(400e) A Coupled Computational Fluid Dynamic/Population Balance Method to Understand Microstructure in Emulsions and Foams

Understanding the rheology and microstructure of foams and emulsions is important for a number of applications from enhanced oil recovery to polymer upcycling, and advance manufacturing methods. We are developing a coupled computational fluid dynamics/population balance method to understand bubble/droplet size distribution during flow in complex geometries. The foam polyurethane, and a silicone oil/water emulsion are both studied.

In this presentation we expand on the previous work [1, 2] to enhance the constructed model framework for bubble/droplet-size predictions by adding both nucleation and breakage terms to the population balance equation. These additions allow us to better capture the evolution of the underlying microstructure of the materials of interests. We use the finite element method to solve the conservation equations: equations of motion, energy balance equation, species conservation with reaction, and transport of moments. The Quadrature Method of Moments (QMOM) is used to study the distribution of bubble sizes [3]. The free surface between the material of interest and the surrounding gas is modeled using either ALE or level set method depending on the material. The new breakage and nucleation kernels [2] allow better predict of early behavior of the polyurethane foam. Results for final densities are compared to both previous model formulations and a variety of experimental data [4]. The material properties density and thermal conductivity over time are also predicted.

Additionally, we have studied emulsion flows in a mixing/turbulent flow regime. We modify the breakage kernel employed in [6] to depend on shear rate and use the experimental data for a silicone/oil mixture in an annular centrifugal contactor [5] to fit the corresponding parameters. This model is used to predict the final droplet size distribution for a range of different mixing speeds and oil viscosities. Results using the viscosity dependent breakage kernels agree well with the experimental data for droplet size distribution.

*Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

References

[1] Rao, Rekha, et al. "Density predictions using a finite element/level set model of polyurethane foam expansion and polymerization." Computers & Fluids 175 (2018): 20-35.

[2] Ortiz, W., Mondy, L., Roberts, C., & Rao, R. (2022). Population balance modeling of polyurethane foam formation with pressure‐dependent growth kernel. AIChE Journal, 68(3), e17529.

[3] Karimi, Mohsen, Hermes Droghetti, and Daniele L. Marchisio. "Multiscale modeling of expanding polyurethane foams via computational fluid dynamics and population balance equation." Macromolecular Symposia. Vol. 360. No. 1. 2016.

[4] Roberts, C., Mondy, L., Soehnel, G., Brady, C., Shelden, B., Soehnel, M., ... & Rao, R. Bubble‐Scale Observations of Polyurethane Foam Expansion. AIChE Journal, e17595.

[5] Wyatt, Nicholas et al. “Drop-Size Distributions and Spatial Distributions in

an Annular Centrifugal Contactor.” AIChE Journal 59.6 (2013): 2219-2226.

[6] Lebaz, Noureddine, et al. "A population balance model for the prediction of breakage of emulsion droplets in SMX+ static mixers." Chemical Engineering Journal 361 (2019): 625-634