Development of a droplet size prediction tool for manufacture of emulsion creams

Abstract

A practical computational tool was designed to estimate droplet size distributions in process equipment for ointment manufacturing, thereby providing guidance in selecting optimal equipment operating parameters for producing emulsions with desired characteristics. For simplicity and computational tractability, hydrodynamics are simulated using a compartment model, which allows for consideration of multiple hydrodynamic environments. The simulation tool employs a general coagulation-breakage population balance equation, using established expressions for coagulation and breakage kernels and a robust method for discretizing the model equations. Experiments were conducted to assess the accuracy of the simulation tool, including tests with two types of non-Newtonian emulsions: petrolatum in water as well as polyacrylic gelling polymer in water formulations representative of topical ointments. Simulation predictions for droplet size distribution demonstrated good agreement with experimental results using only a few adjustable parameters.

Highlights

A two-compartment population balance model was developed for emulsification.

Droplet size distributions were compared to experimental data.

Simulations provide good predictions with little computational effort.

The simulation tool can be used by non-experts for manufacturing.

The simulation tool was applied to non-Newtonian emulsion cream formulations.

Introduction

In the pharmaceutical industry, the quality of topical formulations such as ointments and creams is critically dependent on the consistency and stability of their microstructure, particularly the size distribution of droplets within the emulsion (Vehring, 2007, Onuki et al., 2015, van Heugten and Vromans, 2018). The manufacturing process, involving complex fluid dynamics, significantly influences these characteristics. Homogenizers, piping, and downstream packaging equipment impose varying shear rates and turbulence levels, affecting droplet breakage and coalescence and ultimately impacting the final product’s efficacy and texture (Floury et al., 2000).

Computational fluid dynamics (CFD) can be used to simulate turbulent environments during manufacture of emulsions such as those that comprise ointments and creams. For example, Becker et al. used CFD simulations coupled to a population balance equation (PBE-CFD) to simulate emulsification processes in high-pressure homogenizers (Becker et al., 2014). Their model, applied to food-grade oil-in-water emulsions, highlighted the importance of energy dissipation rates and local flow conditions on droplet breakup. Castellano et al. extended the PBE-CFD framework for industrial homogenizers, customizing coagulation and breakage kernels to account for spatial variations in breakage and coalescence rates (Castellano, 2019). However, widespread application of CFD to simulate production-scale multiphase manufacturing equipment is hindered by high computational costs, intricate setups for multiphase flow modeling, and difficulties simulating inter-phase phenomena such as drag, lift, and multiphase turbulence (Babinsky and Sojka, 2002). These limitations are further compounded when equipment size or configuration changes require new simulations, making it a less feasible approach for routine operational changes and for use by those without deep experience in multiphase flow CFD (Vehring, 2007, Babinsky and Sojka, 2002, Lashkaripour et al., 2024).

Compartment models provide one of the simplest alternatives to CFD, while still attempting to account for hydrodynamic variability in process equipment and the resulting spatial heterogeneity in important process variables such as species concentrations and temperature. This relatively simple approach divides the simulated fluid volume into a finite set of interconnected compartments, each of which is assumed to be spatially homogeneous, but different from neighboring compartments. Compartment models have been applied not only to single-phase chemical reactors, but also to multiphase flow processes involving dispersed phases, including for simulation of coagulation and breakage of particles, droplets, and bubbles (Lebaz and Sheibat-Othman, 2019, Vonka and Soos, 2015, N. Sheibat-Othman, 2018).

In application to stirred tank reactors, Lebaz and Sheibat-Othman utilized compartment model PBEs to investigate droplet size distributions under different flow regimes, emphasizing the role of localized turbulence in governing droplet dynamics (Lebaz and Sheibat-Othman, 2019). Vonka and Soos examined viscosity variations in liquid-liquid dispersions within stirred tanks, showing that compartmental models are capable of capturing effects of localized hydrodynamics (Vonka and Soos, 2015). The application of compartment model-based PBE simulations of stirred reactors has also been extended to continuous processes, demonstrating their effectiveness in capturing complex droplet behaviors under varying operational conditions (N. Sheibat-Othman, 2018). These examples highlight the versatility of compartment models in the treatment of multi-phase systems. A more complex compartment topology could potentially improve simulation predictions, but it would significantly increase the number of model parameters that would have to be estimated.

In this work, we describe development of a compartment model-PBE simulation for predicting droplet size distributions in equipment designed to generate emulsions, such as homogenizers used in the pharmaceuetical industry. While CFD-PBE models have been developed to simulate homogenizers as described above, the purpose of the compartment model-PBE simulation considered here is to provide a computationally efficient tool that balances predictive accuracy with ease of implementation, making it suitable for industrial applications where quick assessments are often required. The simulation tool does not require users have expertise in CFD and multiphase flow. Although the simulation tool can incorporate any number of hydrodynamic compartments, the model is tested by using only two compartments – one to account for the strongly turbulent region near the homogenizer rotor and another compartment for the remaining reactor volume. The model does require specification of fluid physical properties, definition of fluid model topology, and various associated model parameters. To as great of an extent as possible, appropriate values for difficult to obtain model parameters are estimated automatically using existing correlations and heuristics.

The remainder of this report is structured as follows. First, development of the droplet size prediction tool is discussed in detail. Subsequently, emulsification experiments using two emulsion cream formulations are described, as well as the techniques for measuring droplet size distributions in these emulsions. Next, simulation predictions are compared with experimental data to assess the accuracy and robustness of the model predictions.