Geometric modeling of Plateau borders using the orthographic projection method for closed cell rigid polyurethane foam thermal conductivity prediction

The geometric Plateau border model for closed cell polyurethane foam was developed based on volume integrations of approximated 3D four-cusp hypocycloid structure. The tetrahedral structure of convex struts was orthogonally projected into 2D three-cusp deltoid with three central cylinders. The idealized single unit strut was modeled by superposition. The volume of each component was calculated by geometric analyses. The strut solid fraction f _s and foam porosity coefficient δ were calculated based on representative elementary volume of Kelvin and Weaire-Phelan structures. The specific surface area S_v derived respectively from packing structures and deltoid approximation model were put into contrast against strut dimensional ratio ϵ. The characteristic foam parameters obtained from this semi-empirical model were further employed to predict foam thermal conductivity.