin in order to provide an estimate of k. The result is given in Equation 5. Equation 5: &

V total vLD k∝ = V V

where V denotes the tumble bin volume.

2.4.3 Correction for Tumble Bin Fill Level The effects of tumble bin fill volume (i.e. the volume percentage of bin occupied by powder) are twofold. Increasing the fill volume means more powder would need to be processed. This would manifest as an increase to the denominator of Equation 5. However, a higher fill volume would also cause the I-bar to be more fully submerged in

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the powder bed. Therefore material would be processed at a faster rate and this would

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manifest as an increase to the numerator of Equation 5.

The competing effects of tumble bin fill level can be modeled by considering the tumble

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bin geometry illustrated in Figure 1. The figure shows oblique, top, and axial views (with the axis of rotation pointing out of the plane of the page) of the tumble bin. Note that the

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axis of rotation of the tumble bin coincides with the axis of rotation of the I-bar. Relevant bin dimensions a (bin length), b (bin width), c (diagonal length wall-to-wall along axis of

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I-bar), hr (height of rectangular top section of bin) and hp (height of pyramidal bottom section of bin) are also defined. The figure also shows what a powder bed (gray) may

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look like as the tumble bin rotates through two orientations: Orientation 1 and Orientation

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2. The distance ∆x indicates how the bed height might change if additional powder were added to the tumble bin. Finally, the figure also depicts the impact of ∆x on the arc

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length, s, of the submerged portion of the I-bar. For the tumble bins used in this study, the I-bars were approximately centered at 50% fill level of the bins. Thus the I-bar is 50% submerged when the bin is 50% filled with powder. The distance ∆x may be related to the extent that the tumble bin is filled as follows:

Equation 6: x • A = ( ff − 0.5 ) • V where A, ff, and V denote the area of the powder bed surface, fractional fill volume of the tumble bin, and the total volume of the tumble bin, respectively. Note that ∆x=0 when ff=0.5 as expected because the I-bar is 50% submerged (∆x=0) when the bin is 50% filled

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the powder bed surface area, A, changes continuously as the tumble bin rotates. In

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Orientation 1, A=a·b, while in Orientation 2, A is given by: Equation 7:

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hp  1 2a  A = c • hr + c • hp =  hr +  2 2 3

where all bin dimensions are defined above. For simplicity in this work, the average ¯

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value A was approximated by the linear average from Orientations 1 and 2:

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Equation 8: ¯ hp  a 2h A = b + r +  2 3 3 ¯

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This value of A was used to estimate the average distance x when integrated through a complete tumble bin rotation.

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The distance ∆x also impacts the arc length, s, of the submerged portion of the I-bar as

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shown in . The average fractional arc length, f, represents the fraction of the total I-bar

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that is submerged in the powder and is considered as the relevant parameter impacting the mixing rate. The average fractional arc length can be determined from: Equation 9:

¯ ¯   2•s 1 − 1  −2 • x  f = = cos  D  π •D π  

¯

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Replacing ∆x and A in Equation 6 with their averaged counterparts, x and A , and inserting the result into Equation 9 yields an estimate for f as a function of ff: Equation 10:  −2 • V  1 f = cos −1  ff − 0.5 )  ¯ (   π  D• A  Various tumble bins with I-bar capabilities were utilized in this study and their relevant ¯

bin dimensions are summarized in Table 2. Calculated values of A for use in Equation 10 are also tabulated in Table 2.

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As previously stated, the fill volume, ff, is expected to be inversely proportional to the

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mixing rate because as ff increases, more powder must be processed. However, the

mixing rate is expected to be linearly proportional to the fraction of the I-bar, f that is

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submerged in the powder bed. Thus, a correction for tumble bin fill level can be applied

k∝

vLD f • V ff

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Equation 11:

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by multiplying Equation 5 by f/ff as follows:

In this work, the validity of the mixing model was examined both with and without the

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2.4.4 Assumptions

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correction for f/ff.

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In the derivation of Equation 11, a few assumptions are made as follows: 1) It is assumed that the tumble bin is operated at a fill level range in which the I-bar is at least partially submerged in the powder bed, and that the tumble bin continues to rotate at a reasonable rate to ensure an active mixing layer is maintained.

2) For agglomerate removal purposes, it is assumed that the I-bar tip speed is sufficiently fast to cause disintegration upon impact with agglomerates. 3) For scale-up calculations, it is assumed that any compression of powders at the bottom of a tumble bin does not appreciably alter u in Equation 3 at the different scales. 4) Powder bulk density does not change during blending.

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2.5 Study Design

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The analysis performed in relation to Figure 8 was repeated at varying tumble bin scales for a total of 59 blends. For each blend, four or more blend samples were collected at different time points and analyzed to determine the number of remaining agglomerates per gram; 296 samples were analyzed in total. A linear regression was performed for each blend and the rate constants were extracted from the slopes. The 59 rate constants were vLD f vLD evaluated against the quantities and • to assess the validity of the scale-up V ff V models, Equation 5 and Equation 11.

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The study design is shown in Table 3. Data were collected from tumble bins ranging in size from 8 L to 700 L. I-bar tip speeds ranged from 13.9 to 19.5 m/s, and the quantity vLD varied between 1.57 and 15.2 s-1. In addition to the scale and tip speed variations, V the formula composition was also varied. The Formulation Types are further defined in Table 4. In most cases, a starch with silicone formula was used, but the starch grade varied between Spress B820, Starch 1500 and Lycatab C. In two batches a typical roller compaction formulation was used containing Microcrystalline Cellulose and Mannitol.

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2.6 Materials

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The batch formulas for each Formulation Type are given in Table 4. Characteristics of

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the RIO tracer particles were discussed previously (Figure 3, Figure 4, and Table 1). Full characterization was not practical to perform on each of the other excipients since the

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study spanned many lots of most powders. However, nominal particle sizes and other characteristics are available online for most of these powders, which are common to the

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pharmaceutical industry.

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2.7 Method of Manufacture

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The tumble bins and I-bars used in this study have already been described (Figure 1,

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Figure 2, and Table 2). Raw materials were layered into the I-bar equipped tumble bin such that RIO was sandwiched between other powders. Powders were tumbled for 10

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minutes to achieve a uniform dispersion of agglomerates within the powder, and a sample was collected to serve as time point 0. The I-bar was then powered on and the powders

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were blended as specified in Table 3. No attempt was made to assess the spatial uniformity of agglomerates within each blend because the study was designed to

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determine large agglomerate concentration changes over time (i.e. ~4 orders of

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magnitude). These changes far exceeded the expected impacts of spatial uniformity. A single sample was hand scooped from the top of the bin at each blend time. Agglomerate

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concentrations were calculated as the number of agglomerates divided by the sample size. Statistical measurement error was expected to be lower when the number of agglomerates was higher, based on an assumption of Poisson counting statistics.

2.8 X-ray Imaging Methods

Two different X-ray image analysis techniques were used to evaluate samples for this study. X-ray micro-computed tomography (XMCT) was used to analyze small samples (e.g. 10 g) collected at early time points, where a relatively large concentration of agglomerates could be counted (e.g. at least 10 in a 10 g sample). Larger samples (up to 1.4 kg) were collected at later time points, where relatively low concentrations of agglomerates could be determined using X-ray film. Each sample size was selected to provide a sufficient number of agglomerates in the sample to limit measurement error and Page 21 of 76

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to ensure that the concentration in the sample was low enough that agglomerates could be

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manually counted. The total volume of all samples was negligible with respect to the total

2.8.1 X-ray Micro-Computed Tomography

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blend volume.

