International Journal of Pharmaceutics 320 (2006) 14–22 Characterizing powder mixing processes utilizing compartment models Patricia M. Portillo, Fernando J. Muzzio, Marianthi G. Ierapetritou ∗ Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ 08854, United States Received 24 January 2006; received in revised form 27 March 2006; accepted 28 March 2006 Available online 18 April 2006 Abstract Powder mixing has been the subject of substantial research due to its importance in a variety of industrial sectors, including pharmaceuticals, food, and polymer manufacturing. Although a number of different models have been proposed in the literature, most of them are either empirical or require computationally intensive calculations that make them difficult to implement for realistic systems. The aim of this paper is to develop a simplified framework, based on compartment modeling that efficiently and accurately captures the system behavior. Using the V-blender as a model system, the compartment modeling approach was used to illustrate the effects of vessel loading on mixing as well as the impact of sampling methods on the accuracy of mixing characterization. © 2006 Elsevier B.V. All rights reserved. Keywords: Compartment modeling; Mixing models; Powders 1. Introduction Many industrial sectors rely heavily on granular mixing to manufacture a large variety of products. In the pharmaceuti- cal industry, it is very important to ensure homogeneity of the product. The pharmaceutical industry is one of the most rep- resentative examples, where homogeneity is very important to ensure product quality and compliance with strict regulations. Modeling can play an important role in improving mixing pro- cess design by reducing mixing time as well as manufacturing cost, and ensuring product quality. The main difficulty in mod- eling powder-mixing processes is that granular materials are complex substances that cannot be characterized either as liquids or solids (Jaeger and Nagel, 1992). Moreover, granular mixing can be described by multiple mixing regimes due to convection, dispersion, and shear (Lacey, 1954). Fan et al. (1970) reviewed a number of publications where powder mixing is modeled in an attempt to reduce the production cost and improve product qual- ity. Although a complete literature survey is outside the scope of this paper, we will review the most relevant models in this introduction section. The existing approaches used to simulate granular material mixing processes can be categorized as (1) heuristic models, ∗ Corresponding author. Tel.: +1 732 445 2971; fax: +1 732 445 2421. E-mail address: marianth@sol.rutgers.edu (M.G. Ierapetritou). (2) models based on kinetic theory, (3) particle dynamic simu- lations, and (4) Monte Carlo simulations (Ottino and Khakhar, 2000). Geometric arguments and ideal mixing assumptions are some common features of heuristic models. Although these models can generate satisfactory results, they are restricted to batch processes and are case dependent (Hogg et al., 1966; Th ´ yn and Duffek, 1977). Kinetic-theory-based models are used to simulate mixtures of materials with different mechanical prop- erties (size, density and/or restitution coefficient), where each particle group is considered as a separate phase with different average velocity and granular energy. These models typically address shear flow of binary and ternary mixtures based on the kinetic theory of hard and smooth spherical particles (Jenkins and Savage, 1983; Iddir et al., 2005; Lun et al., 1984). The main shortcoming of these models is that they focus on the micro- scopic interactions between particles, neglecting the effects due to convection and diffusion. Particle dynamic simulations, which apply molecular dynamic concepts to study liquids and gases, are extensively used to simulate powder mixing (Zhou et al., 2004; Yang et al., 2003; Cleary et al., 1998). The main limitations of particle dynamic simulations are (a) the maximum number of particles required to model the system is restricted due to the computa- tional complexity of the involved calculations, and (b) the lack of realistic particle morphology. Monte Carlo (MC) simulations begin with an initially ran- dom configuration, which is driven to an energetically feasible 0378-5173/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpharm.2006.03.051