Experimental investigation of pressure drop, fluid velocities and dispersion within TPMS porous media

Triply Periodic Minimal Surface (TPMS) are a family of mathematically well-defined surfaces with almost zero mean curvature that also mimic several naturally occurring porous media. Measurements of pressure drop and fluid velocities with refractive index matched PIV is carried out in three TPMS geometries (Gyroid, Primitive and BCC) for a range of porosity and Reynolds number (Re) covering laminar to turbulent regimes. Usual metrics, such as Darcy and Forchheimer permeabilities are measured, and non-dimensional pressure drop (f) is plotted versus Re based on hydraulic diameter. A lack of collapse in f(Re) curves is found for different TPMS geometries, that is well-known in general porous media. To alleviate this, we define an ‘equivalent diameter’ (d_equiv) that allows collapse of various f(Re) curves (based on d_equiv)  within the laminar region with the ‘Ergun equation’ for packed bed of spheres. With comparison of different TPMS geometries now possible, we observe lower drag in the turbulent region for some TPMS geometries compared to packed spheres as well as more nuanced f(Re) features that cannot be captured by two usual permeabilities as the flow ‘transitions’ from laminar to turbulent. Preliminary longitudinal dispersion measurements show a Peclet number of O(1) in both turbulent and laminar regimes suggesting enhanced laminar mixing.