Texturally Equilibrated Pore Networks

• http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.048001
• doi:10.1103/PhysRevLett.113.048001

Abstract — In texturally equilibrated porous media the pore geometry evolves to minimize the energy of the liquid-solid interfaces, while maintaining the dihedral angle θ at solid-solid-liquid contact lines. We present computations of three-dimensional texturally equilibrated pore networks using a level-set method. Our results show that the grain boundaries with the smallest area can be fully wetted by the pore fluid even for θ>0. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Even small anisotropy in the fabric of the porous medium allows the wetting of these faces at very low porosities, ϕ<3%. Percolation and orientation of the wetted faces relative to the anisotropy of the fabric are controlled by θ. The wetted grain boundaries are perpendicular to the direction of stretching for θ>60° and the pores do not percolate for any investigated ϕ. For θ<60°, in contrast, the grain boundaries parallel to the direction of stretching are wetted and a percolating pore network forms for all ϕ investigated. At low θ even small anisotropy in the fabric induces large anisotropy in the permeability, due to the concentration of liquid on the grain boundaries and faces.

• http://www.sciencedirect.com/science/article/pii/S0021999115003575
• doi:10.1016/j.jcp.2015.05.023

Abstract — Textural equilibrium controls the distribution of the liquid phase in many naturally occurring porous materials such as partially molten rocks and alloys, salt–brine and ice–water systems. In these materials, pore geometry evolves to minimize the solid–liquid interfacial energy while maintaining a constant dihedral angle, θ, at solid–liquid contact lines. We present a level set method to compute an implicit representation of the liquid–solid interface in textural equilibrium with space-filling tessellations of multiple solid grains in three dimensions. Each grain is represented by a separate level set function and interfacial energy minimization is achieved by evolving the solid–liquid interface under surface diffusion to constant mean curvature surface. The liquid volume and dihedral angle constraints are added to the formulation using virtual convective and normal velocity terms. This results in an initial value problem for a system of non-linear coupled PDEs governing the evolution of the level sets for each grain, using the implicit representation of the solid grains as initial condition. A domain decomposition scheme is devised to restrict the computational domain of each grain to few grid points around the grain. The coupling between the interfaces is achieved in a higher level on the original computational domain. The spatial resolution of the discretization is improved through high-order spatial differentiation schemes and localization of computations through domain composition. Examples of three-dimensional solutions are also obtained for different grain distributions networks that illustrate the geometric flexibility of the method.

• http://www.pnas.org/content/early/2017/11/28/1707580114.short
• doi:10.1073/pnas.1707580114

Abstract — The segregation of dense core-forming melts by porous flow is a natural mechanism for core formation in early planetesimals. However, experimental observations show that texturally equilibrated metallic melt does not wet the silicate grain boundaries and tends to reside in isolated pockets that prevent percolation. Here we use pore-scale simulations to determine the minimum melt fraction required to induce porous flow, the percolation threshold. The composition of terrestrial planets suggests that typical planetesimals contain enough metal to overcome this threshold. Nevertheless, it is currently thought that melt segregation is prevented by a pinch-off at melt fractions slightly below the percolation threshold. In contrast to previous work, our simulations on irregular grain geometries reveal that a texturally equilibrated melt network remains connected down to melt fractions of only 1 to 2%. This hysteresis in melt connectivity allows percolative core formation in planetesimals that contain enough metal to exceed the percolation threshold. Evidence for the percolation of metallic melt is provided by X-ray microtomography of primitive achondrite Northwest Africa (NWA) 2993. Microstructural analysis shows that the metal–silicate interface has characteristics expected for a texturally equilibrated pore network with a dihedral angle of ∼85°. The melt network therefore remained close to textural equilibrium despite a complex history. This suggests that the hysteresis in melt connectivity is a viable process for percolative core formation in the parent bodies of primitive achondrites.