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The Skyscan 1172 was used to collect 3D reconstructed images of RIO agglomerates inside powder blend samples with ~5 µm spatial resolution [17]. Samples were analyzed

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by placing approximately 10 g of powder into a small plastic 1 oz container. X-ray images were collected every 0.7° of sample rotation for a total of 180° per sample. Since

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the 3D image reconstructions are gray-scale in nature, a threshold was chosen such that

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voxels (3D pixels) darker than the threshold were considered to be part of an RIO agglomerate. The gray-scale thresholds were chosen such that blends that contained no

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red iron oxide resulted in X-ray images with no detected particles [18]. For consistency with the X-ray film technique, only agglomerates larger than 200 µm were counted.

2.8.2 X-ray Film Inspection

The large blend samples were analyzed using an X-ray radiography technique. Samples of up to 1.4 kg were spread out into a 1-2 cm thick layer on top of X-ray film and exposed. Each X-ray film was then visually inspected under a microscope and the number of agglomerates was manually counted. The minimum agglomerate size that could be reliably identified was 200 µm. Below this limit, the image contrast between agglomerates (black) and background powder (white) was too insignificant to reliably detect agglomerates.

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3.1 X-ray Results

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3 Results and Discussion

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The XMCT and X-ray film results for all sample time points are given in Appendix A. The number of agglomerates in each sample was divided by the sample weight to

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determine the concentration, c, at each time point. The time zero concentration was selected as co and the quantity ln(c/co) was calculated at each time point (also listed in

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Appendix A). In some cases, no agglomerates were measured in the sample and ln(c/co) could therefore not be calculated. The results are plotted in Figure 10. The figure

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indicates high linearity for many of the batches and some positive curvature for several of

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the batches. It is important to note that since the number of agglomerates was generally different for each sample (Table 5), the expected measurement error was also different

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for each data point in Figure 10. Assuming a Poisson distribution the expected error for each sample was 1/sqrt(n).

The curvature of profiles in Figure 10 may be attributed to a distribution of agglomerate strengths where weaker agglomerates disintegrate in close proximity to the I-bar, but stronger agglomerates must come into contact with the I-bar. The stronger agglomerates would be expected to persist over longer periods than indicated by the early time points in Figure 10. To evaluate this hypothesis, an analysis was performed to assess the curvature in relation to the lot number of the RIO agglomerates that were used. Each curve in Figure 10 was fitted with a 2nd order polynomial of the form:

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C  ln   = α + βt + γt 2  C0 

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where the quadratic term γ is an indicator of the overall curvature in the data. The γ

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values from each regression are plotted against RIO lot number in Figure 11 (note that the data points are artificially spread horizontally in order to show each point, but the

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vertical placement is exact). Two lots of RIO were used in the manufacture of all 59 batches. Results indicate that lot number A620090 produced more highly curved profiles

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in general than did lot number A306582. While this does not completely confirm the hypothesis that agglomerate strength values may impact the curvature, it does lend credence to the argument and shows that the two lots behaved differently in terms of

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agglomerate disintegration.

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3.2 Rate Constant Analysis

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For the purposes of assessing the scale-up model, linear regressions (not polynomial

regressions) were used to estimate the overall rate constants, k. Results are displayed in

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Figure 10 and are tabulated in Table 5. Note that the rate constant, k is the negative of the slope value. The best and worst squared correlation coefficients were 0.9993 (Lot M and

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Lot S) and 0.7105 (Lot AN), respectively. A frequency distribution of squared correlation coefficients is presented in Figure 12. The figure shows that of the 59 total batches, 58

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3.3 Scale-up Model Analysis

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were characterized by R2>0.8 and 39 batches were characterized by R2>0.9.

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Validity of the scale-up model is evaluated in Figure 13 which indicates measured k– values as a function of vLD/V. The color, size, and shape of each data point indicate the Ibar diameter, the bin load, and the formulation, respectively. The data labels indicate the lot number, which can be cross-referenced with data in Tables 3 and 5 and with the kinetic profiles in Figure 10.

The data in Figure 13 are roughly linear. The linearity holds despite enormous variations in tumble bin volume (15-700 L), bin speed (8.2-19.9 rpm) bin load (43-72%), I-bar diameter (9.7-27.9 cm), and I-bar tip speed (14.9-19.5 m/s). The data thus support a scale-up model prediction that blending rate is controlled by the quantity vLD/V. A nuance is apparent for RC Formulation II. The square data points (RC formulation II) are linear, but fall on a different trend line than other data in the plot. The squares are

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characterized by both higher rate constants and higher sensitivity to vLD/V (steepness of

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the curve). This result suggests that formula composition affects the survival rate of RIO agglomerates. RC Formulation II resulted in relatively fast disintegration of

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agglomerates. The data are trellised by formulation type in Figure 14 (data for ODT

Formulation and RC Formulation I are removed since there are only two or fewer data

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different formulas deagglomerate at different rates.

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points). The data show greater linearity within a given formulation type suggesting that

3.3.1 Correction for Tumble Bin Fill Level

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Utility of the correction term f/ff is evaluated in Figure 15 which indicates measured k–

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values as a function of vLD/V*f/ff. As in Figure 13, the data are again linear and the same nuances apply. In fact, the correction for f/ff does not significantly affect the plot. This is

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an important observation because it suggests that fill level does not impact blending rate for the range of conditions studied. The finding has significant practical application. In practice, this implies that the bin fill level can be changed during scale-up without affecting the extent of blending. This allows for flexible batch sizes when a limited selection of tumble bin sizes is available. While evaluating the trends in Figure 13, it was considered that for a given tumble bin size, a larger I-bar may cause greater overall fluidization of powder within the tumble bin. This may be expected to increase the blending rate, k. For example, in the limit of a very large I-bar in a very small bin, the entire bin may become fluidized, thus allowing all powders to pass through the I-bar at a faster rate. To test this hypothesis the quantity vLD/V was multiplied by the dimensionless ratio of I-bar diameter to a characteristic

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dimension of the tumble bin, V1/3 and analyzed as shown in Figure 16 and Figure 17. Both figures show a significant improvement in linearity with incorporation of the

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fluidization term D/V1/3. For example the R2 value increases from 0.76 to 0.83 for the

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linear curve fits in Figure 13 and Figure 16, respectively. While this is not sufficient

evidence to validate the hypothesis, inclusion of the fluidization term does improve the

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quality of the fit to the available data.

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3.4 Scale-up Analysis

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The utility of the scale up parameter is qualitatively illustrated in Figure 18. The figure

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shows agglomerate concentrations, trellised by formulation type, plotted against (a) the blend time and (b) the recommended dimensionless scale-up parameter, vLD2t/V4/3.

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While the kinetic profiles in Figure 18(a) are scattered and are strongly affected by blender volume, tip speed, etc., the profiles in Figure 18(b) are clustered more tightly. The improvement is most prominent for the Starch 1500 blends and least prominent for the Lycatab C formulations.

