Analytical model for the prediction of permeability of triply periodic minimal surfaces

Triply periodic minimal surfaces (TPMS) are mathematically defined cellular structures whose geometry can be quickly adapted to target desired mechanical response (structural and fluid). This has made them desirable for a wide range of bioengineering applications; especially as bioinspired materials for bone replacement. The main objective of this study was to develop a novel analytical framework which would enable calculating permeability of TPMS structures based on the desired architecture, pore size and porosity. To achieve this, computer-aided designs of three TPMS structures (Fisher-Koch S, Gyroid and Schwarz P) were generated with varying cell size and porosity levels. Computational Fluid Dynamics (CFD) was used to calculate permeability for all models under laminar flow conditions. Permeability values were then used to fit an analytical model dependent on geometry parameters only. Results showed that permeability of the three architectures increased with porosity at different rates, highlighting the importance of pore distribution and architecture. The computed values of permeability fitted well with the suggested analytical model (R²>0.99, p<0.001). In conclusion, the novel analytical framework presented in the current study enables predicting permeability values of TPMS structures based on geometrical parameters within a difference <5%. This model, which could be combined with existing structural analytical models, could open new possibilities for the smart optimisation of TPMS structures for biomedical applications where structural and fluid flow properties need to be optimised.