# Modeling Polymer Microencapsulation Processes Using CFD and Population Balance Models
###### Abstract  
Computational fluid dynamics (CFD) modeling has emerged as a valuable tool for investigating complex processes like microencapsulation. This paper aims to validate the ability of CFD simulations to predict particle size distribution in a polymer microencapsulation process. The CFD modeling approach employed a Eulerian multiphase framework, incorporating a discrete population balance model to track the evolution of the droplet population. A realizable \(k\)-\(\epsilon\) turbulence model and a multiple reference frame strategy were utilized to capture the system's flow dynamics. The results reveal that while the CFD simulations align well with experimental data at higher agitation speeds (>10,000 rpm), discrepancies arise at lower speeds (<7500 rpm), indicating a challenge in accurately capturing turbulent viscous regimes. Despite these challenges, the CFD model demonstrates robust predictive capabilities for droplet formation and distribution in microencapsulation processes, validated by error margins within the acceptable limits. The validated model can be used as a reliable tool to guide experimental efforts and optimize process parameters, contributing to an enhanced understanding and control of microencapsulation processes. caputational fluid dynamics; microencapsulation; cumulative probability distribution; population balance models; number density +
Footnote †: journal: Medical Imaging  
[PERSON], [PERSON], L.J. systems, such as emulsions and suspensions, encountered in microencapsulation further complicates the process and requires a comprehensive understanding of the interactions between various components [11]. Additionally, scaling up microencapsulation processes from lab-scale to industrial-scale production poses significant challenges, as fluid dynamics and mass transfer characteristics can change significantly with varying operating conditions and geometries [12]. Computational Fluid Dynamics (CFD) modeling can play a crucial role in addressing these challenges by providing valuable insights into the underlying mechanisms, enabling the virtual optimization and screening of process parameters, and facilitating the successful scale-up of microencapsulation technologies [13]. The development of robust CFD models can significantly improve the efficiency, effectiveness, and quality of microencapsulation processes, leading to enhanced product performance and broader applications in fields such as drug delivery [14; 15], the petroleum industry [16], food processing [17; 18], or cosmetics/personal care [19; 20]. The population balance model (PBM) is widely used to model the size distribution of droplets, bubbles, or crystals that evolve and change due to various phenomena such as nucleation, growth, coalescence, and breakage within a flowing system. The population balance model is a balance equation that tracks the changes in the size distribution of these dispersed species, similar to mass, energy, and momentum balances. Early research proposed a solution for the population balance equation in a well-mixed batch system, utilizing the moment transform technique to convert the population balance equations into a set of ordinary differential equations, which enabled tracking of size distribution changes [21]. Later, the moment transform approach was employed to develop a numerical technique for modeling the growth and aggregation of particles in a suspension, such as calcium oxalate monohydrate crystals, facilitating the simulation of kidney stone formation [22]. In recent years, advanced CFD techniques have been utilized to simulate multiphase flow processes. Some researchers have attempted to couple PBMs with transport equations through CFD modeling of slurries, emulsions, and gas-liquid systems. For instance, CFD coupled with a PBM has been used to investigate the aggregation of solid particles in a slurry system [23]. In this work, the Eulerian approach for multiphase flow and a \(-\epsilon\) turbulence model were used to simulate the turbulent two-phase flow.