Predicting bulk density of pharmaceutical powder formulations – industrially applicable approach

Abstract

Bulk density (ρ_b) serves as a fundamental powder parameter across various industries. In the pharmaceutical industry, its implications on powder behaviour are well known through various processing stages and unit operations. Since the measurement of ρ_b is an ordinary analysis during formulation development, the ability to predict ρ_b could streamline this stage, saving both time and material resources.

The objective of this study was to establish an easy-to-use and industrially relevant predictive model for the ρ_b of binary mixtures, leveraging data derived from pure materials. Two distinct methodologies grounded in the principles of flow behaviour in packed beds and the computation of the equivalent hydraulic diameter were developed. The first approach conceptualises the particles of one material as a matrix, the voids within it are being filled by the particles of the second material. The second method entails a theoretical calculation of the particle size distribution of the mixture, using particle size fractions obtained from sieve analysis of the individual materials. The fractions of the calculated distribution are subsequently combined, incorporating the smaller size fractions sequentially into the larger fraction voids.

Finally, the developed method could be considered industry relevant. Its application in the pharmaceutical industry might be easily implemented and widely used during the development stage. Moreover, it can reduce time and financial costs of the designed formulation. While it is yet to be tested, the size selective method is not principally limited to binary mixtures and it can be extended to multi-component mixture without altering the fundamental principle.

Introduction

Bulk density (ρb) is an important parameter of particulate materials and is often used to characterise powders throughout the pharmaceutical and food industries. Moreover, it can be implemented as a part of the product specifications in quality control. ρb is generally defined as a mass of powder m (g) divided by its volume V (cm3) as expressed in eq. (1).
(1)

However, unlike solid materials, in particulate materials, the volume consists of both a solid and a bulk voidage. Based on European pharmacopoeia, ρb is experimentally determined using either a graduated cylinder (250 ml, readable to 2 ml), volumeter or cylindrical vessel and 100 g of tested powder ([1], [2], [3]).

Since powders are dispersed systems, ρb needs to be correlated and/or specified according to the conditions to which powders are subjected. ρb is mainly evaluated as a poured density when the powder is gently poured into the vessel and carefully levelled without compacting (2,3). However, the bulk density of particulate materials and/or powders can be altered via simple processes such as gas fluidization, application of defined repetitions of taps or application of pressure (2). The mere disturbance of the powder bed may result in a changed ρb. Thus, the ρb of a powder is often very difficult to be measured with good reproducibility (3).

The knowledge of ρb can help to clarify powder behaviour at many stages of product preparation. Previous studies have discussed the importance of ρb and powder packing on various unit operations, such as blending, tableting, roller compaction, encapsulation, extrusion, etc. (4,5). For example, the density of the materials closely correlates with parameters during compaction and feeding (6). Moreover, powders with low density (high voidage) are more sensitive to the application of confined conditions or vibration and change their volume more easily. Such powders can evince a broad range of ρb across the operational steps they are subjected to, resulting in very diverse behaviour. This also means ρb should be discussed only under the same conditions as the concerned operational step. As a result, understanding how various testers might influence the ρb of tested material is of great interest (1,7,8). It is also stated that the importance of ρb is not only in its absolute value but is related more to the changes in the values as a response to the effects occurring in the process steps that powders go through. Such changes might be important and valuable indicators regarding the powder rheological properties in various unit operations (1).

The bulk density of particulate materials plays an important role in the success of an operation. ρb is a critical parameter with respect to the filling volume of the tablet dies and capsules. Moreover, the correlation between ρb and tablet hardness was confirmed for mixtures containing lactoses ([9], [10]). Next, powders with low ρb are not generally convenient for roller compaction (11).

ρb itself is affected by many factors. It is well-known that particle characteristics such as particle shape and particle size with particle size distribution play a significant role (12,13,14). Spherical particles and particles with high sphericity show better packing and thus higher density than the more angular ones (1,13,15). For instance, the combination of almost spherical particles having different particle sizes leads to the highest density in a specific mixing ratio. Next, the addition of fine particles to the coarse particles might cause their strong adhesion preventing the percolation of fine particles to the bottom of the powder vessel (1). What is more, attempts to link ρb with the microstructure of cohesive fine powders were also made and defined ρb as an effective tool for the characterisation of structured agglomerates or aggregates of cohesive powders (16,17). In the case of ρb of mixtures, the representation of included components together with their particle characteristics are critical attributes. Mixing of powders with different densities can lead to their segregation during handling ([12], [18], [19]). Already mentioned external factors (e.g. moisture, temperature, vibration, applied pressure) should not be omitted and the application of the vibration and moisture leads to an increase in ρb (11,20,21). In particulate materials, powder cohesive forces (Van der Waals, electrostatic, or capillary forces) can also affect bulk density. These types of forces become the dominant and determining factor as particle size decreases ([17], [22]). Last but not least, ρb might be adjusted by coating or the presence of glidant and anti-caking agents (23,24).

