Research Article Pharmaceutics, Drug Delivery and Pharmaceutical Technology| Volume 110, ISSUE 3, P1172-1181, March 01, 2021

# Theoretical and Experimental Evaluation of Flow Pattern of Pharmaceutical Powder Blends Discharged From Intermediate Bulk Containers (IBCs)

Published:October 09, 2020

## Abstract

The purpose of this study is to assess the prevalence of funnel flow pattern for common pharmaceutical powder blends, upon discharging from modern intermediate bulk containers (IBCs) in drug product manufacturing. The estimation was built upon Jenike’s original radial stress field theory. It was modified to account for the stress-dependence of wall friction angle commonly observed in pharmaceutical powders. A total of 260 flow pattern estimations, based on 20 real-life IBCs and 13 investigational powder blends, were made. The estimated results showed that the mass flow pattern is present in less than 5% of all cases. Funnel flow pattern is clearly prevalent among pharmaceutical powder blends. The prevalence of funnel flow stems from several factors: 1) relatively shallow hopper section shared by all IBCs, 2) the common transition-type geometry, leading to even shallower hopper inclination at the edge of the hopper section, and 3) relatively high wall friction angles resulting from low wall normal stresses. This conclusion was verified through at-scale experiments, by discharging multiple pharmaceutical powder blends from a representative IBC. In general, our study suggests that, unless the powder wall friction can be substantially reduced, pharmaceutical powders are likely to discharge under funnel flow from modern IBCs.

## Introduction

One of the most common processes in the manufacturing of solid dosage forms (such as tables or capsules) is the transport of pharmaceutical powders between unit operations.
• Augsburger L.L.
• Hoag S.W.
Pharmaceutical Dosage Forms-Tablets.
Although powders may be transported pneumatically, gravity-driven powder discharging from bins or hoppers remains to be the prevalent means of powder transport in modern drug product manufacturing. The development of a robust, flawless powder discharging process requires significant efforts in both powder formulation and equipment design. Nevertheless, constraints are present in both aspects in drug product manufacturing, due to the nature of pharmaceutical powder blends and the geometric or space limitations of the equipment. These constraints frequently lead to undesirable flow pattern and powder flow obstructions.
• Prescott J.K.
• Barnum R.A.
On powder flowability.
When a pharmaceutical powder is discharged from a hopper, it can exhibit either the mass flow or funnel flow pattern.
• Schulze D.
Powders and Bulk Solids. Behaviour, Characterization.
Mass flow is generally the desired mode because the entire powder is in motion regardless of its position in the equipment, thereby eliminating the risk of powder segregation because of the “first-in, first out” flow sequence. Contrarily, funnel flow is known to possess greater propensity toward segregation, because a flow channel (aka “funnel”) develops during powder discharging. Under funnel flow pattern, the powder situated in the periphery of the container remains stagnant until the flow channel empties (i.e., “first-in, last-out”). In addition, formation of stable rathole is possible when powder is discharged under the funnel flow pattern. Therefore, although the flow pattern is not widely estimated in actual drug product manufacturing, there is a general consensus that funnel flow should be avoided, if it is at all possible.
The methodology to predict the powder flow pattern from a hopper was available several decades ago, based on the radial stress field theory originally developed by Andrew Jenike.
• Jenike A.W.
Storage and flow of solids. Bulletin 123.
,
• Jenike A.W.
• Leser T.
A flow-no-flow criterion in the gravity flow of powders in converging channels.
According to Jenike’s analysis, the flow pattern is dependent on both the powder properties (wall friction angle, and effective angle of internal friction) and the equipment geometry (hopper vertical angle, the shape of the hopper section, and outlet opening). An approximation of Jenike’s original method is also available, and it has been successfully applied by several research groups to study the hopper flow pattern in pharmaceutical powders.
• Leung L.Y.
• Mao C.
• Pieters S.R.
• Yang C.-Y.
A proposed complete methodology to predict gravity flow obstruction of pharmaceutical powders in drug product manufacturing.
,
• Søgaard S.V.
• Olesen N.E.
• Hirschberg C.
• et al.
An experimental evaluation of powder flow predictions in small-scale process equipment based on Jenike's hopper design methodology.
A salient conclusion derived from these exercises is that one needs to account for the stress-dependence of the powder properties, in particular the wall friction angle. In other words, because the wall friction angle of the powder is a function of wall normal stress, determination of the stress of the powder in the equipment is a prerequisite for flow pattern assessment. Therefore, aside from the main factors implicated in the Jenike’s original methodology, all properties expected to influence the powder stress condition need to be considered for powder flow pattern evaluation.
In modern drug product manufacturing, there is an increasing utility of intermediate bulk containers (IBCs) to enable in-container operations.
• Alexander A.
• Arratia P.
• Goodridge C.
• Sudah O.
• Brone D.
• Muzzio F.
Characterization of the performance of bin blenders: Part 1 of 3: methodology.
The IBCs employed in drug product manufacturing allow for the blending, storage, and transport of pharmaceutical powders in single equipment, thus simplifying the process steps and eliminating the risk of cross-contamination. In light of this recent trend, we conducted a comprehensive study to evaluate the flow pattern of pharmaceutical powders in modern IBCs. A recent article studying wall friction angles of common pharmaceutical powders suggested that funnel flow likely dominates when APIs or pharmaceutical powder blends are discharged from “off-the-shelf” bins and hoppers.
• Hancock B.C.
The wall friction properties of pharmaceutical powders, blends, and granulations.
We intended to evaluate whether funnel flow remains a prevalent occurrence for powder discharging operations in IBCs. Specifically, we attempted to answer this question by 1) conducting a survey of pharmaceutical powders and IBCs used in drug product manufacturing with respect to their attributes relevant to the flow pattern, 2) implementing rigorous calculation of flow pattern by taking into consideration all factors related to the powder stress and stress-dependence of wall friction angles, and 3) verifying the methods through comparison with classic Jenike’s methodology as well as experimental observations of the flow pattern for pharmaceutical powders discharged from an IBC. We believe this study can facilitate a more robust scale-up development for manufacturing of solid dosage forms.

