Numerical simulation of milling processes as an aid to process design

Predicting the Temperature Evolution during Nanomilling of Drug Suspensions via a Semi-Theoretical Lumped-Parameter Model

Although temperature can significantly affect the stability and degradation of drug nanosuspensions, temperature evolution during the production of drug nanoparticles via wet stirred media milling, also known as nanomilling, has not been studied extensively. This study aims to establish both descriptive and predictive capabilities of a semi-theoretical lumped parameter model (LPM) for temperature evolution. In the experiments, the mill was operated at various stirrer speeds, bead loadings, and bead sizes, while the temperature evolution at the mill outlet was recorded. The LPM was formulated and fitted to the experimental temperature profiles in the training runs, and its parameters, i.e., the apparent heat generation rate Q_gen and the apparent overall heat transfer coefficient times surface area UA, were estimated. For the test runs, these parameters were predicted as a function of the process parameters via a power law (PL) model and machine learning (ML) model. The LPM augmented with the PL and ML models was used to predict the temperature evolution in the test runs. The LPM predictions were also compared with those of an enthalpy balance model (EBM) developed recently. The LPM had a fitting capability with a root-mean-squared error (RMSE) lower than 0.9 °C, and a prediction capability, when augmented with the PL and ML models, with an RMSE lower than 4.1 and 2.1 °C, respectively. Overall, the LPM augmented with the PL model had both good descriptive and predictive capability, whereas the one with the ML model had a comparable predictive capability. Despite being simple, with two parameters and obviating the need for sophisticated numerical techniques for its solution, the semi-theoretical LPM generally predicts the temperature evolution similarly or slightly better than the EBM. Hence, this study has provided a validated, simple model for pharmaceutical engineers to simulate the temperature evolution during the nanomilling process, which will help to set proper process controls for thermally labile drugs.

An Enthalpy-Balance Model for Timewise Evolution of Temperature during Wet Stirred Media Milling of Drug Suspensions

PURPOSE

Nanosuspensions have been used for enhancing the bioavailability of poorly soluble drugs. This study explores the temperature evolution during their preparation in a wet stirred media mill using a coupled experimental-enthalpy balance approach.

METHODS

Milling was performed at three levels of stirrer speed, bead loading, and bead sizes. Temperatures were recorded over time, then simulated using an enthalpy balance model by fitting the fraction of power converted to heat ξ. Moreover, initial and final power, ξ, and temperature profiles at 5 different test runs were predicted by power-law (PL) and machine learning (ML) approaches.

RESULTS

Heat generation was higher at the higher stirrer speed and bead loading/size, which was explained by the higher power consumption. Despite its simplicity with a single fitting parameter ξ, the enthalpy balance model fitted the temperature evolution well with root mean squared error (RMSE) of 0.40-2.34°C. PL and ML approaches provided decent predictions of the temperature profiles in the test runs, with RMSE of 0.93-4.17 and 1.00-2.17°C, respectively.

CONCLUSIONS

We established the impact of milling parameters on heat generation-power and demonstrated the simulation-prediction capability of an enthalpy balance model when coupled to the PL-ML approaches.

Analysis of heat generation during the production of drug nanosuspensions in a wet stirred media mill

Although heat is generated during the wet stirred media milling of drug suspensions, leading to notable temperature rise, a comprehensive analysis of heat generation does not exist. Hence, we investigated the impact of stirrer speed, bead loading, and bead size at three levels on the evolution of suspension temperature at the mill outlet during the milling of fenofibrate. The particle sizes and viscosities of the milled suspensions and power were measured. Our results suggest that stirrer speed had the most significant impact on the temperature increase, followed by bead loading and bead size. Both the time when the temperature reached 22 °C and the temperature at 5 min of milling were strongly correlated with the power. Assessing the impacts of the process parameters on the temperature rise, cycle time, power, and median particle size holistically, an optimal milling process was identified: 3000 rpm with 50% loading of 200 or 400 µm beads. A power number correlation was established to calculate power at any milling condition which determines the heat generation rate. Overall, this study indicated the importance of developing a good understanding of heat generation during nanomilling for development of a robust milling process especially for thermally labile drugs.