3.5 Scale-up Recommendations The authors recommend the following simple rules to scale-up an I-bar blending process that has been developed for a given blend/formula at a small scale: 1) Match the I-bar tip speeds, v, as closely as possible at both scales. This ensures equal stresses are applied to powders at both scales. The model has been found to be relatively insensitive to tip speed variations between 14.9 m/s and 19.5 m/s, but

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larger variations may be provide different effects, especially at very low tip speeds.

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2) Match the quantity vLD2t/V4/3 at both scales. This ensures an equal extent of

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deagglomeration (i.e. equivalent agglomerate concentration and equivalent fraction of powder passing through the I-bar) is achieved at both scales. Matching

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vLD2t/V4/3 will typically involve selecting an appropriate blend time, t, since L, D,

and V are typically predetermined at the intended large scale.

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Scale-up calculations are illustrated in Table 6 for the case where blending conditions have been determined at an 8 L scale and I-bar RPM settings and blending times are

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required in larger bins equipped with I-bars of various sizes. The new RPM and blend

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time are expressed as multiples of the values R and t, determined at the 8 L scale.

4 Conclusion

Results were presented to suggest a robust scale-up strategy for I-bar blending unit operations using the dimensionless number, vLD2t/V4/3. A new technique was developed using RIO agglomerates as tracer particles combined with XMCT analysis to measure the extent of deagglomeration over time as an indicator of the fraction of powder that has passed through the I-bar. The model suggests that the dimensionless number vLD2t/V4/3 determines the extent of deagglomeration imparted by the I-bar. Fill level and tumble bin rpm did not impact deagglomeration rate over the ranges studied. Unit formula had a significant impact on the deagglomeration rate. To ensure the same extent of Page 29 of 76

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deagglomeration between two scales, the quantity vLD2t/V4/3 should be held constant. If

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the extent of deagglomeration is maintained between two scales it is expected that the extent of blending would also be maintained between the two scales although blend

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uniformity was not verified/analyzed in this study.

5 Acknowledgments

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The authors would like to acknowledge the many useful conversations and assistance with data gathering activities from Karis Waibel, John Chlapik, and Craig Kemp at Eli

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Lilly and Company.

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6 Appendix A: Particle Counts – Time Series Data

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The XMCT and X-ray film results for all sample time points and agglomerates > 200 µm

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NU

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in size are given in Table 7.

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7 References

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Graphical abstract

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Figure 1:

Tumble Bin Geometry

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Schematic I-bar with two sets of tines.

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Figure 2:

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Figure 3: SEM Images of Red Iron Oxide lot A620090

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1 Minute I-bar Off

3 Minutes I-bar On Figure 4: RIO agglomerates survive 1 min diffusive blend process but are visually dispersed after 3 min of I-bar blending.

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Figure 5:

3D view of RIO agglomerates (white) in a placebo background (dark). The ~10 g sample is contained in a plastic cup.

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Figure 6:

RIO agglomerate concentrations as a function of size (equivalent spherical radius, in µm) and as a function of II-bar equipped tumble bin rotations.

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Figure 7:

Physical interpretation of the I-bar blending process.

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Figure 8: Preliminary experimental data indicating validity of the ideal mixing model to describe I-bar bar blending.

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Figure 9: Schematic of the cylindrical volume that is swept by the I-bar and relation to the volumetric throughput.

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Figure 10: Relative agglomerate concentrations versus I-bar I bar blending time. Blue data points indicate small samples (<10 g) measured by XMCT. Red data points indicate large samples (100 g – 1.4 kg) measured by the X-ray ray film technique.

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AC

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γ

RIO Lot Number Figure 11:

Curvature assessment in mixing model.

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Figure 12:

Frequency distribution of squared correlation coefficients.

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Figure 13:

Evaluation of the scale-up model. Page 45 of 76

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Figure 14:

Scale-up model data trellised by formulation type.

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Figure 15:

Evaluation of the scale-up scale model with tumble bin fill level corrections.

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Figure 16:

Scale Scale-up model compensated for overall fluidization of the blend.

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Figure 17:

Trellis view of the scale scale-up model with fluidization compensation.

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Figure 18: Agglomerate concentrations plotted against the blending time (top) and the recommended scale-up scale parameter (bottom).

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A620090

d50 (um)

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d10 (um)

20.1 0.5 0.4 0.4 0.4 13.2 0.8 0.4 0.4 0.4

D

A306582

Dispersion Pressure (Bar) 0 1 2 3 4 0 1 2 3 4

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Lot Number

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Table 1: Malvern Particle Size Results for Red Iron Oxide Lots

55.0 11.3 0.6 0.7 0.7 29.2 6.5 1.8 1.2 1.2

d90 (um)

449.0 584.6 5.0 5.1 5.6 155.1 13.9 8.9 8.1 6.0

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¯

D (in)

L (in)

I-bar Centerline Fill Position(%)

a (in)

b (in)

25.1

6.6

4.6

53.6

20.6

B

15

9.7

10.9

51.1

25.4

C

15

9.7

10.9

48.7

25.4

D

30

9.7

10.7

50.4

38.1

E

30

9.7

10.9

51.1

F

60

21.6

17.3

52.4

G

60

21.6

22.9

H

90

21.6

I

120

J

hp (in)

¯

A (in2)

10.9

17.3

490.3

30.2

14.2

22.1

754.8

30.2

13.2

21.6

735.5

32.0

16.5

26.2

1258.1

32.0

38.4

17.5

24.1

1161.3

39.1

47.0

20.8

29.2

1722.6

52.0

39.6

47.8

21.3

32.5

1806.4

17.3

51.7

44.7

53.6

23.4

38.6

2303.2

21.6

22.9

52.1

49.5

59.4

25.7

42.7

2819.3

170

21.6

22.9

52.1

55.9

66.8

30.7

49.5

3658.1

K

200

21.6

22.9

49.8

58.7

70.4

31.8

52.1

4019.3

L

227

21.6

22.9

52.2

61.2

73.4

34.3

50.8

4354.8

M

300

27.9

26.4

53.1

66.8

80.3

35.3

60.5

5212.9

N

300

27.9

26.4

50.2

66.8

80.3

34.3

56.9

5096.8

O

600

27.9

26.4

50.0

84.1

101.1

44.5

73.7

8200.0

P

700

27.9

26.4

50.1

87.9

105.4

47.0

77.5

8987.1

Q

700

27.9

26.4

50.3

87.9

105.4

47.0

77.5

8987.1

D

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A

hr (in)

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V (L)

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Bin ID

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Table 2: Tumble Bin Dimensions and Calculated Values of A

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Table 3: Experimental Design Bin Bin Size Load (L) (%)

15

Lot AX

C

Lot U

L (cm)

D (cm)

4.6

vLD/V (1/s)

f/ff

vLD/V*f/ff (1/s)

