The Influence of Particle Size Distribution and Tapping on the Bulk Density of Milled Lactose Powders

Transcription

1 The Influence of Particle Size Distribution and Tapping on the Bulk Density of Milled Lactose Powders Horng Yuan Saw 1,2, Clive E. Davies 1,2, Anthony H.J. Paterson 1 and Jim R. Jones 1 1 School of Engineering and Advanced Technology Massey University, Palmerston North 4442, New Zealand H.Y.Saw@massey.ac.nz 2 Riddet Institute, Massey University, Palmerston North 4442, New Zealand C.Davies@massey.ac.nz Abstract When an external force is applied to a bed of loosely packed powder via tapping, the particles in the bed rearrange themselves and fill up the inter-particle voids, resulting in higher packing density. The rearrangement of particles is dependent on size distribution, level of fines, magnitude of inter-particle forces, and operating parameters like number of taps and powder bed drop height. In this study, we report the tapped density, ρ tap, of thirteen milled lactose powders obtained with a tapping apparatus (3 mm drop height, ~240 strokes min 1 ) in the range of taps, in accordance with the European Pharmacopeia. The ρ tap profiles can be modelled with the Kawakita powder compression equation, [(ρ tap ρ 0 )/ρ tap ]=[a t b t N/(1+b t N)], where ρ 0 is the initial bulk density, N is the number of taps, and a t and b t are fitting parameters that reflect the compression characteristics of the powder. Our a t and b t data are consistent with literature values for lactose powders; a t relates well with particle size but b t data show significant scatter. On a heuristic basis, parameter a t is further correlated with surface-volume mean particle diameter, d* 32, span of the particle size distribution, (d 90 d 10 )/d 50, and the fraction of fines less than 45 μm, F 45. A power law relationship in the form of a t =m([1/d* 32 ][(d 90 d 10 )/d 50 ][exp(f 45 )]) n is found; the product ([1/d* 32 ][(d 90 d 10 )/d 50 ][exp(f 45 )]) accounts for the combined influence of particle size distribution on powder compressibility. Our findings are potentially useful in the handling and packaging of food and pharmaceutical materials. Keywords- bulk density; Kawakita equation; lactose; particle size distribution; powder compression; tapped density I. INTRODUCTION Bulk density is an important physical property in the characterization, handling, and processing of powder systems. It is the mass divided by the total volume occupied, taking into account the inter-particle and intra-particle voids in a bed of powder. There are two common bulk densities, namely loose poured bulk density, ρ LB, and tapped bulk density, ρ tap. Loose poured bulk density is the density of a powder that is poured into a container and allowed to settle gently; it is a measure of random loose packing. Tapped density is the density obtained after a loosely packed powder bed is densified with an external force to achieve higher particle packing; it is a measure of random dense packing, see the review in [1,2]. The ratio ρ tap /ρ LB is known as Hausner ratio, H R [3], and it is commonly used as a crude powder flow descriptor; see for example [1]. The bulk density of a powder is dependent on its particle size distribution. It has been experimentally demonstrated that both ρ LB and ρ tap relate well with surface-volume mean particle diameter, d 32, and the content of fines; H R increases when d 32 decreases and fines level increases [1]. As d 32 decreases, the powder becomes more cohesive and occupies more volume in the loosely poured state than free flowing particles; they have greater interparticle forces and internal bed strength to maintain bed structure. But when an external force is introduced to the cohesive powder bed, the interparticle forces are overcome and the volume reduces significantly, hence giving higher H R values. In this paper, we report the influence of particle size, span of the particle size distribution, and fines level on the bulk density of fine lactose powders, which have wide applications in the food and pharmaceutical industries. A tapping apparatus with a 3 mm drop height and ~240 strokes min 1 tapping rate was used; following the European Pharmacopeia the number of taps was up to 1250 taps [4]. This work forms part of a wider study in which the physical and flow properties of fine powders are characterized. The findings here can potentially benefit the food and pharmaceutical industries in areas like powder compression and packaging of fine materials.

