Design and optimization of stirrer and mixer design for the correct mixing of pharmaceutical powders through DEM

Introduction

The mixing of powders is an essential process in the food and pharmaceutical industries to gurantee a certain final product quality [1,2]. This quality can be represented in terms of taste, quality, flavor, and texture for food products, where these characteristics are affected by mixture homogeneity [3]. However, in the pharmaceutical industry, homogeneity can be considered a more critical parameter since a little irregularity in the excipients per dosage might be threatening to patients [4]. In this context, being aware of the most affecting parameters to the mixing behavior, i.e., particle properties and boundary conditions, is very critical for optimizing the whole process. These parameters can be characterized as particle size, density, shape, moisture content, roughness, and the presence of inter-particle forces [5]. In order to evaluate the powder mixing state, several methodologies were considered, e.g., X-ray microtomography [6], image analysis [7], and traditional sampling [8]. However, these methods have some disadvantages and restrictions. In microtomography, the position of the particles cannot be detected unless the mixing process is terminated. Upon using image analysis, coloring inks are usually involved in order to follow marker particles, which could change the particle surface properties. If the mixing quality of a bulk region is quantified via traditional sampling, the spatial location of the particles may be changed due to the insertion of a sampling probe. Therefore, using an experimental approach to evaluate the mixing quality of powders remains a challenge [9].

In this study Discrete Element Method (DEM) has been used, given that DEM is one of the main approaches to simulate discrete and granular materials [10] and it is able to represent the mixing of powders. Through DEM, not only the movement of the powders can be captured, but also the 3D interactions of the particles. Several mixing techniques have been examined in the literature using DEM such as static mixers [11], tubular [12], screw conveyor-mixers [13,14], rotating drums [[15], [16], [17]], V-blenders [[18], [19], [20]], and Nauta blenders [21].

A focused investigation into ribbon mixers reveals that their complex structure complicates the understanding of mixing mechanisms, which have traditionally been identified as convection without precise empirical validation. One notable study utilizes DEM to develop a novel swept volume measurement approach, confirming convective mixing while highlighting blade width as a critical parameter for enhancing mixing efficiency. This research underscores the potential of numerical modeling to optimize ribbon mixer designs and improve powder mixing outcomes. [22]

Additionally, another investigation examines the predictive capabilities of DEM simulations for a laboratory-scale paddle blade mixer during a powder mixing process. In this study, the visco-elasto-plastic frictional adhesive DEM contact model from Thakur et al. (2014) was employed to represent the cohesive behavior of aluminosilicate powder. Model parameters were determined through experimental flow energy measurements using the FT4 powder rheometer. The DEM simulations effectively reproduced the FT4 flow energy of the powder; however, they exhibited only qualitative agreement with the experimental mixing rates for both dry and wet powders, indicating an under-prediction of mixing. This finding suggests that relying solely on flow energy measurements may not adequately optimize the DEM model for powder mixing. [23]

The main purpose of simulating the particle mixing process is to study the factors, which affect the mixing degree and mixing speed [22]. For quantifying the mixing degree numerically, there are different methods explained in the literature. Choa et al. (2017) represented three different mixing indices namely, Lacey, Kramer, and Lacey-Weidenbaum-Bonilla [23]. He exhaustively investigated the efficiency and limitations of each mixing index, suggesting and developing a new index called the Coordinate mixing index. Apart from the conventional mixing index methods, two other ways of quantifying the mixing degrees were also mentioned in literature [22]. The first method to characterize the mixing degree of particles is contact statistics, i.e., by tracking and recording the total number of contacts between different particles through time, and once the total number of contact oscillates in a relatively small range, the particles are assumed to be evenly mixed [24,25]. The second method is the uniform distribution method, i.e., by dividing the particle bed into equal volume voxels (n samples), the number of characteristic particles in each block is tracked and recorded, after which the standard deviation of the n sample values is calculated. By observing the standard deviation, a uniform mixing is assumed when the oscillations of this value are reduced [[26], [27], [28]].

The main purpose of this study is to check the influence of different factors in terms of geometry and particle properties on the mixing degree. For this study, the calculation of the mixing degree using the conventional mixing index, e.g. Lacey Index, is not considered based on several factors. First, the Lacey Index has been reported in some cases to exceed a value of 1 [29]. This phenomenon occured when a relatively small cell size is considered in the calculations, indicating sensitivity to cell size in the assessment of mixing degree. This conflicts with our approach where a value of 1 represents the ideal mixing degree. This inconsistency raises questions about the reliability of the Lacey Index in accurately reflecting mixing quality under certain conditions. Additionally, in our simulations, calculating the Lacey Index proved to be more time-consuming, requiring an additional 10 to 15 min per simulation compared to the method we employed. This is largely due to the increased complexity involved in counting and analyzing particle distributions required by the Lacey Index, which adds to the computational load without providing added value for our specific case.On the other hand, the positioning of the particles in the system involved in this study does not allow the use of the two other above mentioned methods. Therefore, a new way of quantifying the mixing degree was developed and used.

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Methodology

In this study, two distinct pharmaceutical powders (MEGGLE Wasserburg GmbH & Co. KG, Germany) were employed. SpheroLac 100 was chosen to represent free-flowing lactose powder, commonly employed in various applications, such as capsule filling, blends, premixes, sachets, and triturations [30]. Conversely, Vitamin C (Ascorbic Acid) was selected as a cohesive Active Pharmaceutical Ingredient (API), recognized for its potent antioxidant properties and widespread usage across cosmetic and pharmaceutical sectors [31]. While it is recognized that pharmaceutical formulations often include other components such as lubricants, glidants, and disintegrants, the objective of this study was to focus specifically on two powders with contrasting material properties—free-flowing and cohesive powders. This focus was deliberately chosen to evaluate the mixing performance of the equipment under controlled conditions, rather than to formulate a final medicinal product at this stage.

Nizar Salloum, Thomas Brinz, Aitor Atxutegi, Stefan Heinrich, Design and optimization of stirrer and mixer design for the correct mixing of pharmaceutical powders through DEM, Powder Technology, 2024, 120413, ISSN 0032-5910, https://doi.org/10.1016/j.powtec.2024.120413.

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