(551j) A Coupled Computational Fluid Dynamic/Population Balance Method to Understand Microstructure in Foams and Emulsions

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. Several foams are studied including polyurethane and Gillette Foamy, where validation data is available. In this presentation we expand on the previous work [1, 2] to enhance the constructed model framework for bubble-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. We have new rheology/microscopy data to understand coarsening in a model system and calibrate our coarsening kernel. This model is used to predict material properties including density, thermal conductivity, and bubble size evolution in time. Results for final densities are compared to both previous model formulations and a variety of experimental data [4].

*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.