## Materials and Methods

### Materials

The materials used in the study entail 10 pharmaceutical powder blends, which were collected as samples from the batches produced as part of the internal formulation development or manufacturing activities. Five different APIs were represented in this group of materials. The drug loads for these powder blends range between 3.1% – 40.0% (%wt). Additionally, three common pharmaceutical excipients, namely two grades of microcrystalline cellulose (Avicel® PH 101, and PH 102, FMC Biopolymer, Philadelphia, PA, USA), and spray dried lactose (Fast Flo 316, Foremost Farms, Baraboo, WI), were employed as reference powders. These excipients were each lubricated by blending with 1% (%wt) of magnesium stearate (HyQual™ 2257, Mallinckrodt) prior to testing.

### Measurement of Powder Flow Properties and Wall Friction Angles

Both the powder flow properties and wall friction angles were measured using a ring shear tester (RST-XS.s; Dietmar Schulze, Wolfenbüttel, Germany). All tests were conducted under controlled temperature (between 18-22°C) and humidity (between 50%-65%). For powder flow properties, the measurements were carried out at a pre-consolidation normal stress between 0.6 kPa and 1.0 kPa. The yield loci were obtained through linear regression of the raw data - from which the major principal stresses, unconfined yield strengths, flow function coefficients, powder density, and internal friction angles were derived. The wall friction angle measurements were conducted using the same instrument, by shearing the powders against a testing coupon with 2B surface finish in rotational motion. For each powder blend, the wall friction angles were determined under a number of normal stresses, ranging from 200 Pa to 3000 Pa. The wall friction angle measurements were performed in triplicate. Data are reported as mean +/- standard deviation.

### Powder Discharging Experiments

The powder discharging experiments were conducted on three excipient powders (MCC Avicel® PH 101, PH 102, and spray dried lactose). Each powder was passed through #20 mesh screen for de-lumping and loaded into a bin blender. The powder was then blended with 1% (%wt) of magnesium stearate (screened through #30 mesh) in a bin blender at the rotation speed of 25 RPM/min for approximately 2 min. The blending time for excipients varied slightly to account for the difference in head space inside the bin.
• Kushner J.
• Moore F.
Scale-up model describing the impact of lubrication on tablet tensile strength.
After lubrication, the powder was transferred to a 25-L transition type IBC with the side angle of 30o and outlet opening diameter of 150 mm. A split butterfly valve was installed at the bottom of the IBC. To observe the flow pattern during powder discharging, the top of the IBC was left open, and two video cameras were mounted on the top rim of the IBC with a view of the entire powder bed inside the IBC. The cameras were powered on immediately before the butterfly valve was opened, so that the complete powder discharging process was recorded.

## Results and Discussion

### Intermediate Bulk Containers (IBCs) Used in Current Drug Product Manufacturing

To represent the current state of practice in drug product manufacturing, a total of 20 IBCs was collected from 5 different facilities active in drug product development or manufacturing, and their detailed information was recorded and organized. All IBCs were constructed using the 316L stainless steel. These IBCs covered a broad range of volume (from 5 L to 1000 L) and outlet opening diameter (from 100 mm to 250 mm); and were produced by multiple IBC manufacturers. Key geometric data, as well as the surface roughness information of the product contact surface in these IBCs, are presented in Table 1.
Table 1Key IBC Geometry Data and Information Regarding Roughness of Product Contact Surface.
IBC #IBC Volume (L)Geometry Bin SectionGeometry Hopper SectionSide Angle (o)Valley Angle (o)Outlet Size (mm)Surface FinishManufacturer
A: Servolift; (b) Ability Fabricators; (c) Müller.
15squaretransition30391002BA
210squaretransition30391502BA
319squaretransition30391002BA
424squaretransition30391002BA
525squaretransition30391502BA
645squaretransition30391502BA
750squaretransition3039100N/AB
860squaretransition30391502BA
990squaretransition30391502BA
10100squaretransition3039100N/AA
11113rectangulartransition33402002BB
12200squaretransition4555100N/AA
13200squaretransition3039120N/AA
14220squaretransition30392002BB
15250squaretransition33421502BC
16250squaretransition33421502BC
17325squaretransition30392002BB
18450squaretransition30391502BC
19650rectangulartransition30372502BB
201000rectangulartransition31382502BB
a A: Servolift; (b) Ability Fabricators; (c) Müller.
It is worth noting that all the IBCs share similar geometry: they consist of a square or rectangular upper bin section, joined by a lower hopper section. For these IBCs, the bottom outlet is circular in shape. Therefore, the cross-sectional geometry of the hopper section gradually transitions from a square or rectangle at the top to a full circle at the bottom. A drawing and an image of a typical IBC are provided in Fig. 1. Because of the disparity of the cross-sectional geometry along the axial direction, the value of the hopper vertical angle $θ′$, which measures the wall inclination from vertical, differs depending on the location of measurement. The highest $θ′$ (i.e., most shallow wall inclination) occurs when it is measured from the corner of the square or rectangle (see Fig. 1). The resulting angle, termed “valley angle”, is critical for mass flow/funnel flow determination. According to Jenike
• Jenike A.W.
Storage and flow of solids. Bulletin 123.
’s theory, the presence of the edge can lead to the formation of “in-flow valley”, in which powder tends to be more stable than at the side and thereby favors the funnel flow pattern. As the result, although the vertical angle provided in the IBC drawing usually refers to the side angle, it is the valley angle that is more relevant to the powder flow pattern. For the transition-type IBCs, the valley angle is always greater than the side angle (see Table 1).
Another equipment attribute vital to the powder flow pattern is the roughness of the internal surface in contact with the powders.
• Hancock B.C.
The wall friction properties of pharmaceutical powders, blends, and granulations.
The surface roughness impacts the wall friction angle, as well as the powder stress, both of which contribute to the powder flow pattern. For all the IBCs where data can be identified, the product-contact surfaces possess 2B surface finish (Table 1), which is produced via cold-rolling using highly polished rolls and generally has a roughness value (Ra) of 0.3-0.5 μm range.
ASTM A480/A480M-General
As the result, the wall friction angle measurements in our study were conducted using a testing coupon with 2B surface finish. A word of caution is that the 2B surface finish is not a precise description of surface roughness.
• Schulze D.
• Heinrici H.
7th International Conference for Conveying and Handling of Particulate Solids (CHoPS).
Materials categorized as 2B surface finish can present as multiple surface profiles as long as they are processed using the same procedure and the Ra values fall into the range. Therefore, the wall friction angles of a powder against different “2B” surfaces are expected to vary to some extent.

