A universal model for the permeability of sintered materials

Abstract

Sintered materials are used as permeable filters and flow controllers, for which a validated and general model of porosity and permeability is required. Here, we prepare samples built from mono- and polydisperse glass bead populations sintered for known times at high temperature, and then measure the sample porosity and permeability. We supplement our new dataset with published permeability data for sintered systems including high-temperature in situ determinations of permeability during sintering. We test a range of mathematical models for the change in permeability with porosity as sintering progresses from a value for the initial granular particle packing geometry, down to the percolation threshold at low porosity. We find good agreement between our datasets and a preferred theoretical approach – a percolation theory model – with no explicit requirement for empirical adjustment. However, we propose semi-empirical steps that generalize this theory to a universal description across all porosities. Finally, we quantify the inertial component of fluid transport at high flow rates through these materials. Our model framework is made available via a user-friendly downloadable spreadsheet which takes particle size distribution as an input and provides permeability as an output.