Permeability of granular aggregate of soft gel: Application to the partially molten system

In the upper part of the Earth there exists a region where the rock is partially molten. The magmatic melt rises through the partially molten region as a form of permeable flow. The timescale and efficiency of the melt migration are controlled by the permeability, which is a function of the melt fraction and the distribution of the melt at the grain scale. Using gel as an analog of the solid phase of the partially molten system, the permeability and the electrical conductivity were measured. With deformation the gel deforms into a polyhedron due to its high deformability, and the fluid phase exists at edge and corner regions. The morphology of the mixture system is similar to that of the partially molten system controlled by the interfacial energy. Both of the permeability and the electrical conductivity obey power-law functions of the liquid fraction. The permeability is close to Kozeny–Carman type permeability and the electrical conductivity obeys Archieʹs law at higher liquid fraction (about 10% to 30%). They reduce drastically with reduction of the liquid fraction at lower liquid fraction (about 2% to 10%). These behaviors are considered to result from dispersion of pseudo-dihedral angle. The permeability in the upper mantle would behave like that of the gel–fluid system because the dispersion of dihedral angle exists due to poly-mineralic solid phase of the upper mantle and anisotropic interfacial energy. Also, the permeability is found to be proportional to the square of the electrical conductivity. This relation is useful to estimate the permeability at depth from the electrical conductivity measurement.