### Evaluation of Powder Flow Pattern

#### Characterization of Powder Properties with Respect to Flow Pattern – Stress-Dependence of Wall Friction Angle is Important

To capture the properties of representative pharmaceutical powders, 10 distinct pharmaceutical powder blends originating from our in-house research or development programs were collected for the study. These formulations cover a broad range of drug loads, and employed a variety of excipients available in solid dosage formulation development. Additionally, as references, three common excipient powders, including two grades of microcrystalline cellulose (MCC, Avicel® PH 101 and PH 102), and one grade of spray dried lactose (Fast Flo 316), were also included in the study. In solid dosage formulation development, MCC Avicel® PH 101 can represent non-agglomerated powders exhibiting “borderline” flowability; whereas MCC Avicel® PH 102 and lactose Fast Flo 316, albeit having different bulk density and particle size, are both known to possess good flowability. Studying these well-known pharmaceutical excipients can impart a perspective of the prevalence of funnel flow pattern in practical drug product manufacturing operations.
At the face value, the estimation powder flow pattern (detailed in the following section) requires only two powder properties, that is, effective angle of internal friction ($δ$), and wall friction angle ($ϕ′$). Nevertheless, although $δ$ is generally insensitive of powder stress, $ϕ′$ is known to be strongly dependent on normal stresses.
• Hancock B.C.
The wall friction properties of pharmaceutical powders, blends, and granulations.
As a consequence, a prerequisite of powder flow assessment is to determine the stress of powder upon discharging, so that $ϕ′$ can be reliably estimated. In other words, all material properties affecting the stress of powder inside the IBC, which include the wall friction angle $ϕ′$, effective angle of internal friction $δ$, and powder density ρ, are needed. These properties were obtained for all pharmaceutical powders used in this study, and are presented in Table 2 (due to the stress-dependence of wall friction angle, $ϕ′$ values at normal stress of 0.2 kPa is presented, as 0.2 kPa is an appropriate approximation of the powder stress under the passive stress state
• Leung L.Y.
• Mao C.
• Pieters S.R.
• Yang C.-Y.
A proposed complete methodology to predict gravity flow obstruction of pharmaceutical powders in drug product manufacturing.
,
• Søgaard S.V.
• Olesen N.E.
• Hirschberg C.
• et al.
An experimental evaluation of powder flow predictions in small-scale process equipment based on Jenike's hopper design methodology.
; other material properties are generally stress-independent within the stress regime relevant to powder flow).
Table 2Key Flow Pattern-Related Properties for Pharmaceutical Powders.
NameDrug Load (%)Angle of Internal Friction (o)Powder Density (g/mL)
Powder density was measured using a ring shear tester, under the normal stress of 0.6-1.0 kPa.
Wall Friction Angle (Normal stress = 200 Pa)
The wall friction angle is normal stress dependent. Data under the normal stress of 200 Pa was exhibited here. The actual wall friction angles for flow pattern estimation were determined using the method described in the “Theoretical Calculation of Flow Pattern” section.
(o)
Flow Function Coefficient
Powder blend #120.844.70.3821.8 ± 3.32.8
Powder blend #220.841.90.3822.8 ± 2.94.9
Powder blend #33.140.40.4116.2 ± 0.68.7
Powder blend #420.042.70.3320.4 ± 0.52.8
Powder blend #520.041.00.3722.3 ± 3.22.9
Powder blend #636.044.20.2628.9 ± 0.82.3
Powder blend #710.041.30.4230.2 ± 0.76.3
Powder blend #830.043.30.4631.2 ± 0.63.4
Powder blend #920.042.10.4229.8 ± 0.45.7
Powder blend #1040.043.60.4632.7 ± 0.44.7
MCC (Avicel® PH 101)99.0
All excipient powders were mixed with 1% magnesium stearate.
46.40.3619.8 ± 2.34.1
MCC (Avicel® PH 102)99.0
All excipient powders were mixed with 1% magnesium stearate.
41.50.3715.2 ± 2.06.8
Spray dried lactose99.0
All excipient powders were mixed with 1% magnesium stearate.
34.60.6822.2 ± 3.218.6
a Powder density was measured using a ring shear tester, under the normal stress of 0.6-1.0 kPa.
b The wall friction angle is normal stress dependent. Data under the normal stress of 200 Pa was exhibited here. The actual wall friction angles for flow pattern estimation were determined using the method described in the “Theoretical Calculation of Flow Pattern” section.
c All excipient powders were mixed with 1% magnesium stearate.
Of all the 13 pharmaceutical powders tested, the wall friction angles underwent a monotonic decrease with increasing normal stress. The changes of wall friction angle as the function of normal stress are more precipitous at low normal stresses, and can be properly fitted using a power law function with a negative exponent. Examples of wall friction angles under different normal stresses are shown in Fig. 2. The same observations were reported by other researchers studying wall frictions of pharmaceutical powders.
• Leung L.Y.
• Mao C.
• Pieters S.R.
• Yang C.-Y.
A proposed complete methodology to predict gravity flow obstruction of pharmaceutical powders in drug product manufacturing.
,
• Hancock B.C.
The wall friction properties of pharmaceutical powders, blends, and granulations.
,
• Jager P.D.
• Bramante T.
• Luner P.E.
Assessment of pharmaceutical powder flowability using shear cell-based methods and application of Jenike’s methodology.
Accounting for the stress-dependence of the wall friction angle is critical for the study of the powder flow pattern. This is because the stress of powders inside the IBC is strongly affected by wall friction angle, which itself is a function of powder stress. Due to the inter-dependence between the powder stress and wall friction angle, it is not adequate to use a single value of the wall friction angle to calculate the powder flow pattern. In fact, the calculation of powder flow pattern entails an iterative process to allow the wall normal stress to converge. This will be described in greater detail in the ensuing section.

