Permeabilities, interfacial areas and curvatures of partially molten systems: Results of numerical computations of equilibrium microstructures

Abstract

The general mathematical constraints for thermomechanical equilibrium of partial melts under hydrostatic or nearly hydrostatic stress conditions are well known. However, melt phase geometries under equilibrium conditions have previously been understood only qualitatively. Because of its importance in determining bulk physical and chemical properties of partially molten regions of the crust and the mantle, we have computed the geometries of the liquid phase for a range of melt fractions and dihedral angles. We describe here a theoretical interfacial topology model and its associated calculational algorithms which yield numerically precise equilibrium solid‐liquid interfacial surfaces where the only constraints imposed on the system are constant mean curvature and constant wetting angle in accordance with equilibrium. The calculated geometries are used to determine the permeability of partial melts to fluid flow, interfacial areas, surface energy, minimum channel cross section, surface mean curvature, and maximum trappable melt fraction for melt fractions up to 5% and wetting angles between 20° and 80°. For wetting angles less than 60° the melt is distributed in an interconnected network of channels along the grain edges, and therefore melt mobilization is possible as soon as melt forms. For wetting angles greater than 60° the melt phase will be distributed in isolated pockets at the grain corners if the melt fraction is less than a critical value, whereas an interconnected network of melt channels will be established if the critical melt fraction is exceeded. Wetting angle exerts a first‐order control on the permeability of partially molten systems through its effect on the connectivity of the melt phase. Once a connected melt phase has formed, the permeability is only mildly sensitive to wetting angle.

Mantle Pb paradoxes: the sulfide solution

“…For large values of ", a small amount of melt will form isolated pockets at four grain junctions if the surface energy of the solid is isotropic. Decreasing " increases the tendency for melt to wet threegrain junctions until, at " = 60 ° or less, an interconnected network will form even for very small amounts of melt (e.g., Smith 1964;von Bargen and Waff 1986). Several studies show that the dihedral angle between sulfide melt and olivine decreases strongly as the oxygen and sulfur content of the sulfide melt increases (Minarik et al 1996;Gaetani and Grove 1999;Rose and Brenan 2001;Terasaki et al 2005).…”

Differentiation and core formation in accreting planetesimals

“…For isotropic systems the values n = 2 and τ ≈ 1600 to 3000 have been derived numerically (von Bargen & Waff 1986;Cheadle et al 2004), whereas experimental data yield n ≈ 3 and τ ≈ 10 to 270 (Wark & Watson 1998;Connolly et al 2009). …”

“…Furthermore, an interconnected melt network is required as the melt won't separate easily from the residual crystals if trapped in disconnected pockets. The pockets occur if the so called dihedral angle exceeds value of 60 • and the melt fraction stays below a certain value termed critical melt fraction ϕ c (von Bargen & Waff 1986). Thereby the dihedral angle is measured at the triple junctions of two grains and melt and is defined as the angle between the grains.…”

Wetting properties of anorthite aggregates: Implications for fluid connectivity in continental lower crust

“…AlSiMag, the Pt capsules (2f) were inserted into predrilled AlSiMag cylinder (6 mm diameter and 12 mm long). NiO, the sample in experiments were carried out using a sample assembly of the method of Watson [1999]; Ni cylinders were predrilled and oxidized on the surface, and the holes subsequently fitted with Pt sleeves to contain the samples. In this case, closure of the containers against the fluid loss was accomplished by pressure sealing during initial sample pressurization in the piston cylinder apparatus [Ayers et al, 1992].…”

“…[3] At the low fluid fractions f < $0.01 believed to be applicable to the lower crustal condition, the behavior of fluid in texturally equilibrated materials strongly depends on wetting properties between solid and fluid [e.g., Watson and Brenan, 1987;von Bargen and Waff, 1986;McKenzie, 1987]. The grainscale distribution and connectivity of the fluid phase in isotropic rocks is controlled by the dihedral angle (q), formed at the intersection of a grain boundary with two solid-fluid interfaces.…”