The Packing Coefficient: a Suitable Parameter to Assess the Flow Properties of Powders

A parameter, defined by Gabaude et a!. in a previous work [ 1], was further investigated for its ability to evaluate flow properties of particulate materials. It is based on the volume reduction of the powder bed under low compaction pressure. Compaction data and the packing coefficient (C1= [ (H0 Hp) /H0].100) were analysed over a [0-1] MPa pressure range. Comparison of the C1 value with the flowability index (i) determined by ]enike shear cell measurements demonstrated the reliability of this packing coefficient to assess powder flow properties using small quantities of powder ( < 1 g). This method appeared to be helpful for an adequate determination of flowability in the early stages of drug development. Finally, because the packing assessment is performed in a compression die, improvement in the prediction of the weight variation of tablets is expected, as compared with other methods of flowability assessment.


Introduction
There is a need in the pharmaceutical industry for easy tests to enable characterisation of the flow properties of materials to be used in tab letting or capsule filling. Indeed, poor flowability of powders or granules can result in irregular weight and low production performances. During the past 40 years, a lot of methods have been developed to assess the flow properties, including the measurement of angle of repose, mass flow rate or compressibility (reduction in volume of a powder bed due to the application of taps). Even though these methods are quite simple, they do have their limitations. The results obtained are significantly affected by experimental conditions [2], and a lack of accuracy has been reported in the case of cohesive powders [3,4]. It is also admitted that these methods measure derived properties and are unable to represent the intrinsic flow properties of powders [5]. Finally, they also require large amounts of product ( Pharmacopeia for the determination of tapped density, for example).
Against the inadequacy of the methods cited above, more sophisticated and accurate techniques such as shear cell measurements have been used for testing the flowability of powders [5,6]. The flowability index measured by the Jenike shear cell in particular has been shown to correlate with tablet weight variations [2]. Despite the accuracy in predicting flowability during tab letting, shear measurements are seldom used in the development of a drug product because they are time-and product-consuming.
Another approach to assess flowability consists in investigating the first compression stage of a compression cycle. Actually, several stages have been identified during the compression of powders [7]: (i) filling of the die; (ii) densification by particle slippage and packing; (iii) elastic and plastic deformation of particles; (iv) cold welding, with or without fragmentation. York [7] used the Heckel equation to analyse compressional data and attributed the initial curvature of the Heckel plot to particle slippage and rearrangement. However, he did not correlate the packing fraction that quantified this part of the curve with the flow properties of the powders, but only linked the increase of the packing fraction to the decrease of the particle size. Furthermore, in our opinion, the breakage of aggregates to primary particles is likely to be included in this parameter as the pressure range taken into account in that paper can extend to 10 MPa.
In the present study, a parameter to assess flow properties, derived from the work of York [7] and presented in a previous work [1], is further investigated. The method is based on the volume reduction of the powder bed corresponding to the first part of the force-displacement compaction curve. The purpose of this complementary work is to determine more precisely the end-compaction pressure to be considered for the calculation of the packing coefficient: where Hp is the powder bed height under pressure P and H 0 the initial height.
Hence the C 1 values of a large range of products (powders, mixtures and granules of various sizes, shapes and behaviour during compaction) have been investigated using as end-compaction pressure P, a pressure ranging from 0 to 1 MPa and correlated to the Jenike flowability index.

Materials
The products used (Table I) constituted a representative selection of pharmaceutical products, with Powders (drug and excipients) were used as received.
Mixture 2 (M2) is a binary mixture with the same chemical composition as mixture 1 but, in this blend, the two excipients Oactose and cellulose) are associated in the co-processed Cellactose®.
Mixture 3 is a formulation by simple blend supplied by the Pharmaceutical Sciences Department of Sanofi-Synthelabo Recherche (patented product). Dry granules (G3D) and lubricated dry granules (G3DL) of mixture 3 were also analysed. The compaction was manufactured on an Alexanderwerk WP 150 roller compactor followed by sizing of compact on a mesh screen of 1.25 mm, and hydrogenated oil was used as lubricant mixed with G3D leading to G3DL.