### Theoretical Calculation of Flow Pattern

The traditional method to assess powder flow pattern arises from Jenike
• Jenike A.W.
Gravity Flow of Bulk Solids. Bulletin No 108.
’s original radial stress field theory. To date, its utility in pharmaceutical industry is scarce due to the need of numeric analysis to solve the equations. Alternatively, a simpler, analytical solution was more widely employed
• Roberts A.W.
Characterisation for hopper and stockpile design.
and it has been previously reported in pharmaceutical literature with success.
• Søgaard S.V.
• Olesen N.E.
• Hirschberg C.
• et al.
An experimental evaluation of powder flow predictions in small-scale process equipment based on Jenike's hopper design methodology.
Specifically, the method is based on an equation for the critical vertical angle ($θcritical′$) determination as follows:
$Equation 1.$
(1)

where $δ$ is the effective angle of internal friction. The term $β$ represents the angle between the direction of the major principal stress and the wall normal stress, and takes the following form:
$Equation 2.$
(2)

where $ϕ′$is the wall friction angle. A powder is predicted to undergo funnel flow if the valley angle of the IBC is greater than the critical vertical angle, $θcritical′$.
As mentioned in the preceding section, the utility of Equations (1), (2) is confounded by the inter-dependence between the powder stress and wall friction angle. To be more specific, application of Equations (1), (2) requires a known wall normal stress for $ϕ′$ determination, which itself dictates the wall normal stress. This issue can be addressed via an iterative method; it entails the following specific steps.
• 1)
An initial wall normal stress value ($σw$) is guessed.
• 2)
The wall friction angle ($ϕ′$) is determined from the experimental data, using the initial $σw$ from Step 1.
• 3)
The major principal stress of the powder at the outlet of the IBC ($σ1$) is determined from $ϕ′$, obtained from the Step 2:
$Equation 3.$
(3)

where B is the diameter of the IBC outlet opening. $θ′$ represents either the vertical angle of the IBC (under mass flow condition) or the vertical angle of the flow channel (under funnel flow condition).
It was shown that in the vast majority of the cases using modern IBCs, the funnel flow pattern prevails (detailed in ensuing section), and because the flow channel developed in the IBC is always nearly vertical, a $θ′$ value of 5o is taken for the analysis.
• Leung L.Y.
• Mao C.
• Pieters S.R.
• Yang C.-Y.
A proposed complete methodology to predict gravity flow obstruction of pharmaceutical powders in drug product manufacturing.
The terms X and Y in Equation 3 are shown as follows:
$Equation 4.$
(4)

$Equation 5.$
(5)

Step 3 allows for the determination of the major principal stress at the IBC outlet under the passive stress state (i.e. after powder discharging from IBC is initiated). Detailed derivation of Equations (3), (4), (5) can be found in the original research articles in which the method was proposed.
• Arnold P.
• McLean A.
Improved analytical flowfactors for mass-flow hoppers.
,
On the theory of arching in mass flow hoppers.
• 4)
Calculate the wall normal stress $σw$ from $σ1$ obtained in Step 3:
$Equation 6.$
(6)

• 5)
Perform iteration (Steps 1-4) until the value of $σw$ converges.
• 6)
Determine $ϕ′$ from the converged value of $σw$. Then calculate $θcritical′$ using Equations (1), (2), and use the data to assess the powder flow pattern.
It is to note that the choice of mass flow versus funnel flow in Step 3 of the calculation is not expected to alter the conclusion. For example, increasing $θ′$ value from 5o (assuming funnel flow pattern) to 39o (assuming mass flow pattern) for MCC PH 102 leads to a decrease of $θcritical′$ by approximately 3o, regardless of the IBC outlet size. This change results from the fact that high $θ′$ value (less steep flow channel) gives rise to lower stress at the IBC outlet and therefore lower wall friction angle. For the case of MCC PH 102, there is a decrease of the wall friction angle by 2.3-2.5o if the mass flow pattern is assumed in the calculation regardless of IBC geometry. This level of variability is of the same magnitude as the experimental errors observed in the wall friction angle measurement in pharmaceutical powders (see Table 2). Taken together, the use of funnel flow in this calculation is a rational choice.

