pharmaceutics Article Kinetic and Microhydrodynamic Modeling of Fenofibrate Nanosuspension Production in a Wet Stirred Media Mill Gulenay Guner 1 , Dogacan Yilmaz 2 and Ecevit Bilgili 1, *   Citation: Guner, G.; Yilmaz, D.; Bilgili, E. Kinetic and Microhydrodynamic Modeling of Fenofibrate Nanosuspension Production in a Wet Stirred Media Mill. Pharmaceutics 2021, 13, 1055. https://doi.org/10.3390/ pharmaceutics13071055 Academic Editor: Nadia Passerini Received: 31 May 2021 Accepted: 7 July 2021 Published: 10 July 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA; gg357@njit.edu 2 Department of Mechanical and Industrial Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA; dy234@njit.edu * Correspondence: bilgece@njit.edu; Tel.: +1-973-596-2998; Fax: +1-973-596-8436 Abstract: 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 micro- hydrodynamic 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 (R 2 ≥ 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. Keywords: poorly water-soluble drugs; wet stirred media milling; breakage kinetics; process model- ing; microhydrodynamic model; statistical model; subset selection 1. Introduction The majority of drug molecules coming out of high-throughput screening have poor water solubility due to their high lipophilicity and molecular weight [1]. Forty percent of marketed drugs are poorly water-soluble, which results in low bioavailability. There are several formulation approaches to overcome this challenge, such as amorphous solid dispersions, lipid-based formulations, and nanoparticle-based formulations [2]. Drug nanoparticles have been commonly used, as they are shown to improve the dissolution rate and bioavailability of drugs due to increased specific surface area, higher saturation solubility, and a reduction in the thickness of the diffusion layer [3–5]. The higher saturation solubility of nanoparticles—typically < 500 nm—has been mostly attributed to the high curvature of such particles, and explained by the Gibbs–Kelvin or Ostwald–Freundlich equations [6,7]. On the other hand, nanoparticles with sizes greater than 100 nm prepared via mechanical methods could also exhibit higher saturation solubility than bulk crystals [8], due to mechanically induced disorder and crystal defects [8–11], amorphization, and solubilization by the stabilizers [12,13]. Kesisoglou and Wu [14] estimated the solubility Pharmaceutics 2021, 13, 1055. https://doi.org/10.3390/pharmaceutics13071055 https://www.mdpi.com/journal/pharmaceutics