Compaction around a rigid, circular inclusion in partially molten rock

Abstract

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.

Torsion of a cylinder of partially molten rock with a spherical inclusion: Theory and simulation

“…In this case, the pressure shadows around the inclusion that are identified by perturbations in the porosity field rotate and advect with the matrix, with the top moving to the right and the bottom to the left, as shown in Figures 2a and 2c (note that all To study the behavior of pressure shadows in more detail, we compute integrals of porosity on the twodimensional slice through the inclusion. Integration is from the local radius of the edge of the inclusion r 5 a to one inclusion radius outward at r52a, for a series of azimuths between 0 and 2p around the circular cross section of the inclusion [Qi et al, 2013;Alisic et al, 2014]:…”

“…This behavior was described in detail by McKenzie and Holness [], Alisic et al . [], and Rudge [] and is discussed further in section B1.…”

“…Furthermore, they find that melt-rich bands, also observed in experiments without beads [e.g., Holtzman et al, 2003], emerge and tend to connect with the large-porosity lobes of the pressure shadow. Previous analysis of pressure shadows [McKenzie and Holness, 2000;Rudge, 2014] and their interaction with banding instabilities [Alisic et al, 2014] suggests that the observed relationship between these two modes of compaction could constrain the bulk viscosity of the two-phase system.…”

A new formulation for coupled magma/mantle dynamics

“…This is expected, as our formulation only addresses the increase of ξ as the porosity φ → 0. However, this sensitivity to ξ/η might not be problematic for realistic applications, as this ratio is expected to be on the order of 1-100 (Hewitt & Fowler 2008;Takei & Holtzman 2009;Simpson et al 2010;Katz 2010;Schmeling et al 2012;Alisic et al 2014).…”

Melt-band instabilities with two-phase damage

“…Thus a detailed study of grain size distributions within the experiments could form a useful test of the theory we have presented here. The natural next step for the development of the theory is to perform a full numerical solution of the governing equations, which will allow a detailed description of the time evolution of the bands (Katz et al 2006;Butler 2012;Alisic et al 2014). With a numerical solution it will be possible to study the connection between the local instantaneous rheology (which we have shown to be effectively strain-rate weakening) and the overall stress-strain curve observed over longer times (which may differ due to the development of the melt bands that concentrate deformation).…”