### Results of Flow Pattern Calculation – Funnel Flow Pattern Prevails

For each of the 13 powders tested in this study (Table 2), the above method was employed to calculate the flow pattern for all 20 IBCs collected (Table 1). This exercise led to a total of 260 sets of flow pattern predictions. The results are shown in Fig. 3. As stated previously, funnel flow pattern is predicted when the valley angle of the hopper section of the IBC is greater than the critical vertical angle $θcritical′$. Fig. 3 clearly shows that the funnel flow pattern prevails in a majority of cases. Out of 260 scenarios, only 12 cases, or less than 5%, are predicted to adopt the mass flow pattern. Those materials capable of undergoing mass flow include MCC (Avicel® PH 102), spray dried lactose (Fast Flo 316), and Blend #3 (which contains only 3.1% of drug and more than 90% of MCC Avicel® PH 102 and spray dried lactose), in combination with IBCs possessing most steep hopper section and largest outlet opening. In other words, the results show that pharmaceutical powders with high drug loading are prone to funnel flow. The prevalence of funnel flow pattern is in part due to the common IBC design adopted by drug product manufacturers, which consists of relatively shallow hopper section to limit total IBC height and to enable more efficient powder mixing, combined with the higher wall friction angle common for drug substance.
• Hancock B.C.
The wall friction properties of pharmaceutical powders, blends, and granulations.
Detailed analysis is presented in ensuing sections.

### Critical Material Attributes for Flow Pattern – Wall Friction Angle and Powder Density

With regard to material attributes, the wall friction angle ($ϕ′$) is the main factor governing the flow pattern of powders discharged from the IBC. Mass flow is favored for powders exhibiting low $ϕ′$, as it facilitates the powders’ movement against the wall. The effective angle of internal friction ($δ$) also plays a role, but because $δ$ for the pharmaceutical powders usually do not differ significantly (Table 2), $ϕ′$ is therefore the dominant material attributes. The effect of $ϕ′$ on powder flow pattern is exemplified in Fig. 4, in which the calculated critical vertical angle for mass flow/funnel flow ($θcritical′$) is shown as the function of $ϕ′$ for the MCC Avicel® PH 101 ($δ$ = 46.4o). $θcritical′$ exhibits precipitous, monotonic decrease with increasing $ϕ′$ in Fig. 4, indicating the significantly deleterious effect of high wall friction angle toward mass flow. Similar graphs (with different $δ$ values) can be found in original articles by Jenike in this topic.
• Jenike A.W.
Storage and flow of solids. Bulletin 123.
,
• Jenike A.W.
• Leser T.
A flow-no-flow criterion in the gravity flow of powders in converging channels.
A recent survey conducted by Hancock
• Hancock B.C.
The wall friction properties of pharmaceutical powders, blends, and granulations.
showed that $ϕ′$ for pharmaceutical powders against 2B surface finish has an average value of 22.2o (under the normal stress of 622 Pa, generally in line with our stress estimation), and 90% of the powders tested exhibit $ϕ′$ greater than 12.3o. For a typical pharmaceutical powder (such as the one shown in Fig. 4), the $ϕ′$ value of 12.3o translates to $θcritical′$ of approximately 36o, which is lower than valley angles of essentially all the IBCs collected in our study. Therefore, because of the relatively high wall friction angle for pharmaceutical powders, funnel flow is expected to be a prevalent event for powder blends discharging from the IBCs in drug product manufacturing.
Aside from the wall friction angle, powder density is also a material attribute which could significantly influence the powder flow pattern. In theory, powder density is not a property directly related to flow pattern. Nevertheless, changes in powder density can lead to corresponding changes in major principal stress and wall normal stress inside the IBC (as demonstrated by Eq. 3). For pharmaceutical powders, the wall friction angle decreases with increasing wall normal stress. A reduced wall friction angle is therefore associated with the powder with high density. For this reason, dense pharmaceutical powders are more likely to undergo mass flow than light powders. To demonstrate this effect, $θcritical′$ of the “MCC Avicel® PH 101-like” powder (i.e., a powder possessing the same $δ$ and $ϕ′$ as MCC PH 101) in an IBC (outlet diameter = 150 mm), with varying powder density, was estimated. The results are shown in Fig. 5. For such material, a change of powder density from 0.2 g/mL to 0.6 g/mL leads to an increase of $θcritical′$ from 27o to 37o. This change is driven by the elevation of wall normal stress at the bin outlet, which increases from 0.2 kPa to 0.9 kPa as the result of the increase of powder density (Fig. 5). In practice, pharmaceutical powders are densified by means of granulation. Therefore, the process of granulation not only improves powder flowability (in the form of enhanced flow function coefficient), but also increases the likelihood of powder discharging under mass flow pattern.