6.7

5.36 0.89

4.75

20.0

4000

13.93

60 Lycatab C

19.9

3826

19.46

10.9

9.7

13.74 1.09

15.04

15

60 Starch 1500

17.6

3670

18.67

10.9

9.7

13.18 1.03

13.58

B

15

60 Lycatab C

18.0

3477

17.69

10.9

9.7

12.49 1.09

13.67

Lot T

B

15

60 Lycatab C

16.2

3825

19.46

10.9

9.7

13.74 1.09

15.04

Lot R

B

15

60 Lycatab C

18.2

3477

17.69

10.9

9.7

12.49 1.09

13.67

Lot P

B

15

60 Lycatab C

18.2

3480

17.7

10.9

9.7

12.5 1.09

13.68

Lot O

B

15

60 Lycatab C

19.8

3130

15.92

10.9

9.7

11.24 1.09

12.31

Lot AV

C

15

50 Starch 1500

17.6

3670

18.67

10.9

9.7

13.18 0.97

12.80

Lot AT

C

15

60 Starch 1500

17.6

2942

14.97

10.9

9.7

10.57 1.03

10.89

Lot AP

C

15

50 Starch 1500

17.6

2942

14.97

10.9

9.7

10.57 0.97

10.26

Lot AZ

C

15

70 Starch 1500

17.6

3670

18.67

10.9

9.7

13.18 1.11

14.69

Lot S

B

15

60 Lycatab C

16.2

3130

15.92

10.9

9.7

11.24 1.09

12.31

Lot AR

C

15

70 Starch 1500

17.6

2942

14.97

10.9

9.7

10.57 1.11

11.78

Lot W

D

30

58 Lycatab C

15.4

3306

16.76

10.7

9.7

5.81 1.08

6.26

Lot AG

D

30

60 RC Formulation

15.4

3306

16.76

10.7

9.7

5.81 1.09

6.36

Lot AS

G

60

70 Starch 1500

14.0

1319

14.86

17.2

21.5

9.19 0.99

9.09

Lot X

F

60

58 Lycatab C

13.7

1483

16.76

23.0

21.6

13.83 0.96

13.33

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ODT Formulation

v (m/s)

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Lot Q

50

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Shell I-bar Speed speed (rpm) (rpm)

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A

AC

Lot V

Formulation Type

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Bin ID

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Lot Number

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Bin Bin Size Load (L) (%)

Formulation Type

Shell I-bar Speed speed (rpm) (rpm)

f/ff

vLD/V*f/ff (1/s)

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Bin ID

v (m/s)

L (cm)

D (cm)

23.0

vLD/V (1/s)

21.6

15.21 0.96

14.66

23.0

21.6

12.45 0.96

12.00

17.2

21.5

11.47 0.95

10.89

F

60

58 Lycatab C

13.7

1631

18.43

Lot Z

F

60

58 Lycatab C

13.7

1335

15.08

Lot AW

G

60

50 Starch 1500

14.0

1647

18.56

Lot BA

G

60

70 Starch 1500

14.0

1647

18.56

17.2

21.5

11.47 0.99

11.35

Lot AY

G

60

60 Starch 1500

14.0

1647

18.56

17.2

21.5

11.47 0.96

11.06

Lot AQ

G

60

50 Starch 1500

14.0

1319

14.86

17.2

21.5

9.19 0.95

8.72

Lot AU

G

60

50 Starch 1500

14.0

1319

14.86

17.2

21.5

9.19 0.95

8.72

Lot AA

I

120

57 Lycatab C

Lot F

J

170

55 Lycatab C

Lot L

J

170

65 Spress B820

Lot A

J

170

60 Spress B820

Lot B

J

170

65 Lycatab C

Lot C

J

170

Lot D

J

Lot E

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1483

16.76

23.0

21.6

6.91 0.98

6.81

13.2

1632

18.44

23.0

21.6

5.37 0.98

5.27

10.8

1334

15.07

23.0

21.6

4.39 1.06

4.65

12.0

1483

16.76

23.0

21.6

4.88 1.02

4.97

13.2

1334

15.07

23.0

21.6

4.39 1.06

4.65

55 Spress B820

10.8

1632

18.44

23.0

21.6

5.37 0.98

5.27

170

60 Lycatab C

12.0

1483

16.76

23.0

21.6

4.88 1.02

4.97

J

170

55 Spress B820

13.2

1334

15.07

23.0

21.6

4.39 0.98

4.31

Lot AI

J

170

60 Lycatab C

12.0

1483

16.76

23.0

21.6

4.88 1.02

4.97

Lot H

J

170

55 Lycatab C

10.8

1334

15.07

23.0

21.6

4.39 0.98

4.31

Lot I

J

170

65 Lycatab C

10.8

1632

18.44

23.0

21.6

5.37 1.06

5.68

Lot J

J

170

60 Spress B820

12.0

1483

16.76

23.0

21.6

4.88 1.02

4.97

Lot K

J

170

60 Lycatab C

12.0

1483

16.76

23.0

21.6

4.88 1.02

4.97

AC

CE

12.2

Page 54 of 76

ACCEPTED MANUSCRIPT

f/ff

vLD/V*f/ff (1/s)

RI

Shell I-bar Speed speed (rpm) (rpm)

v (m/s)

L (cm)

D (cm)

Lot M

J

170

43 Lycatab C

10.8

1334

15.07

23.0

21.6

4.39 0.86

3.79

Lot N

J

170

48 Lycatab C

10.8

1334

15.07

23.0

21.6

4.39 0.92

4.06

Lot G

J

170

65 Spress B820

13.2

1632

18.44

23.0

21.6

5.37 1.06

5.68

Lot AH

L

227

60 RC Formulation

11.0

1483

16.76

23.0

21.6

3.66 1.04

3.79

Lot AC

L

227

45 Lycatab C

11.0

1483

16.76

23.0

21.6

3.66 0.86

3.14

Lot AB

L

227

56.7 Lycatab C

11.0

1483

16.76

23.0

21.6

3.66 1.00

3.67

Lot AD

L

227

72 Lycatab C

11.0

1483

16.76

23.0

21.6

3.66 1.26

4.60

Lot AE

M

300

58.1 Lycatab C

Lot AJ

N

300

60 API

Lot AK

N

300

70 API

Lot AL

N

300

50 API

Lot AF

O

600

60 Lycatab C

Lot BD

P

700

Lot AM

Q

Lot AN

SC

Bin Bin Size Load (L) (%)

NU

Bin ID

MA

Formulation Type

PT ED

Lot Number

PT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

vLD/V (1/s)

1146

16.81

26.4

28.0

4.15 0.97

4.04

10.8

1146

16.77

26.4

27.9

4.12 1.06

4.37

12.0

1273

18.62

26.4

27.9

4.58 1.16

5.33

9.5

1019

14.91

26.4

27.9

3.67 0.99

3.65

9.3

1146

16.81

26.4

28.0

2.07 1.12

2.33

50 Starch 1500

9.3

1272

18.61

26.4

27.9

1.96 1.00

1.96

700

60 API

9.3

1146

16.77

26.4

27.9

1.77 1.14

2.01

Q

700

70 API

10.4

1273

18.62

26.4

27.9

1.96 1.43

2.80

Lot AO

Q

700

50 API

8.2

1019

14.91

26.4

27.9

1.57 0.99

1.56

Lot BF

P

700

50 Starch 1500

9.3

1019

14.91

26.4

27.9

1.57 1.00

1.57

Lot BG

P

700

70 Starch 1500

9.3

1272

18.61

26.4

27.9

1.96 1.43

2.80

Lot BC

P

700

70 Starch 1500

9.3

1019

14.91

26.4

27.9

1.57 1.43

2.24

Lot BB

P

700

60 Starch 1500

9.3

1019

14.91

26.4

27.9

1.57 1.14

1.80

AC

CE

10.5

Page 55 of 76

ACCEPTED MANUSCRIPT

700

9.3

1272

v (m/s)

L (cm)

D (cm)

18.61

26.4

27.9

vLD/V (1/s)

f/ff

vLD/V*f/ff (1/s)

1.96 1.14

2.24

PT ED

MA

NU

60 Starch 1500

Shell I-bar Speed speed (rpm) (rpm)

RI

P

Formulation Type

SC

Bin Bin Size Load (L) (%)

CE

Lot BE

Bin ID

AC

Lot Number

PT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

Page 56 of 76

ACCEPTED MANUSCRIPT

PT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

Starch 1500

Lycatab C

Spress B820

RC Form. I

RC Form. II

ODT Form.