Packing measurements
The evolution of the apparent density of a powder bed in a volumetric cylinder subjected to successive vertical vibrations was followed using the Erweka Model SVM2 unit (Erweka GmbH, Heusenstamm, Germany). The measurements were made in a 250-mL cylinder with 100 g of product, except for HAP200 and HAP400 which were only available in small quantities. For these granules, the experiments were conducted in a 125-mL cylinder with 25 g of product.
The reduction in powder volume was estimated by two parameters: -the difference between the volumes after 10 and 500 shocks <Vw-V5oo).
-the Carr index calculated as follows: ere max lS e maxlffiUm tappe max density and d 0 the bulk density after filling

Flow rate measurements
Mass flow through a funnel was determined according to the European Pharmacopeia recommendations (3rd edition, 2.9.16 <<ecoulement>>).

Shear cell measurements
The product flow properties were analysed using a shear cell designed by Jenike [5,6] (Figure 1). The apparatus is composed of a base and a ring, which are filled with the tested material, and a cover on which a vertical force V is applied. Preconsolidation of the product is carried out by applying a vertical consolidation force Vc (corresponding to a consolidation stress ac varying between 3 and 10 kPa) and a num- ber of oscillating twists. Consolidation is completed in a second stage by applying a shear force S and causing the specimen to flow under the same normal force Vc until a steady state is reached. When consolidation is completed, the vertical compacting force Vc is replaced by a smaller vertical force V, and a shearing force S is applied until a failure plane has developed corresponding to the shear strength 't. The measurement of several points (cr, 't) allows determination of a yield locus (Figure 2). From one yield locus, two Mohr semi-circles are drawn. The first one is drawn through the origin tangentially to the yield locus. The point of intersection of this semi-circle with the a-axis determines the value of the unconfined yield strength fc. The second Mohr semi-circle is drawn through the end-point (a, 't) tangentially to the yield locus. The major consolidating stress a 1 is determined by the intersection of the circle with the a-axis. The determination of the flowability of the bulk solid requires the determination of (fc, a 1 ) values for at least three consolidation stresses ac. From these points, the flow-function FF (fc=f(a 1 )) can be drawn. As indicated on Figure 3, the flowability of bulk solids can be classified according to the flowability index (i), which corresponds to the inverse of the slope of the flow-function. This procedure has been retained in order to ensure a more accurate determination of the i-values and fit in a better way the experimental points, as the flow-function is not a straight line through the origin.

Compression
Compression was performed using a Lloyd 6000R uniaxial press, Lloyd instruments Ltd., Segensworth East, England, UK. The die, 1 cm 2 in surface and 1 em in depth, was lubricated with magnesium stearate before compaction. The die (1 cm 3 ) was manually Yield loci f'c f"c f"'c Flow-function and classification according to the flowability index (i) [5] filled with an accurate mass of product, calculated from the bulk density of the materiaL Compression was performed by the displacement of the upper punch at a speed set at 1.14 mm/min. The pressure was measured by an accurate gauge and the upper punch displacement was measured with an external LVDT extensometer. Compression data (displacement as a function of pressure) were collected until the predefined pressure was reached. Only the beginning of the curve will be discussed here (0 to 1 MPa).
In the work of Gabaude [1], a packing coefficient C 1 was defined to quantify the first compression period that was assumed to correspond to packing and slippage of the particles. It was suggested that this packing of the powders was fully achieved when the pressure at the upper punch had reached 0.5 MPa.
The packing coefficient was based on the powder bed In the present work, the packing coefficient has been calculated not only for 0.5 MPa but in steps of 0.05 MPa for pressures ranging from 0 to 1 MPa in order to determine more precisely the pressure influence on the calculation of the C 1 value. Three compression cycles were analysed for each sample.

Packing and flow rate measurements
It is generally accepted that a V 10 -V 500 value greater than 20 ml indicates the presence of air entrapped between the particles and consequently a high compressibility which hinders the flowability of the product [10,11]. Concerning the flow rate, a value of at least 10 g/s is required to ensure uniform flow. On the basis of these parameters and according to Carr's classification [12], results presented in Table II  of Cellactose®, a co-processed excipient especially designed for direct compression, is not sufficient to correct the very poor flow properties of anhydrous theophylline as shown by the high Icarr value of M2 (27.2%). All granules, except the wet granules of mixture 1 (GlW), are considered to have passable flow properties based on their Icarr index being higher than 18%.

