On the porosity-dependent permeability and conductivity of triply periodic minimal surface based porous media

With the fast development in the field of additive manufacturing, triply periodic minimal surface (TPMS) based porous media have recently found many uses in mechanical property tuning. However, there is still a lack of understanding in their porosity-dependent permeability and electrical as well as thermal conductivity. Here, we perform finite volume simulations on the solid and void domains of the Schoen gyroid (SG), Schwarz primitive (SP) and Schwarz primitive beam (SPB) TPMS with porosities between 63% and 88% in Ansys Fluent. A simple cubic lattice (CL) of equivalent porosity served as reference. The SPB and CL showed up to one order of magnitude higher permeabilities than the SG and SP. However, SG and SP have about 1.3 and 2.6 times the electrical and thermal conductivity of SPB and CL, respectively. Furthermore, the properties of SPB and CL are largely affected by the surface area density, whereas tortuosity variation does not impact permeability and conductivity to a major extent. Finally, empirical relations are adapted to describe the presented data and thus, they may enable future designers of TPMS based porous structures to fine-tune the geometries according to the requirements on permeability and electrical as well as thermal conductivity.