Ball milling is a technique that is utilised by the pharmaceutical industry for granular size reduction of drugs or excipients. There are many reasons to mill particulate materials. Very often, the milled product is required to have a specific surface area, or it might be a process requirement that the fragments are consistent in shape throughout the whole batch. This is because the shape, size and the surface-area-to-volume ratio of the particles are parameters that affect critical properties of the material, such as its solubility or its reactivity in the chemical processes for which it is employed. Variables such as the rotation speed of the drum and the physical properties of balls and milling material have the most significant influence on the final quality of the product. It is also necessary to consider the optimum filling level of both milling material and balls. In order to achieve maximum production yield with minimal costs, it is important to determine how each factor affects the average size of the particulate fragments in the final product. Traditional approaches often fail to predict the mechanisms of fragmentation of granules or particle reduction.
Dr Alexander Krok and Dr Sandra Lenihan, from Munster Technological University, Ireland, have developed advanced computational models to achieve optimal size reduction of granules with non-uniform shape and different size in ball milling for the pharmaceutical industry. Drs Krok and Lenihan aim to study and validate the effectiveness of a computational method known as the discrete element method (DEM), instead of a technique used in previous research where the breaking behaviour was estimated through the impact energy of ball collisions as the driving force for fracturing.
Effect of milling speed on granule fragmentation
The optimisation of energy consumption in milling has traditionally been undertaken by the population balance modelling (PBM) approach. Some of the parameters used in PBM calculations must be determined experimentally, making this entire process time consuming. As a consequence, DEM has been growing in popularity among researchers in the field, providing significant insights into the operation of pharmaceutical granule milling.
The shape, size and the surface area to volume ratio of the particles are parameters that affect critical properties of the material, such as its solubility.
Drs Krok and Lenihan investigated the fragmentation of bonded particles into DEM granules of different shape and size during the ball milling process and have reported their findings in a recently published paper. The study explores the effect of the rotation speed and other parameters on the breakage behaviour of DEM granules during the ball milling process. One of the conclusions of the study was that the collisions between the balls and the product granules increased proportionally with rotation speed until a critical speed was reached, with mill power also increasing proportionally with rotation speed. The relationship between the number of fragments produced and the milling speed was also linear.
Predicting the breakage pattern of the granules
The material used for the study was unlubricated and unsieved granule lactose, an excipient commonly used in the pharmaceutical industry. The granule shape was described taking into account the parameters of sphericity and roundness. In their paper, the researchers defined sphericity as the ratio between the outer and internal diameters of the granules. Roundness indicates the sharpness of particle corners and was defined as the ratio of the average radius of curvature of the corners of a particle to the radius of the maximum inscribed circle. The researchers used a system of equations, so that the granule shape can be determined by the calculated parameters of sphericity and roundness.
The predicted shapes of the different granules were sorted into three main types. The ‘elongated’ granules had a calculated sphericity between 0.75 and 0.93, and roundness between 0.2 and 1 (the value 1 describes perfect sphericity/roundness). The ‘blocky’ granules had narrower ranges of sphericity and roundness, specifically between 0.65 and 0.92 for sphericity and between 0.25 and 0.6 for roundness. The ‘rounded’ shape granules where sphericity varied between 0.6 and 0.85, and roundness varied between 0.25 and 0.6.
A rotation speed of 190 rpm was the most effective milling speed in the study and led to optimal reduction in particle size.Configuration of the mill drum
In the pilot study, the mill drum was conceived as a steel cylindrical shell with an inner diameter of 50 mm and a depth of 10 mm. The drum was fitted with eight lifters, each measuring 1.2 mm in height and 0.8 mm in width. The milling action was provided by ten steel balls with a density of 7800kg/m3. The number of balls to be employed was carefully optimised, as it was observed that a reduced number of balls is more energy efficient as it produces less over-grinding and reduces power consumption. For their calculations, the researchers conceived the drum as a counter-clockwise rotating cylinder consisting of four individual zones: an ‘empty zone’ in the top left quarter of the cylinder’s section, a ‘dead zone’ at the top of the bottom right quarter, an ‘abrasion zone’, just below the ‘dead zone’ in the bottom right quarter and a ‘high impact zone’ in the bottom left quarter of the cylinder’s section, where the mill balls and granules are in optimal conditions to collide effectively.
Conclusions of the study
Drs Krok and Lenihan, along with their collaborators, conducted a systematic simulation study on the process of pharmaceutical ball milling. The aim of their study was to investigate the parameters that most efficiently reduce the size of granular lactose particles. The commercial software ABAQUS was used to perform the numerical simulation of the ball milling process. The team demonstrated through their DEM approach a strong correlation between the impact speed and the number of fragments, in agreement with previous data published in the scientific literature. A rotation speed of 190 rpm (revolutions per minute) was the most effective milling speed in the study and led to optimal reduction in particle size. Increasing the rotation speed above this value was counterproductive and was characterised by centrifugal motion, which negatively impacted the fragmentation process. On the other hand, lower rotation speeds caused a rolling-cascading particle motion, which was not adequate for effective ball milling. However, the researchers point out that while increasing the rotation speed up to 190 rpm produced the most effective collisions between the granules and the balls, it also significantly increased the calculated power consumption of the milling process.
The computational method developed Drs Krok and Lenihan optimises the quality of the final product, while minimising the costs associated with ball milling. Reducing the size of the granules and ensuring that they are homogeneous with regards to their shape will result in the optimum physical and chemical properties within the desired pharmacological context of the final product.
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