Rod Mill Product Control and Its Relation to Energy Consumption: A Case Study

Energy consumption and pollution are current strategic issues that need to be addressed in the mining industry. Both have an economic and environmental impact on production, so their optimization, control, and mitigation are, at the very least, mandatory. Although rod milling has fallen into disuse in recent decades, some companies still use it in their processing plants. This is due to the ability of rod milling to reduce particle size while avoiding overgrinding. In this study, a material that is particularly difficult to characterize was used to study how to control rod-milling particle size distribution product: potash ore, which is deliquescent and soluble under certain conditions. A laboratory-scale tumbling rod mill was designed for this study, and six operative parameters were tested and analyzed in order to detect the main influences on the mill product, attending to material requirements for further processes such as recirculation load or froth flotation for beneficiation. Although the rotational speed of the mill is the parameter that shows the greatest reduction in energy consumption, reaching almost 40% improvement in specific energy applied to the particles, it is not possible to control particle size reduction ratio. However, when a low percentage of grinding media is used, it reduces around 25% of the energy used and, in turn, reduces the amount of overgrinding (40% reduction in the F300 control parameter, for example), which is a strategic objective of this study. In addition, by controlling other process parameters, such as slurry density or lifter geometry, energy consumption and its subsequent saving and pollution can be controlled, depending on process plant requirements.

Kinetic and Microhydrodynamic Modeling of Fenofibrate Nanosuspension Production in a Wet Stirred Media Mill

This study examined the impact of stirrer speed and bead material loading on fenofibrate particle breakage during wet stirred media milling (WSMM) via three kinetic models and a microhydrodynamic model. Evolution of median particle size was tracked via laser diffraction during WSMM operating at 3000-4000 rpm with 35-50% (v/v) concentration of polystyrene or zirconia beads. Additional experiments were performed at the center points of the above conditions, as well as outside the range of these conditions, in order to test the predictive capability of the models. First-order, nth-order, and warped-time kinetic models were fitted to the data. Main effects plots helped to visualize the influence of the milling variables on the breakage kinetics and microhydrodynamic parameters. A subset selection algorithm was used along with a multiple linear regression model (MLRM) to delineate how the breakage rate constant k was affected by the microhydrodynamic parameters. As a comparison, a purely empirical correlation for k was also developed in terms of the process/bead parameters. The nth-order model was found to be the best model to describe the temporal evolution; nearly second-order kinetics (n ≅ 2) was observed. When the process was operated at a higher stirrer speed and/or higher loading with zirconia beads as opposed to polystyrene beads, the breakage occurred faster. A statistically significant (p-value ≤ 0.01) MLRM of three microhydrodynamic parameters explained the variation in the breakage rate constant best (R² ≥ 0.99). Not only do the models and the nth-order kinetic-microhydrodynamic correlation enable deeper process understanding toward developing a WSMM process with reduced cycle time, but they also provide good predictive capability, while outperforming the purely empirical correlation.

Mechanistic Modeling of Wet Stirred Media Milling for Production of Drug Nanosuspensions

Drug nanocrystals have been used for a wide range of drug delivery platforms in the pharmaceutical industry, especially for bioavailability enhancement of poorly water-soluble drugs. Wet stirred media milling (WSMM) is the most widely used process for producing dense, stable suspensions of drug nanoparticles, also referred to as nanosuspensions. Despite a plethora of review papers on the production and applications of drug nanosuspensions, modeling of WSMM has not been thoroughly covered in any review paper before. The aim of this review paper is to briefly expose the pharmaceutical scientists and engineers to various modeling approaches, mostly mechanistic, including computational fluid dynamics (CFD), discrete element method (DEM), population balance modeling (PBM), coupled methods, the stress intensity-number model (SI-SN model), and the microhydrodynamic (MHD) model with a main focus on the MHD model for studying the WSMM process. A total of 71 studies, 30 on drugs and 41 on other materials, were reviewed. Analysis of the pharmaceutics literature reveals that WSMM modeling is largely based on empirical, statistically based modeling approaches, and mechanistic modeling could help pharmaceutical engineers develop a fundamental process understanding. After a review of the salient features and various pros-cons of each modeling approach, recent advances in microhydrodynamic modeling and process insights gained therefrom were highlighted. The SI-SN and MHD models were analyzed and critiqued objectively. Finally, the review points out potential research directions such as more mechanistic and accurate CFD-DEM-PBM simulations and the coupling of the MHD-PBM models with the CFD.

