(333c) An Enthalpy-Balance Model for Timewise Evolution of Temperature during Wet Stirred Media Milling of Drug Suspensions

In this study, milling experiments were performed at three different stirrer speeds, bead loadings, and bead sizes using 10% Fenofibrate, 8% hydroxypropyl cellulose and 0.05% sodium dodecyl sulfate (w/v) formulation. If and when the mill outlet temperature reached 45 oC, the mill was shut down and cooling was continued. If not, the milling continued for a total of 60 min and the temperatures were recorded at each minute. Chiller temperature was recorded at each time point as well. Timewise evolution of the mill outlet temperature and the chiller temperature for milling part and the cooling part were used as input files for our MATLAB code. Two dynamic enthalpy balances (ordinary differential equations in time) were developed: one for the mill content and another for the holding tank content. For the mill, we considered only a fraction of the mechanical power that is converted to heat (ξ) as well as the enthalpy of the recirculating suspension between the mill chamber and the holding tank. Both the mill and the holding tank have cooling jackets through which cooling water passes through and returns to the chiller. The heat removal rate through the jackets was calculated using the Newton’s law of cooling with the respective overall heat transfer coefficient. Thermophysical properties for the mill chamber and the holding tank were found or calculated by using correlations from the literature. All physical properties were known except for the ξ, which was found by dynamic optimization of the experimental data and the model by fmincon function of MATLAB. Overall, the model could fit the experimental data well as signified by the low residual sum of squares.
While breakage kinetics during WSMM have been studied in the literature (see ref [6], and the references cited in there) using statistical and mechanistic models, another major concept, the heat dissipation, has not been experimentally studied or modelled. Heat dissipation (generation) is a crucial aspect in pharmaceutical applications that limits the selection of process conditions and restricts the process design space accordingly. Guner et al. [7] highlighted the importance of simultaneous consideration of heat dissipation besides the breakage kinetics and energy consumption. Since the drugs and polymers used in the formulation may be thermolabile, the temperature should be controlled stringently. Not all of the mechanical energy that was put into system is used for particle breakage and most of it is converted to heat causing the temperature to increase. Overheating was mentioned and prevented by applying intermitting milling–cooling cycles in some applications [8, 9], however, there is no comprehensive study that investigates the heat dissipation in WSMM using a macroscopic enthalpy balance approach.
Nanosuspensions have been established as one of the platform approaches to address the poor solubility of drugs over the last few decades [1]. Nanoparticles can improve the bioavailability of such drugs owing to their higher surface area, increased saturation solubility, and reduction in the diffusion layer compared with micron-sized particles [2]. Additionally, nanosuspensions offer a high drug dose that allows less oral unit administration and reduced toxicity and side effects [3]. Among all techniques [4, 5], wet stirred media milling (WSMM) has been the first choice for drug nanosuspension production. In WSMM, drug particle size and breakage kinetics can be easily adjusted by tuning the process parameters and/or bead properties.
The next step is making simulations and predictions of the temperature profile for any given condition. Power consumption (P) is an input in the MATLAB code, which is read from the mill screen during the experiment. Also, we found ξ by fitting the model to experimental temperatures. If one can find a way to predict P and ξ, one can predict the temperature profiles as well. Two approaches were used to predict P and ξ: power law model and machine learning approaches. P was fitted by a power law model of dimensionless process condition numbers and for ξ, after trying several power law models based on process conditions, it was found to be the most correlated with P so it was predicted based on that. On the other hand, several machine learning algorithms were tried to predict P and ξ based on the process parameters (stirrer speed, bead loading and bead size), and k-nearest neighbor with k = 3 provided the best predictions. Figure shows the experimental data, enthalpy balance model fit and predictions by machine learning and power law approaches of 5 experiments that were used to test the models. It can be seen while all models provide a fairly realistic simulation of the temperature profiles, machine learning approach was slightly better compared to the power law approach. To conclude, this study was the first to use an enthalpy balance model that captures all relevant thermophysical properties of WSMM process to investigate the temperature profiles when process conditions are varied. Furthermore, it was shown that it is possible to predict a temperature profile for any given condition without performing additional experiments, which would be a great help for engineers when selecting the proper process conditions.

References
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