From the explanation described above it is apparent that ρb is an important parameter of particulate systems and experimentally determining this parameter is not complicated nor so time-consuming. However, multiple measurements need to be done during the development of new formulations since several excipients and their combinations are usually considered for their preparation. Moreover, the price of used API as well as some excipients (such as co-processed excipients) could be very high. So, the ability to predict ρb leads to sizeable time and money savings. Some studies have also paid attention to the prediction and modelling of ρb or related porosity and finding their relation to some parameters. With respect to this, several packing models have been introduced that can be essentially sorted into two groups, empirical models, and analytical ones. Empirical models are typically based solely on experimental data, from which density parameters are predicted ([25], [26], [27]). The analytical models work with a packing idea introducing packing mechanisms (filling, loosening, wedging effects for fine particles, and occupying, wall effects for coarse particles). The majority of these models are based on a linear approach and assume that ρb changes linearly with the change of volume ratio of pure materials ([28], [29], [30], [31], [32], [33]). However, the relationship between the material density and their volumetric fractions in mixture is not completely linear. Therefore, some non-linear models have also been created ([34], [35], [36], [37]). These linear as well as non-linear models have predicted systems containing spherical particles (28,29,34,[38], [39], [40], [41], [42]). They were lately expanded to models for non-spherical and angular/rounded particle systems (31,[41], [42], [43], [44], [45], [46]). It is in general difficult to determine the packing of powders which contain flake-like or rod-shaped particles (47). However, by applying the discrete element method (DEM), the relationship between interparticle interactions and porosity has also been evaluated and clarified over the last few years ([48], [49]). Some efforts have also been made to predict systems consisting of both, cohesive and non-cohesive particles (50).

The aim of this study was to develop a predictive model for ρb that would be industrially applicable and could be broadly applied. The main goal was to define ρb of binary mixtures based on data of pure materials. The motivation was the situation when the database of excipient densities is accessible, just formulated API would be the only necessary to be measured to define ρb for many mixtures in a short period of time with a small amount of used materials. Two “matrix-conception” approaches were created to predict the ρb using the principle of flow through packed beds and a calculation of the equivalent hydraulic diameter. The first technique utilizes a component-selective approach and assumes that the particles of one material serve as a matrix, and the particles of the second material are incorporated in such a matrix. The second technique utilizes a particle size-selective approach and takes the matrix at the level of particle size fraction. In this approach, the particle size fractions of a mixture are theoretically obtained from particle size fractions of pure materials at first. Then the largest mixture fraction is set as the matrix and its voids could be gradually filled with the possible amount of particles of fractions having smaller particle sizes.

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Materials

Ibuprofen  (IBU) was chosen as a model API. In this study, two grades from two different suppliers (SHANDONG XINHUA Pharmaceutical Co. Ltd., Shandong, China and Hubei Biocause Pharmaceutical Co. Ltd., Jingmen, China) were utilized. These grades are set as Shandong and Hubei respectively throughout the whole document. Three types of lactose (lactose monohydrate SuperTab® 14SD (DFE, Goch, Germany), lactose monohydrate Tablettose® 80 (MEGGLE GmbH, Wasserburg am Inn, Germany), anhydrous lactose (DFE, Goch, Germany)) and two types of microcrystalline cellulose (Avicel® PH200 (JRS Pharma, Rosenberg, Germany) and Avicel® PH102 (DuPont Nutrition, Athlone, Ireland)) were selected as representatives of common excipients in pharmaceutical industry. In addition to this, two batches of anhydrous lactose from one supplier were used when batch A was mixed with IBU Shandong and batch B was mixed with IBU Hubei.

Pavlína Komínová, Simona Römerová, Michaela Gajdošová, David Smrčka, Petr Zámostný, Predicting bulk density of pharmaceutical powder formulations – industrially applicable approach, Powder Technology, Volume 476, 2026, 122398, ISSN 0032-5910, https://doi.org/10.1016/j.powtec.2026.122398.

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