Red Iron Oxide (Rockwood Color Pigments)

0.50

0.50

0.50

0.50

0.50

0.50

Partially Pregelatinized Starch 1500 (Colorcon, Inc.)

99.00

9.50

9.50

-

-

-

Lycatab C Pregelatinized Starch (Roquette)

-

89.50

-

-

-

-

Spress B820 Pregelatinized Starch (Grain Processing Corp.)

-

-

89.50

-

-

-

Pearlitol SD 100 Mannitol (Roquette)

-

-

-

62.30

-

-

Pearlitol Flash CoProcessed Mannitol/Starch (Roquette)

-

-

-

-

-

80.30

Microcrystalline Cellulose - PH200 (FMC Biopolymer)

-

-

-

31.20

81.00

10.00

Magnesium Stearate (Mallinckrodt)

-

-

-

1.00

0.15

-

Sodium Croscarmellose Ac-DiSol (FMC Biopolymer)

-

-

-

5.00

2.40

-

Hydroxypropyl Cellulose – LS (ShinEtsu)

-

-

-

-

-

8.00

NU

MA

D TE

AC CE P

SC

Formulation Compositions (wt%)

RI

Table 4: Approximate Compositions of Formulation Types

Page 57 of 76

ACCEPTED MANUSCRIPT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

-

-

-

-

Silicone Fluid 350 CS (Dow Corning)

0.50

0.50

0.50

-

-

Sodium Bicarbonate (Church & Dwight)

-

-

-

-

Colloidal Silica (Cabot Corporation)

-

-

-

-

SC

15.50 0.50

-

AC CE P

TE

D

MA

NU

-

1.20

PT

-

RI

Sucralose (Tate & Lyle)

Page 58 of 76

ACCEPTED MANUSCRIPT

Table 5: Results of linear regressions for each batch.

PT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

k Intercept R2 (1/min)

Lot Number

k Intercept R2 (1/min)

Lot AJ

1.34

-2.16

0.8644

Lot L

0.84

-1.08

0.9128

Lot AK

1.64

-1.87

0.8706

Lot M

0.65

-0.04

0.9993

Lot AL

1.2

-1.13

0.937

Lot N

0.7

Lot AM

0.96

-1.4

0.9146

Lot V

0.29

Lot AN

0.92

-2.56

0.7105

Lot W

0.97

Lot AO

0.79

-0.86

0.9199

Lot X

Lot BF

0.42

0.13

0.9968

Lot Y

Lot BE

0.6

-0.28

0.9918

Lot Z

Lot BC

0.43

-0.23

0.9921

Lot BD

0.42

0.28

0.9863

Lot BB

0.36

0.26

0.985

Lot BG

0.66

-0.48

Lot O

1.39

-0.18

Lot P

1.49

-0.31

Lot Q

1.76

Lot R

SC

RI

Lot Number

0.982

-0.74

0.8397

-0.78

0.938

2.05

-1.2

0.9038

2.12

-1.63

0.877

1.96

-1.13

0.9268

Lot AA

1.19

-1.56

0.8825

Lot AB

1.01

-0.72

0.9772

Lot AC

0.72

-0.09

0.9928

0.9704

Lot AD

0.89

-1.95

0.821

0.9895

Lot AE

0.89

-1.23

0.896

0.9792

Lot AF

0.7

-0.96

0.9223

-0.26

0.9908

Lot AG

1.2

-1.12

0.9238

1.67

-0.11

0.9794

Lot AH

1.02

-0.82

0.9731

Lot S

1.43

-0.04

0.9993

Lot AI

0.92

-1.38

0.8797

Lot T

1.63

-0.4

0.9752

Lot AY

2.43

-2.21

0.8164

Lot U

1.58

-0.29

0.9862

Lot AQ

1.72

-1.56

0.8763

Lot A

0.97

-0.97

0.945

Lot AU

1.7

-1.67

0.8538

Lot B

0.83

-1.13

0.9115

Lot AW

2.2

-1.69

0.8606

Lot C

1.07

-0.9

0.9625

Lot AP

1.36

-1.14

0.9029

Lot D

0.99

-1.09

0.9356

Lot AZ

2

-1.52

0.8498

Lot E

0.8

-0.59

0.9737

Lot BA

2.3

-1.8

0.8539

Lot F

0.99

-1.36

0.9043

Lot AR

1.47

-1.67

0.8501

Lot G

1.11

-1.38

0.9113

Lot AS

1.89

-1.35

0.9191

Lot H

0.85

-0.76

0.9503

Lot AT

1.47

-1.4

0.8614

MA

D

TE

AC CE P

NU

-0.32

Page 59 of 76

ACCEPTED MANUSCRIPT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

-1.64

0.8885

Lot AV

2.06

-0.03

Lot J

1

-0.97

0.9474

Lot AX

1.96

-1.48

Lot K

0.92

-1.12

0.9188

0.9262

PT

1.12

0.8771

AC CE P

TE

D

MA

NU

SC

RI

Lot I

Page 60 of 76

ACCEPTED MANUSCRIPT

PT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

SC

I-bar Time (s) t 0.45t 1.17t 0.36t 0.62t 0.69t 1.10t 1.37t 1.62t 1.21t 3.06t 3.76t

NU

I-bar RPM R 0.68R 0.68R 0.31R 0.31R 0.31R 0.31R 0.31R 0.31R 0.24R 0.24R 0.24R

MA

L (cm) 1.8 4.3 4.2 6.8 6.8 9.0 9.0 9.0 9.0 10.4 10.4 10.4

D

D (cm) 2.6 3.8 3.8 8.5 8.5 8.5 8.5 8.5 8.5 11.0 11.0 11.0

AC CE P

TE

Bin Volume (L) 8 15 30 60 90 120 170 200 227 300 600 700

RI

Table 6: Example Scale-up calculations

Page 61 of 76

ACCEPTED MANUSCRIPT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

PT

Table 7: X-ray Results Lot ID

Blend Time

Sample Size (g)

Agg. Count

C (1/g)

ln(C/Co)