### Critical Equipment Attributes for Flow Pattern – Hopper Vertical Angle and Outlet Diameter

Ideally, the steeper the hopper section of the IBCs, namely the lower the hopper vertical angle ($θ′$), the more likely powder will discharge by following the mass flow pattern. However, our study showed that $θ′$ of the IBCs used for drug product manufacturing is usually not low enough to enable mass flow. For all the IBCs collected by us, the side angle ranges between 30o to 45o (Table 2). This design possibly results from the consideration to enable effective powder discharging, while maintaining mixing efficiency and limiting equipment height. Furthermore, because the hopper sections of all IBCs are present in the form of the transition-type geometry, the wall inclination is even shallower at the edge, with the lowest valley angle being 37o in the set. In other words, to enable mass flow in drug product manufacturing, $θcritical′$ of the powder needs to be greater than 37o even for IBCs with the most steep hopper section. For a typical pharmaceutical powder (such as the one presented in Fig. 4), this threshold translates to a maximum wall friction angle of approximately 11o. According to the literature,
• Hancock B.C.
The wall friction properties of pharmaceutical powders, blends, and granulations.
a vast majority of pharmaceutical powders moving against the wall with 2B surface finish exhibit $ϕ′$ values greater than 11o, further suggesting that the mass flow in drug product manufacturing is an infrequent occurrence.
Another IBC geometry attribute contributing to the powder flow pattern is the diameter of the hopper outlet opening. Similar to the powder density, the impact of the outlet diameter is indirectly imposed due to the fact that the wall friction angle decreases with increasing wall normal stress for pharmaceutical powders. Under the passive stress state, greater outlet diameter gives rise to higher external stress as well as wall normal stress (Eqs. (3), (6)). For a given pharmaceutical powder discharged through a wider outlet, the wall friction angle is therefore reduced, leading to higher probability for mass flow. To exemplify this effect, $θcritical′$ of the MCC PH 102 discharged from an IBC ($θ′$ = 39o) with different outlet diameters was estimated (Fig. 6). For the IBC with the constant vertical hopper angle, an expansion of the outlet diameter from 100 mm to 250 mm results in an increase of $θcritical′$ by more than 5 degree, essentially making mass flow a possibility. Therefore, from the perspectives of powder discharging, building IBCs with wide outlet opening is generally beneficial. It not only reduces the incidence of flow obstruction and formation of rathole, but also increases the tendency for powders to discharge under the mass flow pattern. Therefore, despite the engineering challenges to build IBC with wide outlet opening, it indeed benefits powder discharging in many aspects, and is therefore strongly recommended.

### Experimental Verification

In principle, the method we proposed in this study should be consistent with the original analysis developed by Jenike,
• Jenike A.W.
Storage and flow of solids. Bulletin 123.
using the radial stress field theory. Such comparison is not always feasible because our method accounts for the stress-dependence of the wall friction angle, whereas the Jenike’s methodology can only employ a single wall friction angle in the analysis. But despite this difference, it is still possible to verify our method by comparing it against the classic Jenike’s methodology. Namely, these two approaches should yield very similar results if a constant wall friction angle is used.
The critical vertical angle for mass/funnel flow ($θcritical′$) was calculated for all 13 pharmaceutical powders, using fixed wall friction angles under the normal stress of 0.2 kPa (Table 2). To follow Jenike’s methodology, the “flow factor contour” charts from the original Jenike
• Jenike A.W.
Storage and flow of solids. Bulletin 123.
’s publication were employed for analysis. Because the only charts available in the literature were those with the effective angle of friction ($δ$) being an increment of 10 (i.e.$δ$ = 30o, 40o, 50o, etc.), $θcritical′$ was determined through linear interpolation of the values obtained from the charts with $δ$ bracketing the actual effective angle of internal friction of the powder. As shown in Fig. 7, the estimated $θcritical′$ values using our proposed method are nearly identical to those obtained by following Jenike’s charts. The root mean square error (RSME) between these two sets of data is merely 0.3o. This result suggests that, aside from accounting for the stress-dependence of wall friction angles, our method is consistent with the original Jenike methodology in the powder flow pattern assessment.
Separately, verification was also conducted through real-life hopper discharging experiments. As shown in Fig. 3, among all powders estimated, those capable of discharging under mass flow consists of only the spray dried lactose (Fast Flo 316), the coarse grade of MCC (Avicel® PH 102), or powder blend primarily composed of these two components. Mass flow pattern is possible for these two powders mainly because of the low wall friction angle associated with them (Table 2). Furthermore, the density of the spray dried lactose is significantly higher than other powders assessed in this study (Table 2), which leads to higher wall normal stress and further lowers its wall friction angle, as described in the preceding section.