2 II. EXPERIMENTAL III. ANALYSIS A. Sample Preparation A total of 13 model milled lactose powders were used, and each powder was designated a code, see Table 1. Three powders, which were commercial lactose of DMV-Fonterra Excipients, New Zealand, were used as received (unsieved), namely lactose monohydrate Pharmatose 70M (LP1), Pharmatose 350M (LP4), and Hydrous Refined Lactose 100- Mesh (LM1). The other ten powders were made by sieving either LP1 or LM1; further details are available in [5]. B. Measurement of Particle Size Distribution Particle size distribution was measured on the volumeweighted basis by the laser diffraction method (Mastersizer 2000, Malvern Instruments Ltd., UK); the 300 RF lens and small volume sample unit with isopropanol as the dispersant were used. The refractive index of lactose (1.533) and isopropanol (1.378), and the default Polydisperse model were selected. Table 1 lists the size distributions; diameters d 10, d 50, and d 90 represent particle size at 10%, 50%, and 90% in a cumulative size distribution respectively. The span of a size distribution is given by (d 90 d 10 )/d 50. Parameter d* 32 is the surface-volume mean diameter calculated with the Mastersizer data using bins equivalent to a full sieve analysis according to BS 410; powder in the range 0 38 μm was grouped together and assigned a mean diameter 19 μm, see [5]. Parameter F 45 is the fraction of fines smaller than 45 μm. C. Measurement of Loose Poured and Tapped Densities Loose poured bulk density, ρ LB, was measured following a modified New Zealand standard [6]. About g of material were poured vertically into a 500 ml cylindrical container through a cone (46.6 o internal angle; 12.7 mm orifice diameter); the distance between the cone outlet and container brim was ~70 mm. In cases where the powder did not flow through the cone, manual stirring with an art brush was applied. Excess powder on the container was gently scraped off with a steel ruler, and the filled container was weighed. Measurements were done in triplicate; the mean values were calculated. Tapped density, ρ tap, measurements were based on a method for dry dairy products [7] and the European Pharmacopeia [4]. A Stampfvolumeter tapping machine (STAV 2003, Engelmann, Germany) with a 3 mm drop height and a tapping rate of ~240 taps min 1 was used. The machine comprised a 100 ml cylindrical cup of mm internal diameter, which was extendable by 35 mm in height with a stainless steel extension. For very fine lactose powders, a cylindrical cardboard tube of a similar diameter and 100 mm in height was needed and attached to increase the powder mass. The number of taps used was 10, 35, 100, 180, 500, 1000, and At each increment, the extension was removed carefully and excess material on the 100 ml cup was gently scraped off with a steel ruler; the amount of material in the cup was then weighed. Repeat measurements were made on selected samples and the results were reproducible. In the first part of this work, the relationships between d* 32 and (d 90 d 10 )/d 50, and between d* 32 and F 45 were evaluated; d* 32 was plotted against (d 90 d 10 )/d 50, and 1/d* 32 was plotted against F 45. In the second part, the Kawakita model [8], Equation 1, was used to assess tapped density as a function of number of taps; N is number of taps, m tap is sample mass after Nth tap, m 0 is sample mass in the loose poured state, and a t and b t are fitting parameters that reflect the characteristics of the powder. Rearranging Equation 1, and taking into account a constant volume tapping system, Equation 2 was obtained; the values of a t and b t were obtained by linear regression. ρ tap ρ 0 ρ tap = a t b t N 1+ b t N (1) m tap N m tap m 0 = 1 a t N + 1 a t b t (2) Lastly, the relationships between parameters a t and b t and particle size distribution were investigated; both a t and b t were respectively plotted against d 50, 1/d* 32, and the product ([1/d* 32 ][(d 90 d 10 )/d 50 ][exp(f 45 )]). IV. RESULTS Table 1 shows the particle size distribution, d* 32, and fines level of the milled lactose powders. TABLE I. PARTICLE SIZE DISTRIBUTION, SURFACE-VOLUME MEAN PARTICLE DIAMETER, AND FINES LEVEL OF MILLED LACTOSE POWDERS Lactose Particle diameter [μm] Level of d 10 d 50 d 90 d* 32 fines <45 μm, F 45 [-] LP LM LM LM LM LM LM LP LM LM LP LM LP Figure 1 shows d* 32 plotted against span (d 90 d 10 )/d 50 ; the mean particle diameter increases with decreasing span. There are also irregularities in the plot; the sieved powders deviate from the trends exhibited by the powders that are used as received. In Figure 2, the reciprocal of d* 32 is plotted against F 45 ; as expected mean particle diameter decreases as fines level increases. The data for unsieved and sieved powders seems to fall on one line.

