Compaction around a rigid, circular inclusion in partially molten rock

Conservation laws that describe the behavior of partially molten mantle rock have been established for several decades, but the associated rheology remains poorly understood. Constraints on the rheology may be obtained from recently published experiments involving deformation of partially molten rock around a rigid, spherical inclusion. These experiments give rise to patterns of melt segregation that exhibit the competing effects of pressure shadows and melt-rich bands. Such patterns provide an opportunity to infer rheological parameters through comparison with models based on the conservation laws and constitutive relations that hypothetically govern the system. To this end, we have developed software tools to simulate finite strain, two-phase flow around a circular inclusion in a configuration that mirrors the experiments. Simulations indicate that the evolution of porosity is predominantly controlled by the porosity-weakening exponent of the shear viscosity and the poorly known bulk viscosity. In two-dimensional simulations presented here, we find that the balance of pressure shadows and melt-rich bands observed in experiments only occurs for bulk-to-shear viscosity ratio of less than about five. However, the evolution of porosity in simulations with such low bulk viscosity exceeds physical bounds at unrealistically small strain due to the unchecked, exponential growth of the porosity variations. Processes that limit or balance porosity localization should be incorporated in the formulation of the model to produce results that are consistent with the porosity evolution in experiments