Abstract
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 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.
Highlights
The commercial relevance of flexible or rigid polyurethane (PU) foams has stimulated extensive research interest in their production and product-optimization processes
All numerical implementations were carried out with our inhouse FOAM solver based on the finite-volume method, and resident in the Complex Rheology Simulation (CoRheoS)
Accounting for spatial inhomogeneity in the expansion source term (S p ) (i.e., α > 0), the local variations which arises as a consequence of the spatial changes in temperature and the mixture viscosity influences the distribution of foam fraction in the PU foam system, Figure 9a,b
Summary
The commercial relevance of flexible or rigid polyurethane (PU) foams has stimulated extensive research interest in their production and product-optimization processes. They simulated and discussed the effect of gas depletion and the proximity of neighboring bubbles in the physically blown polymer, and predicted the evolution and size distribution of the bubbles in reasonable agreement with available experimental data. We adopted the modelling approach of Reference [19], which summarizes the specie consumption with the Kamal law [20] for the degree of cure, with an adequately modified expansion source term and accounting for local contributions of the mixture temperature and viscosity to the expanding system This approach does not quantify the bubbles in the foam, it gives a qualitative description of the distribution of void fractions in the domain.
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