3 Figure 4 shows the relationship between parameter a t and d 50, and in Figure 5 the relationship between parameter b t and d 50 ; for comparison purposes some data from the literature [9,10] are included. Parameter d 50 is used because d* 32 values are not reported in the work cited. By inspection of Figure 4, a t generally increases with decreasing d 50 ; our data are consistent with the milled lactose data by Soh et al. [9] and Ilić et al. [10]. However, agglomerated and spray-dried lactose powders seem to show different trends. Referring to Figure 5, the milled lactose data are scattered and there is difficulty in defining clear trends. And consistent with Figure 4, the agglomerated and spray-dried lactose powders seem to exhibit trends different from the milled lactose. Figure 1. Plot of d* 32 versus span (d 90 d 10)/d 50. Figure 4. Plot of parameter a t versus d 50 for lactose powders. Figure 2. Plot of 1/d* 32 versus F 45. Figure 5. Plot of parameter b t versus d 50 for lactose powders. Figure 3. Plot of ρ tap versus N for lactose LP4 and LP3. Figure 3 shows the tapped density profiles of lactose LP4 and LP3, plotted to illustrate the significance in density changes when powder cohesiveness increases. For free flowing LP3, the change in ρ tap is relatively small with increasing taps. But with LP4, which is the most cohesive sample used, ρ tap increases significantly from ~530 to ~780 kg m 3. Figure 6 shows a t increasing almost linearly with 1/d* 32 for both unsieved and sieved lactose powders. In Figure 7, the b t data are scattered, but seem to increase to a peak and then decrease. In Figure 8, a t is plotted against ([1/d* 32 ][(d 90 d 10 )/d 50 ][exp(f 45 )]) and a power law relationship is observed for both unsieved and sieved lactose powders, giving Equation 3 with an R 2 of a t = d * 32 d 90 d 10 exp(f 45 ) d (3)

4 Figure 6. Plot of parameter a t versus 1/d* 32. Figure 7. Plot of parameter b t versus 1/d* 32. Figure 8. Plot of parameter a t versus ([1/d* 32][(d 90 d 10)/d 50][exp(F 45)]). V. DISCUSSION There are three ways to densify a bed of powder, viz tapping, vibration, and mechanical compression; in this work only tapping was used. During tapping, powder densification happens in an unconfined condition; the particles are forced to jump and lose contacts with adjacent particles. Due to the relative particle motion, the particles rearrange themselves and fill up the voids in the powder bed, resulting in higher particle packing [1,2]. We have assumed that no particle deformation occurs to the crystalline lactose particles. The relationship between ρ tap and N can be modelled; many empirical mathematical expressions are available, see for example the list compiled by Kawakita and Lüdde [8], and their use is common and convenient. We have chosen the Kawakita equation because of its applicability with different powders and low number of taps, as demonstrated by others [9 12]. The model is simple and contains only two fitting parameters, a t and b t. However, though any physical significance is unclear we have examined our data for correlation between these fitting parameters and the physical properties of the test powders. The parameter a t for various types of powders has been reported to increase with decreasing particle size [8,11]; the lactose data in Figure 4 show a similar trend. The data in the figure also suggest that the a t :d 50 relationship is material specific; agglomerated and spray-dried lactose powders do not seem to follow the milled lactose trend. The reason can be attributed to the differences in particle shape, asperities, and moisture content, which are factors that can affect particle packing. Microscopic images and more experimental data are required to make further deductions. Referring to Figure 6, parameter a t correlates well with the reciprocal of d* 32, which is a measure of the ratio of particle surface area to volume; 1/d* 32 has been used previously in a correlation that relates the cohesion of compacted powder beds to surface area per unit volume and compaction forces [5]. According to Yamashiro et al. [11], parameter b t generally increases with increasing particle size; when their data are plotted, scatter and discontinuities are observed because their powders, e.g. glass beads, calcium carbonate, iron powders, and talcum, are very different in their physical properties. Referring to Figure 5, scatter and discontinuities are also seen with lactose powders, possibly because of the unaccounted differences