Lot AJ

0.0

4.5

299

66.444

0.00

Lot AJ

1.0

4.5

10

2.222

-3.40

Lot AJ

2.0

254.5

28

0.110

-6.40

Lot AJ

3.5

518.9

8

0.015

-8.37

Lot AJ

6.0

1044.5

1

0.001

-11.15

Lot AJ

8.0

1046.8

1

0.001

-11.15

Lot AK

0.0

4.5

322

71.556

0.00

XMCT

Lot AK

1.0

4.5

6

1.333

-3.98

XMCT

Lot AK

2.0

246.3

0.089

-6.69

Lot AK

3.5

493.8

6

0.012

-8.68

Lot AK

6.0

985.9

2

0.002

-10.47

RI

XMCT

SC

NU

MA

D

TE

AC CE P

Lot AL

22

Analysis Method

XMCT X-Ray Film X-Ray Film X-Ray Film X-Ray Film

X-Ray Film X-Ray Film X-Ray Film

0.0

4.5

176

39.111

0.00

XMCT

1.0

4.5

21

4.667

-2.13

XMCT

2.0

253.7

156

0.615

-4.15

3.5

504.2

22

0.044

-6.80

6.0

987.9

9

0.009

-8.37

Lot AL

8.0

1019.3

2

0.002

-9.90

Lot AM

0.0

4.5

227

50.444

0.00

XMCT

Lot AM

1.0

4.5

32

7.111

-1.96

XMCT

Lot AM

3.0

251.3

31

0.123

-6.01

Lot AM

4.0

492.3

53

0.108

-6.15

Lot AM

8.0

992.8

5

0.005

-9.21

Lot AL Lot AL Lot AL Lot AL

X-Ray Film X-Ray Film X-Ray Film X-Ray Film

X-Ray Film X-Ray Film X-Ray Film Page 62 of 76

ACCEPTED MANUSCRIPT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

10.0

998.0

2

0.002

-10.13

X-Ray Film

Lot AN

0.0

4.5

238

52.889

0.00

XMCT

Lot AN

1.0

4.5

14

3.111

-2.83

XMCT

Lot AN

3.0

252.6

4

0.016

-8.11

Lot AN

4.0

513.7

7

0.014

-8.26

Lot AN

10.0

1038.2

2

0.002

-10.22

Lot AO

0.0

4.5

175

38.889

0.00

XMCT

Lot AO

1.0

4.5

62

13.778

-1.04

XMCT

Lot AO

3.0

224.1

140

Lot AO

4.0

511.5

111

Lot AO

8.0

1010.8

Lot AO

10.0

984.5

Lot BF

0.0

5.3

RI

SC

NU

MA

X-Ray Film X-Ray Film X-Ray Film

X-Ray Film X-Ray Film X-Ray Film X-Ray Film

-4.13

0.217

-5.19

25

0.025

-7.36

15

0.015

-7.85

605

114.583

0.00

XMCT

D

0.625

TE

AC CE P

Lot BF

PT

Lot AM

2.3

5.3

274

51.504

-0.80

XMCT

4.5

5.6

139

24.821

-1.53

XMCT

11.0

500.0

656

1.312

-4.47

12.0

1000.0

856

0.856

-4.90

0.0

5.7

887

156.714

0.00

XMCT

2.0

5.2

168

32.246

-1.58

XMCT

Lot BE

4.3

5.1

34

6.733

-3.15

XMCT

Lot BE

10.5

500.0

85

0.170

-6.83

Lot BE

11.5

1000.0

156

0.156

-6.91

Lot BC

0.0

5.8

891

152.830

0.00

XMCT

Lot BC

2.3

5.3

183

34.725

-1.48

XMCT

Lot BF Lot BF Lot BF Lot BE Lot BE

X-Ray Film X-Ray Film

X-Ray Film X-Ray Film

Page 63 of 76

ACCEPTED MANUSCRIPT

PT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

Lot BC

4.5

5.0

91

18.127

-2.13

Lot BC

11.0

500.0

508

1.016

-5.01

Lot BC

12.0

1000.0

826

0.826

-5.22

Lot BD

0.0

5.6

545

96.975

0.00

XMCT

Lot BD

2.0

5.2

345

66.092

-0.38

XMCT

Lot BD

4.3

5.1

145

28.713

-1.22

XMCT

Lot BD

10.5

500.0

639

1.278

-4.33

Lot BD

11.5

1000.0

1201

1.201

-4.39

Lot BB

0.0

5.3

424

Lot BB

2.3

5.0

275

Lot BB

4.5

5.0

Lot BB

11.0

500.0

Lot BB

12.0

1000.0

RI

SC

NU

X-Ray Film X-Ray Film

0.00

XMCT

55.000

-0.37

XMCT

D

MA

X-Ray Film X-Ray Film

79.849

123

24.453

-1.18

XMCT

721

1.442

-4.01

1489

1.489

-3.98

TE

AC CE P

Lot BG

XMCT

X-Ray Film X-Ray Film

0.0

5.3

486

91.182

0.00

XMCT

2.0

5.3

90

17.045

-1.68

XMCT

4.3

5.2

7

1.346

-4.22

XMCT

10.5

500.0

21

0.042

-7.68

11.5

1000.0

46

0.046

-7.59

0.0

8.5

759

89.820

0.00

XMCT

Lot O

1.0

9.6

133

13.850

-1.87

XMCT

Lot O

2.0

8.8

46

5.210

-2.85

XMCT

Lot O

3.5

998.3

603

0.600

-5.00

X-Ray Film

Lot P

0.0

6.8

683

100.890

0.00

XMCT

Lot P

1.0

8.6

91

10.560

-2.26

XMCT

Lot BG Lot BG Lot BG Lot BG Lot O

X-Ray Film X-Ray Film

Page 64 of 76

ACCEPTED MANUSCRIPT

PT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

2.0

9.1

36

3.960

-3.24

XMCT

Lot P

3.5

1004.7

445

0.440

-5.43

X-Ray Film

Lot Q

0.0

6.9

626

90.330

0.00

XMCT

Lot Q

1.0

9.1

81

8.930

-2.31

XMCT

Lot Q

2.0

9.4

17

1.800

-3.91

XMCT

Lot Q

3.5

1003.3

171

0.170

-6.27

X-Ray Film

Lot R

0.0

6.9

661

95.660

0.00

XMCT

Lot R

1.0

9.9

105

10.610

-2.20

XMCT

Lot R

2.0

9.0

42

4.690

-3.02

XMCT

Lot R

3.5

1009.2

221

0.220

-6.08

X-Ray Film

Lot S

0.0

5.6

506

90.360

0.00

XMCT

Lot S

1.0

9.6

185

19.270

-1.55

XMCT

Lot S

2.0

8.9

47

5.260

-2.84

XMCT

SC

NU

MA

D

TE

RI

Lot P

1004.0

590

0.590

-5.04

X-Ray Film

0.0

6.1

530

87.460

0.00

XMCT

1.0

9.1

65

7.130

-2.51

XMCT

2.0

9.0

18

2.000

-3.78

XMCT

3.5

1011.6

246

0.240

-5.89

X-Ray Film

0.0

6.9

658

95.220

0.00

XMCT

Lot U

1.0

9.7

101

10.370

-2.22

XMCT

Lot U

2.0

8.8

24

2.720

-3.56

XMCT

Lot U

3.5

1006.2

327

0.320

-5.68

X-Ray Film

Lot A

0.0

7.7

775

100.519

0.00

XMCT

Lot A

1.5

8.1

43

5.342

-2.94

XMCT

Lot T Lot T Lot T Lot T Lot U

AC CE P 3.5

Lot S

Page 65 of 76

ACCEPTED MANUSCRIPT

PT

Investigation of an Intensifier-Bar Tumble Bin Scale-Up Model Hilden et Al

Lot A

3.0

8.3

8

0.970

-4.64

Lot A

6.0

249.4

19

0.076

-7.19

Lot A

8.0

1002.0

31

0.031

-8.09

Lot B

0.0

8.1

773

95.080

0.00

XMCT

Lot B

1.5

8.5

37

4.363

-3.08

XMCT

Lot B

3.0

8.0

9

1.124

-4.44

XMCT

Lot B

6.0

500.6

82

0.164

-6.36

Lot B

8.0

1010.5

74

0.073

-7.17

Lot C

0.0

7.8

782

Lot C

1.5

8.6

46

Lot C

3.0

8.6

Lot C

6.0

498.8

Lot C

8.0

1024.7

RI

SC

NU

MA

X-Ray Film X-Ray Film

X-Ray Film X-Ray Film

0.00

XMCT

5.330

-2.94

XMCT

6

0.696

-4.98

XMCT

34

0.068

-7.30

12

0.012

-9.06

D

100.773

TE

AC CE P

Lot D

XMCT

X-Ray Film X-Ray Film

0.0

7.7

714

92.487

0.00

XMCT

1.5

8.5

33

3.869

-3.17

XMCT

3.0

8.5

6

0.703

-4.88

XMCT

6.0

516.7

28

0.054

-7.44

8.0

1001.7

23

0.023

-8.30

0.0

7.6

720

94.488

0.00

XMCT

Lot E

1.5

8.5

87

10.296

-2.22

XMCT

Lot E

3.0

8.8

29

3.299

-3.36

XMCT

Lot E

6.0

499.6

186

0.372

-5.54

Lot E

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1010.0

114

0.113

-6.73

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3.008

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0.348

-5.63

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6.0

510.1

28

0.055

-7.47

Lot F

8.0

1034.0

19

0.018

-8.57

Lot G

0.0

8.6

783

91.153

0.00

XMCT

Lot G

1.5

8.3

20

2.407

-3.63

XMCT

Lot G

3.0

8.3

2

0.241

-5.93

XMCT

Lot G

6.0

521.2

8

0.015

-8.69

Lot G

8.0

1039.5

9

Lot H

0.0

8.3

801

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XMCT

89

10.011

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1.549

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119

0.237

-6.01

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85

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7.9

768

96.847

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XMCT

1.5

8.6

13

1.510

-4.16

XMCT

3.0

8.4

1

0.118

-6.71

XMCT

6.0

500.9

18

0.036

-7.90

8.0

1046.1

4

0.004

-10.14

Lot J

0.0

8.3

837

100.360

0.00

XMCT

Lot J

1.5

8.2

45

5.481

-2.91

XMCT

Lot J

3.0

8.5

7

0.823

-4.80

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Lot J

6.0

534.4

38

0.071

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1001.1

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34

