Textural equilibrium melt geometries around tetrakaidecahedral grains

TL;DR

This paper presents numerical calculations of textural equilibrium melt geometries around tetrakaidecahedral grains, revealing various melt topologies, their properties, and permeability transitions based on porosity and dihedral angle.

Contribution

It introduces a detailed numerical analysis of melt geometries in tetrakaidecahedral grains, including topology transitions and permeability behavior.

Findings

Wetting occurs at porosity > 11% for small dihedral angles.

Melt geometries exhibit energy, pressure, and curvature variations.

Permeability transitions from quadratic to cubic with porosity.

Abstract

In textural equilibrium, partially molten materials minimise the total surface energy bound up in grain boundaries and grain-melt interfaces. Here, numerical calculations of such textural equilibrium geometries are presented for a space-filling tessellation of grains with a tetrakaidecahedral (truncated octahedral) unit cell. Two parameters determine the nature of the geometries: the porosity and the dihedral angle. A variety of distinct melt topologies occur for different combinations of these two parameters, and the boundaries between different topologies has been determined. For small dihedral angles, wetting of grain boundaries occurs once the porosity has exceeded 11%. An exhaustive account is given of the main properties of the geometries: their energy, pressure, mean curvature, contiguity, and areas on cross-sections and faces. Their effective permeabilities have been calculated, and demonstrate a transition between a quadratic variation with porosity at low porosities to a cubic variation at high porosities.