in other physical properties besides particle size. In Figure 7, b t seems to peak at a value of 1/d* 32 of about 20,000 m 1 ; we are also not able to explain the apparent increasing and decreasing trend. Parameter a t represents the asymptotic value of [(ρ tap ρ 0 )/ρ tap ] when N approaches infinity and equals [1 (1/H R )]; see [12,13]. Yu and Hall [12] related a t and b t empirically to a limiting Hausner ratio the ratio at very high number of taps, H R, achieved with manual tapping and proposed Equations 4 and 5 for alumina and silicon carbide powders. A similar approach but using Hausner ratio at 1250 taps, H R,1250, gives Equation 6 with an R 2 of 0.99; thus a t is equal to [1 (1/H R,1250 )] for the milled lactose powders. No satisfactory correlation is found for b t ; it is numerically small compared to a t and is consistent with the limit of Equation 1 as b t approaches zero. Averaging the b t data gives a value of with a standard deviation of

5 a t = H R, b t = H R, a t = H R, To date, there is no conclusive report in the literature on how parameters a t and b t relate to the key descriptors of a particle size distribution, namely d* 32, (d 90 d 10 )/d 50, and fines content F 45 for example, which also influence each other, see Figures 1 and 2. On a heuristic basis and as shown in Figure 8, a t relates satisfactorily with the function ([1/d* 32 ][(d 90 d 10 )/d 50 ][exp(f 45 )]), which can represent the influence of a size distribution. The term exp(f 45 ) is also found in correlations for the characterization of bed collapse phenomena in fluidized beds [14]. CONCLUSIONS Thirteen milled lactose powders were densified via tapping following the European Pharmacopeia procedure and the changes in bulk density were characterized with the Kawakita equation that comprised fitting parameters a t and b t. The parameters showed initial trends relating to particle size, and further attempts were taken to correlate them with 1/d* 32, (d 90 d 10 )/d 50, and F 45. Parameter a t was observed to be a function of ([1/d* 32 ][(d 90 d 10 )/d 50 ][exp(f 45 )]) and related well to Hausner ratio at 1250 taps. Parameter b t was numerically small and no conclusive correlation with material properties was identified. (4) (5) (6) References [1] E. C. Abdullah, and D. Geldart, The use of bulk density measurements as flowability indicators, Powder Technol., vol. 102, pp , [2] A. Santomaso, P. Lazzaro, and P. Canu, Powder flowability and density ratios: the impact of granules packing, Chem. Eng. Sci., vol. 58, pp , [3] H. H. Hausner, Friction conditions in a mass of metal powder. Int. J. Powder Metall., vol. 3, pp. 3 17, [4] A. Schüssele, and A. Bauer-Brandl, Note on the measurement of flowability according to the European Pharmacopoeia, Int. J. Pharm., vol. 257, pp , [5] H. Y. Saw, C. E. Davies, J. R. Jones, G. Brisson, and A. H. J. Paterson, Cohesion of lactose powders at low consolidation stresses, Adv. Powder Technol., vol. 24, pp , [6] SANZ, Method for determining voids content, flow time and percentage oversize material in sand, in NZS 3111:1986 Methods of Test for Water and Aggregate for Concrete, Wellington: Standards Association of New Zealand, 1986, pp [7] Niro, Method No. A2a Packed bulk density by the Niro method for milk powders and protein products, in Analytical Methods for Dry Milk Products, Copenhagen: A/S Niro Atomizer, 1978, pp [8] K. Kawakita, and K. H. Lüdde, Some considerations on powder compression equations, Powder Technol., vol. 4, pp , [9] J. L. P. Soh, C. V. Liew, and P. W. S. Heng, New indices to characterize powder flow bases on their avalanching behavior, Pharm. Dev. Technol., vol. 11, pp , [10] I. Ilić, P. Kása Jr., R. Dreu, K. Pintye-Hódi, and S. Srčič, The compressibility and compactibility of different types of lactose, Drug Dev. Ind. Pharm., vol. 35, pp , [11] M. Yamashiro, Y. Yuasa, and K. Kawakita, An experimental study on the relationships between compressibility, fluidity and cohesion of powder solids at small tapping numbers, Powder Technol., vol. 34, pp , [12] A. B. Yu, and J. S. Hall, Packing of fine powders subjected to tapping, Powder Technol., vol. 78, pp , [13] J. Malave, G. V. Barbosa-Canovas, and M. Peleg, Comparison of the compaction characteristics of selected food powders by vibration, tapping and mechanical compression, J. Food Sci., vol.50, pp , [14] D. Geldart, and A. C. Y. Wong, Fluidization of powders showing degrees of cohesiveness 2. Experiments on rates of de-aeration, Chem. Eng. Sci., vol. 40, pp , 1985.