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Article

Computational Analysis of Nonuniform Expansion in Polyurethane Foams

Department Flow and Material Simulation, Fraunhofer Institute for Industrial Mathematics, Fraunhofer-Platz 1, D-67663 Kaiserslautern, Germany
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Polymers 2019, 11(1), 100; https://doi.org/10.3390/polym11010100
Received: 4 December 2018 / Revised: 21 December 2018 / Accepted: 21 December 2018 / Published: 9 January 2019
(This article belongs to the Special Issue Functional Polyurethanes – In Memory of Prof. József Karger-Kocsis)
This paper computationally investigates heterogeneity in the distribution of foam fraction in chemically expanding blown polyurethane foam. The experimentally observed disparity in the volumes of expanded foam when an equal mass of the foaming mixture was injected into tubes of different dimensions motivated this study. To understand this phenomenon, attributed to local variations in the thermal and rheological properties of the expanding system, we explore available data from free-rise foam-expansion experiments in different geometries. Inspired by the mathematical framework for the microstructure modelling of bubble growth in viscous liquids, we study the reacting mixture as a continuum and formulate appropriate mathematical models that account for spatial inhomogeneity in the foam-expansion process. The nonlinear coupled system of partial differential equations governing flow was numerically solved using finite-volume techniques, and the associated results are presented and discussed with graphical illustrations. The proximity of the foaming-mixture core to the external environment and the thickness of a thermal-diffusion layer formed near the bounding geometry was seen to influence the distribution of the foam fraction. Our simulations showed an average spatial variation of about 1.1% in the distribution of solid foam fraction from the walls to the core, as verified with data from μ CT scan analysis of the expanded foam. This also reflects the distribution of void fraction in the foam matrix. The models were validated with experimental data, and our results favourably compared with the experiment observations. View Full-Text
Keywords: polyurethane foams; nonuniform expansion; foam fraction distribution; reaction injection molding; chemorheology; finite-volume method polyurethane foams; nonuniform expansion; foam fraction distribution; reaction injection molding; chemorheology; finite-volume method
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MDPI and ACS Style

Niedziela, D.; Ireka, I.E.; Steiner, K. Computational Analysis of Nonuniform Expansion in Polyurethane Foams. Polymers 2019, 11, 100. https://doi.org/10.3390/polym11010100

AMA Style

Niedziela D, Ireka IE, Steiner K. Computational Analysis of Nonuniform Expansion in Polyurethane Foams. Polymers. 2019; 11(1):100. https://doi.org/10.3390/polym11010100

Chicago/Turabian Style

Niedziela, D., I. E. Ireka, and K. Steiner 2019. "Computational Analysis of Nonuniform Expansion in Polyurethane Foams" Polymers 11, no. 1: 100. https://doi.org/10.3390/polym11010100

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