Modeling of the Effective Permittivity of Open-Cell Ceramic Foams Inspired by Platonic Solids

Open-cell solid foams are rigid skeletons that are permeable to fluids, and they are used as direct heaters or thermal dissipaters in many industrial applications. Using susceptors, such as dielectric materials, for the skeleton and exposing them to microwaves is an efficient way of heating them. The heating performance depends on the permittivity of the skeleton. However, generating a rigorous description of the effective permittivity is challenging and requires an appropriate consideration of the complex skeletal foam morphology. In this study, we propose that Platonic solids act as building elements of the open-cell skeletal structures, which explains their effective permittivity. The new, simplistic geometrical relation thus derived is used along with electromagnetic wave propagation calculations of models that represent real foams to obtain a geometrical, parameter-free relation, which is based only on foam porosity and the material's permittivity. The derived relation facilitates an efficient and reliable estimation of the effective permittivity of open-cell foams over a large range of porosity.