For verification, the flow pattern of three common pharmaceutical excipients evaluated in our study, namely the two grades of MCC (Avicel® PH 101 and Avicel® PH 102, abbreviated as MCC 101 and MCC 102, respectively), and the spray dried lactose (Fast Flo 316), were observed experimentally. Specifically, these powders were individually discharged from a 25-L, transition-type IBC with the outlet diameter of 150 mm and side angle of 30o (IBC #5 in Table 1). Cameras were mounted above the top opening of the IBC to capture the flow pattern during the process of powder discharging (see detailed description in the “Materials and Methods” section).
The calculated $θcritical′$ values for MCC PH 101, PH 102, and spray dried lactose, as well as the predicted and observed flow patterns, are given in Table 3. For MCC 101, the calculated $θcritical′$ is significantly lower than the valley angle of the IBC, predicting a high likelihood for funnel flow. For MCC 102 and spray dried lactose, $θcritical′$ values are approximately equal to the valley angle of the IBC, suggesting that either mass flow or funnel flow is possible. It is worthy to note that due to the potential variability in the wall friction angle measurement, there is always some level of uncertainty associated with the flow pattern prediction. In fact, for mass flow hopper design, it is a routine practice to select a vertical angle 3-5o below the estimated $θcritical′$ in recognition of this uncertainty.
• Jenike A.W.
Storage and flow of solids. Bulletin 123.
Table 3The Calculated $θcritical′$ values for MCC Avicel® PH 101, PH 102, and Spray Dried Lactose, and the Estimated and Experimentally Observed Flow Patterns. The Powders Were Discharged From a 25-L,Transition-type IBC With Outlet Diameter of 150 mm and Side Angle of 30o.
Powder Type$θcritical′$ (o)IBC Valley Angle (o)Estimated Flow PatternObserved Flow Pattern
MCC Avicel® PH 1013339Funnel FlowFunnel Flow
MCC Avicel® PH 1023939BorderlineFunnel Flow
Spray dried lactose3939BorderlineMass Flow
These assessments were verified experimentally. The flow patterns were monitored and the snapshots of the powders inside the IBC during powder discharging are presented in Fig. 8. There was no flow obstruction at the IBC outlet for either material, thanks to the relatively wide outlet opening. For both MCC 101 and 102, a distinct funnel flow pattern was observed. A flow channel was developed as soon as the powder was set in motion, and was present throughout the entire discharging process (Fig. 8a and 8b). The powder flow followed the “first-in, last-out” flow sequence representative of the funnel flow pattern. In contrast, for the spray dried lactose, a flow channel was never developed. The entire powder bed inside the IBC was in motion after the bottom valve was opened, indicative of the mass flow pattern. A velocity gradient was indeed observed for the case of spray dried lactose, with the powder in the center of the IBC moving faster than at the periphery. As the consequence of the velocity gradient, the height of the powder is always lower in the center than the periphery during the process of powder discharging (see Fig. 8c). This phenomena is often observed for materials discharged under the mass flow pattern.
• Prescott J.K.
• Barnum R.A.
On powder flowability.
Table 3 shows that the predicted flow patterns are in general consistent with the observed outcome. Our assessment accurately predicted the funnel flow pattern of MCC 101. For MCC 102 and spray dried lactose, the calculation suggests that the mass flow is a possibility. While the mass flow was indeed observed for the spray dried lactose, MCC 102 continues to discharge following the funnel flow pattern. This disparity may be attributed to the uncertainty associated with the wall friction angle determination. In our study, the wall friction angles were measured using a ring shear cell, by shearing powders against a 316L stainless steel coupon with the 2B surface finish. As mentioned previously, the roughness and texture can vary to some extent for surfaces characterized as “2B”. Although both the product contact surface of the IBC and the testing coupon share the same “2B” assignment, the exact surface roughness and profile may be different, potentially leading to some level of discrepancy between the measured and actual wall friction angle. Ideally, the wall friction angle should be measured using the wall coupon constructed by the same material as the hopper section of the IBC. Additionally, because the polished metal surface possesses grain which is oriented along certain direction, it is preferred to measure the wall friction angle by allowing powders to move in translational motion (rather than circular motion) against the wall coupon, at the relative direction identical to that of the actual powder discharging. These practices can lead to more accurate determination of the wall friction angle, which is critical to understand the flow behaviors of powders inside the IBC.
In drug product development, MCC 102 is known to be an excipient powder exhibiting good flow properties,
• Thoorens G.
• Krier F.
• Leclercq B.
• Carlin B.
• Evrard B.
Microcrystalline cellulose, a direct compression binder in a quality by design environment—a review.
and the IBC used for the experiments possesses the lowest hopper side angle known to us. The fact that funnel flow pattern persists in this “ideal” powder discharging situation corroborates our argument that the funnel flow is the prevalent flow pattern for pharmaceutical powder blends in drug product manufacturing. Mass flow may be possible for powders exhibiting properties similar to those of spray dried lactose. For typical drug product development, such powder properties can potentially be achieved by processes such as high shear wet granulation or spheronization, which can lead to significant powder densification, fine removal, and size enlargement.