4.271

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XMCT

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3.0

8.1

5

0.620

-4.92

XMCT

Lot K

6.0

507.2

40

0.079

-6.98

Lot K

8.0

997.1

36

0.036

-7.76

Lot L

0.0

8.2

730

89.133

0.00

XMCT

Lot L

1.5

7.6

37

4.868

-2.91

XMCT

Lot L

3.0

8.6

9

1.042

-4.45

XMCT

Lot L

6.0

501.7

66

Lot L

8.0

1001.7

75

Lot M

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Lot M

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Lot M

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9.3

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0.075

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774

96.509

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XMCT

268

33.005

-1.07

XMCT

125

13.426

-1.97

XMCT

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0.132

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500.8

877

1.751

-4.01

8.0

1008.3

539

0.535

-5.20

0.0

8.5

688

81.037

0.00

XMCT

1.5

8.1

141

17.494

-1.53

XMCT

3.0

8.1

49

6.027

-2.60

XMCT

6.0

496.9

320

0.644

-4.84

Lot N

8.0

1006.1

311

0.309

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Lot V

0.0

5.1

593

0.00

XMCT

Lot V

0.5

5.4

276

-0.81

XMCT

Lot V

1.0

5.8

206

-1.18

XMCT

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129

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96

-2.02

XMCT

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7.5

36

-3.18

XMCT

Lot W

0.0

7.1

669

94.491

0.00

XMCT

Lot W

1.0

8.5

172

20.164

-1.54

XMCT

Lot W

2.0

8.9

29

3.247

-3.37

XMCT

Lot W

3.5

9.0

8

0.894

-4.66

XMCT

Lot W

6.0

505.4

28

18.050

-7.44

Lot W

8.0

517.0

25

Lot X

0.0

7.6

635

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7.1

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499.0

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XMCT

12

1.680

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XMCT

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49.900

-8.34

19

55.053

-8.44

D

20.680

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8.3

671

80.746

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XMCT

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7.2

12

1.659

-3.88

XMCT

1.5

8.5

1

0.117

-6.53

XMCT

3.0

540.0

14

38.571

-8.04

4.0

1077.0

8

134.625

-9.29

0.0

7.7

619

80.704

0.00

XMCT

Lot Z

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8.6

27

3.135

-3.25

XMCT

Lot Z

1.5

7.6

5

0.657

-4.81

XMCT

Lot Z

3.0

272.0

11

24.727

-7.60

Lot Z

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1034.0

24

43.083

-8.15

Lot AA

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0.336

-5.54

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6.9

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0.432

-5.29

XMCT

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5.0

259.2

7

37.028

-8.06

Lot AA

7.0

1013.3

12

84.441

-8.89

Lot AB

0.0

7.2

581

80.582

0.00

XMCT

Lot AB

1.0

8.3

78

9.420

-2.15

XMCT

Lot AB

2.0

7.2

20

2.793

-3.36

XMCT

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8.6

12

1.399

-4.05

XMCT

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6.0

255.0

22

11.591

-6.84

Lot AB

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1035.0

14

73.929

-8.69

Lot AC

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7.0

483

69.397

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XMCT

Lot AC

1.0

7.4

289

38.949

-0.58

XMCT

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XMCT

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7.9

32

4.061

-2.84

XMCT

6.0

245.0

206

1.189

-4.41

8.0

999.0

237

4.215

-5.68

0.0

7.9

708

90.191

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XMCT

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8.2

32

3.888

-3.14

XMCT

Lot AD

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7.8

5

0.639

-4.95

XMCT

Lot AD

3.5

7.2

1

0.140

-6.47

XMCT

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6.0

251.0

18

13.944

-7.14

Lot AD

8.0

1132.0

28

40.429

-8.20

Lot AE

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2.310

-3.49

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7.6

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0.263

-5.66

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6.0

251.0

21

11.952

-6.80

Lot AE

8.0

1007.0

44

22.886

-7.45

Lot AF

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8.9

722

80.942

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XMCT

Lot AF

1.0

8.5

176

20.657

-1.37

XMCT

Lot AF

3.0

7.7

11

1.423

-4.04

XMCT

Lot AF

4.0

7.7

6

0.782

-4.64

XMCT

Lot AF

8.0

251.1

25

10.044

-6.70

Lot AF

10.0

1007.4

56

17.989

-7.28

Lot AG

0.0

7.8

691

88.476

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XMCT

Lot AG

1.0

7.5

72

9.574

-2.22

XMCT

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0.136

-6.48

XMCT

6.0

529.0

4

132.250

-9.37

8.0

539.2

4

134.800

-9.39

0.0

7.8

814

104.359

0.00

XMCT

1.0

7.6

90

11.796

-2.18

XMCT

Lot AH

2.0

7.2

33

4.571

-3.13

XMCT

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3.5

6.7

5

0.746

-4.94

XMCT

Lot AH

6.0

250.7

21

11.938

-7.13

Lot AH

8.0

1001.7

20

50.085

-8.56

Lot AI

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8.3

751

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501.9

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0.076

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Lot AI

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1001.5

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32.307

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Lot AY

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659

128.460

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5.2

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0.384

-5.81

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5.4

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0.186

-6.54

XMCT

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2.5

119.0

4

0.034

-8.25

Lot AY

3.5

1086.4

7

Lot AQ

0.0

6.5

805

Lot AQ

0.8

5.2

Lot AQ

1.5

5.5

Lot AQ

3.0

102.8

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123.089

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2.326

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XMCT

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0.727

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XMCT

16

0.156

-6.67

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5.7

698

122.028

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XMCT

0.8

5.9

14

2.369

-3.94

XMCT

1.5

5.4

3

0.555

-5.39

XMCT

3.0

111.6

12

0.108

-7.03

4.3

1115.6

41

0.037

-8.11

Lot AW

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5.5

699

126.401

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XMCT