Shear cell measurements
The flow properties of the products that were available in large quantities were only investigated using the shear cell method (Figures 4 and 5 and Table  III). From these measurements, the excipients appear to be free-(Cellactose® and Pharma 200/70) or easy-flowing powders (Avicel PH101), whereas theophylline is cohesive. The three mixtures are classified as easy-flowing according to their flowability index, but it must be said that the flow-functions of Ml and M3 are located in the cohesive area ( Figure 5). As expected, granulation improved the flow properties of Ml and M3 since the flow-functions of GlD/GlW and G3D are located in the easyflowing area. The effect of lubrication appears clearly with the improvement of the flowability index of G3DL versus G3D (from i=6.5 to 25.7).

Volume reduction on uniaxial press
The evolution of the packing coefficient as a function of the pressure is presented on Figures 6 and 7. All products display an inflection point P (mentioned in Table IV Evolution of the C, value (%) as a function of the compaction pressure (MPa) P is the pressure at the intersection C 1 p is the C, value at the intersection tion between C 10 . 5 and the C 1 corresponding to the slope change is about 8%, but this leads only to a very small modification in the ranking of the products as shown in Table V (the classification of GlD and G3D only are modified). Furthermore, this variation has no consequence on the classification of the products: all powders (except pharma 200/70), the three mixtures, and HAP200 have a packing coefficient above 25%, whereas granules are classified as products having good flow properties, whatever the calculation method used. For the purpose of defining a standardised parameter to compare the packing of different products, it seems that the choice of 0.5 MPa is appropriate. For most of the products, the packing stage can be considered as completed without any fragmentation or deformation of the particles as the applied pressure is very low.

Discussion
The comparison of the packing coefficient C 1 with the flowability index i ( Figure 8  stress region applied. Globally, materials with a low C 1 have easy-or free-flowing properties according to the Jenike classification, whereas products with a high packing coefficient have a low flowability index, which is characteristic of poor flow properties. Thus a rapid assessment of the flow properties of a product can be obtained from the analysis of the first part of its compression curve. It should be noted that some products classified as easy-flowing (Avicel and the three mixtures) or freeflowing (Cellactose®) according to Jenike are considered to have inadequate flow properties according to their packing coefficient. This observation indicates that this new parameter seems to be more "reliable" than the flowability index determined by Jenike shear cell measurements. One hypothesis that could explain this discrepancy is the fact that considering only the flowability index reduces the information given by the flow-functions. In particular, the flow-functions of mixtures M1 and M3 ( Figure 5), which are classified as easy-flowing products based on their flowability index, are situated in the cohesive area which is in accordance with their high C 1 value. Likewise the flowability index of Cellactose® is one of the best of the products under consideration, whereas the C 1 value is not as favourable (higher than 25%). In fact, mass flow through a funnel and tapped density measurements confirm this result; in spite of a high flow rate (16.2 g/sec), the flow properties of Cellactose® are not as good, as shown by the Icarr value (17.5%), which indicates relatively high compressibility of the product. This tabletting limiting characteristic is indicated by the packing coefficient of Cellactose® around the limit value of 25%. Thus, this method permits better discrimination of the products with poor flow properties, as for example M3 and G3D, than the flowability index measured by Jenike shear cell, and fits rather well with our objective which is to characterise and classify products available in small quantities in the early stages of drug development.
Particulate materials with a C 1 value below 25% can be considered to have adequate flow properties for industrial use, while a higher packing coefficient indicates too much compressibility that has to be corrected by the formulation and/ or the manufacturing process.

Conclusion
This work has confirmed the possibility of investigating the flow properties of particulate materials by means of the packing coefficient calculated at 0.5 MPa. This new method has the advantage of being very easy, rapid and above all of requiring very small amounts of product. It has been shown to be in good correlation with flow-functions results and furthermore to better discriminate cohesive materials. In a recent paper, J.K. Prescott and R.A Barnum [13] specified that flowability is not an inherent material property, but is rather a result of the combination of material physical properties and the equipment used. As the packing assessment is performed in experimental conditions close to the industrial ones, i.e. in a compression die, improved prediction of the weight variation of tablets as compared to other methods may be expected, although parameters such as speed or punch shapes have not been taken into account. In addition, the flow properties assessed by the packing coefficient are less favourable as compared to the results from other methods, more efficiently preventing flow problems that can occur in a given application. 92