### Practical Significance

The powder flow pattern is an important but often overlooked attribute during IBC design or formulation development for drug product manufacture. Through this study, we discovered that several common features of the pharmaceutical IBCs, including the transition-type hopper section design and the relatively shallow hopper wall inclination, are in favor of the funnel flow pattern. Notably, the lowest side angle of all IBCs collected by us is 30o, which, in combination with its transition-type hopper design, gives rise to relatively high valley angles (≥37o) even for the IBC with the “steepest” wall inclination.
The pharmaceutical powders involved in our study cover a broad range of bulk density (from 0.26 g/mL to 0.68 g/mL), wall friction angle (from 15.2o to 32.7o against 2B surface finish under 200 Pa normal stress), and flowability (flow function coefficient from 2.3 to 18.6). The fact that the estimated cases of mass flow accounts for less than 5% of the total assessment suggests that the flow pattern is likely not a primary consideration in IBC design and selection for drug product manufacturing.
As shown in the preceding sections, determination of the powder flow pattern requires input from multiple powder properties and no single material attribute accounts for the entirety of the flow pattern. However, if one is to classify powder flow using a single property, that property would be the wall friction angle. This was demonstrated in Fig. 9, in which $θcritical′$ values of powders discharged from IBC #5 (see Table 1) were plotted with respect to powders’ bulk density, wall friction angle (under 0.2 kPa normal stress), and flow function coefficient, respectively (Table 2). It is clear that there is no clear correlation between $θcritical′$ with bulk density or flow function coefficient. In other words, heavier powders or more “flowable” powders do not always favor mass flow. A correlation was indeed observed between $θcritical′$ and the wall friction angle, although the correlation is not perfect (R2 = 0.90). This is due to the fact that the wall friction angle is stress-dependent, as highlighted in preceding sections. Nevertheless, if the flow pattern is to be investigated in a formulation or process DoE study, the wall friction angle would be the most critical attribute.
A closer examination of our data showed that the only powders used in our study, which are capable of undergoing mass flow, are the coarse grade of MCC (Avicel® PH 102), spray dried lactose (Fast Flo 316), or materials mainly composed of these two components. These two excipients share two common characteristics: 1) they are both present in the form of agglomerates, and 2) they both exhibit low wall friction angle compared to other powders tested in this study (the low wall friction angle of spray dried lactose results from its high density, which leads to high wall normal stress and consequently low friction angle). Essentially, for the type of IBCs available in drug product manufacturing, having exceedingly low wall friction angle is the key to allow for mass flow. Based on our evaluation, a maximum effective wall friction angle of 11o is required, beyond which the funnel flow is likely to dominate. The low wall friction angle may be achieved by means of either formulation and process changes or equipment changes. In current drug product development, the texture and roughness of the product contact surface for the IBCs are often limited due to equipment availability. The most efficient means is therefore through formulation and process adjustments, in particular granulation of powders. In most cases, granulation gives rise to coarse particles exhibiting higher bulk density as well as lower extent of particle-wall interaction, both of which serve to reduce effective wall friction angle. Hancock
• Hancock B.C.
The wall friction properties of pharmaceutical powders, blends, and granulations.
assessed the wall friction angles of 30 API-containing granules and showed that the average wall friction angle against the 2B surface finish (under 622 Pa normal stress) is 17.0o. The value is reduced to 11.3o for the electro-polished 2B surface finish. The data suggests that the mass flow pattern may be enabled for granules, especially for IBCs fabricated with smoother product-contacting surface. Therefore, the prevalence of funnel flow for pharmaceutical granules could differ from this study, and may be of an interest in drug product manufacturing. However, for pharmaceutical powders upstream of the granulation process, the chance powder discharging under mass flow is slim.
The method we presented here can also be employed as a part of the formulation and process quality risk assessment. Because powder flow and wall friction measurements through ring shear testing are common practices in drug development, such information can be recruited as independent variables, from which the critical angle for mass/funnel flow can be determined as a dependent variable. Consequently, a response surface model, which involves the flow pattern, may be generated to assist the formulation and process development.
Finally, it is reminded that the method presented in this study only applies to batch manufacturing operations, in which powder can fall freely through the outlet opening of an IBC. In light of the emerging continuous manufacturing, modification to this method is necessary. The main reason is that in continuous manufacturing, a feeder is usually installed beneath the hopper outlet in order to control the feeding rate.
• Blackshields C.A.
• Crean A.M.
Continuous powder feeding for pharmaceutical solid dosage form manufacture: a short review.
Owing to this design, the lower surface of the powder bed cannot be considered as unconfined during powder feeding, and therefore the passive stress condition, as delineated in Equations (3), (4), (5), no longer applies. The stress distribution of the powder in this set-up is intricate because the assumption underlying the passive stress state calculation (the hypothetical apex of the hopper has zero stress) is no longer valid, and erratic flow patterns (such as eccentric flow) can take place.
• Schulze D.
Stresses in silos part 2: stresses in hoppers–disturbances to the stress distribution.
The powder flow pattern in the continuous manufacturing setting is therefore of great relevance and warrants future studies.

## Conclusion

The use of Intermediate Bulk Container (IBCs) for powder processing is becoming an increasingly common practice in modern drug product manufacturing. In light of this trend, we conducted the study to assess the flow pattern of the pharmaceutical powders when they are discharged from the IBCs. The flow pattern was estimated on the basis of the radial stress field theory originally developed by Andrew Jenike.
• Jenike A.W.
Storage and flow of solids. Bulletin 123.
The method was modified by us to take into account the stress-dependence of wall friction angle, which is critical but currently not considered as a routine practice.
The methodology was applied to 13 distinct pharmaceutical powders exhibiting diverse flow properties. For each powder, the flow pattern was estimated in 20 IBCs possessing different size and geometry. A total of 260 powder flow patterns were calculated. The results showed that the funnel flow dominates; mass flow only accounts for less than 5% of the estimated cases.
The prevalence of funnel flow pattern is attributed to both the equipment geometry and material properties. Due to practical considerations, the hopper section of the IBCs is usually not exceedingly steep. Furthermore, the hopper section exhibits the transition-type geometry, giving rise to higher valley angles favoring the funnel flow pattern. With respect to the material attributes, a monotonic decrease of wall friction angle with increasing wall normal stress was observed for all pharmaceutical powders tested. Because the wall normal stress applied by the hopper wall is low under the passive stress state, the wall friction angle is typically not low enough to enable mass flow. Through this exercise, we also discovered that the powder density and outlet diameter of the IBC can have an impact on powder flow pattern. These attributes are apart from the material properties and hopper attributes known to contribute to the flow pattern based on the radial stress field theory. The effect of powder density and outlet diameter stems from the stress-dependence of wall friction. Use of dense powder or IBCs with wide outlet increases wall normal stress, leading to reduced wall friction angle and therefore, improves the chance of mass flow.
Our methodology was experimentally verified through observation of the real-life powder flow pattern, upon discharging the three common pharmaceutical excipients from a 25-L transition-type IBC. The method accurately predicted the funnel flow pattern for the fine grade of MCC. For both the coarse grade of MCC and spray dried lactose, the predicted outcome is borderline mass flow/funnel flow, indicating a possibility for mass flow in these materials. Indeed, a distinct mass flow pattern was observed for the spray dried lactose, while the funnel flow pattern persisted for the coarse MCC. The difference between these two materials, despite the identical predicted flow pattern, is likely due to the uncertainty associated with the wall friction angle measurement.
In summary, both the theoretical calculation and the experimental observation demonstrate that the funnel flow is the prevalent flow pattern, concerning discharging of pharmaceutical powder blends from modern IBCs. Mass flow may still be possible, in particular through granulation processes giving rise to materials with substantially high density and low wall friction angle, and in combination with using IBCs with steep hopper section and large outlet opening diameter.

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