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0.8

6.0

6

1.008

-4.83

XMCT

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1.3

5.3

4

0.749

-5.13

XMCT

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2.5

133.5

10

0.075

-7.43

Lot AW

3.5

1409.1

31

0.022

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5.4

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124.627

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5.1

22

4.339

-3.36

XMCT

Lot AP

1.8

5.1

13

2.534

-3.90

XMCT

Lot AP

3.5

119.6

22

0.184

-6.52

Lot AP

5.0

1064.1

103

0.097

-7.16

Lot AZ

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5.7

638

112.920

0.00

XMCT

Lot AZ

0.8

5.7

9

1.585

-4.27

XMCT

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2.5

117.0

5

0.043

-7.88

Lot AZ

4.0

1283.6

31

Lot BA

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6.0

746

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5.9

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1.3

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110.4

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1.026

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0.394

-5.76

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5

0.046

-7.92

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0.017

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5.1

584

115.644

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5.7

9

1.573

-4.30

XMCT

1.8

5.8

4

0.686

-5.13

XMCT

3.5

113.7

8

0.070

-7.40

5.0

1297.2

46

0.035

-8.09

Lot AS

0.0

5.1

627

123.913

0.00

XMCT

Lot AS

0.8

5.0

12

2.390

-3.95

XMCT

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1.5

5.7

6

1.056

-4.76

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105.9

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0.116

-7.00

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118.761

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24

4.034

-3.38

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1.8

5.3

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0.759

-5.05

XMCT

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3.5

115.6

8

0.069

-7.45

Lot AT

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1208.6

72

0.060

-7.60

Lot AV

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5.0

609

120.833

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XMCT

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0.8

5.1

259

51.085

-0.86

XMCT

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1.5

5.4

25

4.673

-3.25

XMCT

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2.5

107.9

17

Lot AV

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1002.5

69

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0.069

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114.579

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XMCT

19

3.293

-3.55

XMCT

2

0.398

-5.66

XMCT

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0.158

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0.109

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0.026

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A scale-up model for intensifier bar equipped tumble bins is proposed. X-ray imagery confirmed extent of mixing for iron oxide agglomerates. A characteristic dimension is derived and held constant for scale-up.

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Highlights

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[1] Wang, R.H. and L.T. Fan (Kansas State University), “Methods for Scaling-Up Tumbling Mixers” Chemical Engineering, May 27, 1974 [2] Bridgwater, John (University of Cambridge), “Mixing of powders and granular materials by mechanical means – A perspective” Particuology, Volume 10, Issue 4, August 2012, 397-427

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[3] Muzzio, Fernando J. and Albert W Alexander (Rutgers University), “Scale Up of Powder-Blending Operations” Pharmaceutical Technology, Scaling Up Manufacturing 2005, s34-s41 [4] Chaudhuri, Bodhisattwa, Amit Mehorotra, Fernando J. Muzzio and M. Silvina Tomassone (Rutgers University),”Cohesive effects in powder mixing in a tumbling blender” Powder Technology 165 (2006) 105-114.

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[5] Sudah, Osama S., D. Coffin-Beach and F.J. Muzzio, “Quantitative characterization of mixing of freeflowing granular material in tote (bin)-blenders” Powder Technology 126 (2002) 191-200

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[6] Kushner, Joseph, and Francis Moore. "Scale-up Model Describing the Impact of Lubrication on Tablet Tensile Strength." International Journal of Pharmaceutics 399.1-2 (2010): 19-30. [7] Sato, Yoshinobu, Hideya Nakamura and Satoru Watano, “Numerical analysis of agitation torque and particle motion a in high shear mixer” Powder Technology 186 (2008) 130-136

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[8] Chirkott, Tom (Patterson-Kelley), ”Scale-Up and Endpoint Issues of Pharmaceutical Wet Granulation in a V-Type Low Shear Granulator” Drug Development and Industrial Pharmacy, Vol. 28, No. 7, pp. 871888, 2002 [9] Makishima, Shin-Ichi and Takashi Shirai, “Experimental study on the power requirements for agitating beds of solid particles, and proposal of a new model”, J. Chem. Eng. Jpn. - J CHEM ENG JPN. 1 (1968) 168–174. doi:10.1252/jcej.1.168. [10] P.C. Knight, J.P.K. Seville, A.B. Wellm, T. Instone, “Prediction of impeller torque in high shear powder mixers”, Chem. Eng. Sci. 56 (2001) 4457–4471. doi:10.1016/S0009-2509(01)00114-2. [11] C. André, J.F.Demeyre, “Dimensional analysis of a planetary mixer for homogenizing of free flowing powders: Mixing time and power consumption”, Chem. Eng. J. s 198–199 (2012) 371–378. doi:10.1016/j.cej.2012.05.069. [12] C. André, J.F. Demeyre, C. Gatumel, H. Berthiaux, G. Delaplace, “Derivation of dimensionless relationships for the agitation of powders of different flow behaviours in a planetary mixer”, Powder Technol. 256 (2014) 33–38. doi:10.1016/j.powtec.2014.02.002. [13] I. Gijón-Arreortúa, A. Tecante, Mixing time and power consumption during blending of cohesive food powders with a horizontal helical double-ribbon impeller, J. Food Eng. 149 (2015) 144–152. doi:10.1016/j.jfoodeng.2014.10.013. [14] Patterson-Kelley “High Speed Intensifier Bar Scale-Up” Derivation Bulletin, Patterson-Kelley Group (currently Buflovak) [15] Michaels, James N. (Merck & Co.), “Toward rational design of powder processes” Powder Technology 138 (2003) 1-6

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[16] Barry Crean, Andrew Parker, Delphine Le Roux, Mark Perkins, Shen Y. Luk, Simon R. Banks, Colin D. Melia, Clive J. Roberts “Elucidation of the internal physical and chemical microstructure of pharmaceutical granules using X-ray micro-computed tomography, Raman microscopy and infrared spectroscopy”, European Journal of Pharmaceutics and Biopharmaceutics, Volume 76, Issue 3, November 2010, Pages 498–506

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