Nanomilling of Drugs for Bioavailability Enhancement: A Holistic Formulation-Process Perspective

Preparation of drug nanoparticles via wet media milling (nanomilling) is a very versatile drug delivery platform and is suitable for oral, injectable, inhalable, and buccal applications. Wet media milling followed by various drying processes has become a well-established and proven formulation approach especially for bioavailability enhancement of poorly water-soluble drugs. It has several advantages such as organic solvent-free processing, tunable and relatively high drug loading, and applicability to a multitude of poorly water-soluble drugs. Although the physical stability of the wet-milled suspensions (nanosuspensions) has attracted a lot of attention, fundamental understanding of the process has been lacking until recently. The objective of this review paper is to present fundamental insights from available published literature while summarizing the recent advances and highlighting the gap areas that have not received adequate attention. First, stabilization by conventionally used polymers/surfactants and novel stabilizers is reviewed. Then, a fundamental understanding of the process parameters, with a focus on wet stirred media milling, is revealed based on microhydrodynamic models. This review is expected to bring a holistic formulation-process perspective to the nanomilling process and pave the way for robust process development scale-up. Finally, challenges are indicated with a view to shedding light on future opportunities.

Continuous production of drug nanoparticle suspensions via wet stirred media milling: a fresh look at the Rehbinder effect

Nanoparticles of BCS Class II drugs are produced in wet stirred media mills operating in batch or recirculation mode with the goal of resolving the poor water-solubility issue. Scant information is available regarding the continuous production of drug nanoparticles via wet media milling. Griseofulvin and Naproxen were milled in both recirculation mode and multi-pass continuous mode to study the breakage dynamics and to determine the effects of suspension flow rate. The evolution of the median particle size was measured and described by an empirical breakage model. We found that these two operation modes could produce drug nanosuspensions with similar particle size distributions (PSDs). A reduced suspension flow rate slowed the breakage rate and led to a wider PSD and more differentiation between the two operation modes. The latter part of this study focused on the roles of stabilizers (hydroxypropyl cellulose and sodium lauryl sulfate) and elucidation of the so-called Rehbinder effect (reduction in particle strength due to adsorbed stabilizers such as polymers and surfactants). Milling the drugs in the absence of the stabilizers produced primary nanoparticles and their aggregates, while milling with the stabilizers produced smaller primary nanoparticles with minimal aggregation. Using laser diffraction, BET nitrogen adsorption, scanning electron microscopy imaging, and a microhydrodynamic analysis of milling, this study, for the first time, provides sufficient evidence for the existence of the Rehbinder effect during the milling of drugs. Not only do the polymers and surfactants allow proper stabilization of the nanoparticles in the suspensions, but they also do facilitate drug particle breakage.

Pharmaceutical nanocrystals by nanomilling: critical process parameters, particle fracturing and stabilization methods

OBJECTIVES

Wet milling is a common technique to produce drug nanocrystals. Stability of the nanocrystals is a critical question, and different kinds of stabilizers, e.g. polymers, celluloses, surfactants and lipids, have been tested for various drugs. Still, the question about how to select the best stabilizer to a certain drug material and also to a selected process is open.

KEY FINDINGS

Many different factors, such as surface energy, hydrophobicity, solubility, viscosity and functional groups, affect the stability of the formed nanosuspensions. Affinity of the stabilizer to the particle surfaces seems to be the most important parameter. This affinity is partly related to the surface energy and hydrophobicity of the surfaces and stabilizers.

SUMMARY

In this review the most important factors affecting nanocrystal formulation and efficacy of stabilizers are presented. In order to widen understanding of the milling process, the most important variables related to milling techniques and particle fracturing processes during the milling are briefly presented.

Comparison of dry- and wet-based fine bead homogenizations to extract DNA from fungal spores

The present study explored DNA extraction kinetics from fungal spores, i.e., Aspergillus niger, Penicillium chrysogenum and Cladosporium sphaerospermum, by fine bead mill homogenization. In particular, the study aimed to investigate basic differences between the dry- and wet-based methods. The results showed higher initial rates of the DNA extractions by the dry-based method than by the wet-based method, due to higher collision efficiency among fine beads and fungal spores. Based on the experimental results, we constructed kinetic models. While the results by the wet-based method were fitted well with an existing first-order release-degradation model, the results by the dry-based method were not fitted well. Meanwhile, a newly constructed first-order release-degradation model, assuming a proportion of the DNA remained inside the disrupted spore cells and protected from further sheer stress, showed good correlations. The real-time PCR assays showed the PCR efficiencies of the DNA obtained by the dry-based method were higher than those by the wet-based method likely due to increased moderate fragmentation of the DNA by the dry-based method. Thus, although wet-based methods have been commonly used, dry-based methods might also be applicable to achieve efficient extraction and PCR amplification of fungal DNA.