Abstract. Geochemical and field evidence suggest that melt transport in some regions of the mantle is localized into mesoscale "channels" that have widths of 0.1-100 m or larger. Nevertheless, the mechanisms for formation of such channels from a grain-sere distribution of melt are poorly understood. The purpose of this paper is to investigate one possible mechanism for channel formation: the reaction infiltration instability (RII). We present numerical solutions of the full equations for reactive fluid flow in a viscously deformable, permeable medium. We show that dissolution in a cornpactible solid with a vertical solubility gradient can lead to significant flow localization such that > 90% of the melt flux is channelized in < 20% of the available area. In particular, the ability of the solid to compact enhances the instability by forming impermeable regions between channels. The combination of reaction, diffusion, and solid compaction leads to strong selection of preferred length scales with channel spacing smaller than the compaction length (6 ,,• 10 •-104 m). We explore the evolution of dissolution channels over parameter space and show that the behavior of the full nonlinear solutions is consistent with predictions from linear stability analysis. We also briefly consider the behavior of the instability in the presence of melting due to adiabatic decompression and demonstrate that significant localization can occur even in the presence of uniform melting and compaction. Using the linear analysis to extend these results for parameters expected in the Earth's manfie suggests that robust channel systems could form through the RII from a homogeneous system in ,,400,000 years with dominant channel spacing of 1-200 m.

We demonstrate finite structures formed as a consequence of the “reactive infiltration instability” (Chadam et al., 1986) in a series of laboratory and numerical experiments with growth of solution channels parallel to the fluid flow direction. Regions with initially high porosity have high ratios of fluid volume to soluble solid surface area and exhibit more rapid fluid flow at constant pressure, so that dissolution reactions in these regions produce a relatively rapid increase in porosity. As channels grow, large ones entrain flow laterally inward and extend rapidly. As a result, small channels are starved and disappear. The growth of large channels is an exponential function of time, as predicted by linear stability analysis for growth of infinitesimal perturbations in porosity. Our experiments demonstrate channel growth in the presence of an initial solution front and without an initial solution front where there is a gradient in the solubility of the solid matrix. In the gradient case, diffuse flow is unstable everywhere, channels can form and grow at any point, and channels may extend over the length scale of the gradient. As a consequence of the gradient results, we suggest that the reactive infiltration instability is important in the Earth's mantle, where partial melts in the mantle ascend adiabatically. Mantle peridotite becomes increasingly soluble as the melts decompress. Dissolution reactions between melts and peridotite will produce an increase in liquid mass and lead to formation of porous channels composed of dunite (>95% olivine). Replacive dunite is commonly observed in the mantle section of ophiolites. Focused flow of poly baric partial melts of ascending peridotite within dunite channels may explain the observed chemical disequilibrium between shallow, oceanic mantle peridotites and mid‐oceanic ridge basalts (MORB). This hypothesis represents an important alternative to MORB extraction in fractures, since fractures may not form in weak, viscously deforming asthenospheric mantle. We also briefly consider the effects of crystallization, rather than dissolution reactions, on the morphology of porous flow via a second set of experiments where fluid becomes supersaturated in a solid phase. Formation of short‐lived conduits parallel to the flow direction occurs rapidly, and then each conduit is eventually choked by interior crystallization; fluid flow then passes through the most permeable portion of the walls to form a new conduit. On long time scales and length scales, transient formation and destruction of conduits will result in random and diffuse flow. Where liquid cools as it rises through mantle tectosphere on a conductive geotherm, it will become saturated in pyroxene as well as olivine and decrease in mass. This process may produce a series of walled conduits, as in our experiments. Development of a low‐porosity cap overlying high porosity conduits may create hydrostatic overpressure sufficient to cause fracture and magma transport to the surface in dikes.

We present results of a theoretical study aimed at understanding melt extraction from the upper mantle. Specifically, we address mechanisms for focusing of porous flow of melt into conduits beneath mid‐ocean ridges in order to explain the observation that most oceanic residual peridotites are not in equilibrium with mid‐ocean ridge basalt. The existence of such conduits might also explain geological features, termed replacive dunites, that are observed in exposed mantle sections. We show here, by linear analysis, that flow in a chemically reactive porous media is unstable in the presence of a solubility gradient, such as induced by adiabatic ascent of melt underneath mid‐ocean ridges. The initially homogeneous flow becomes focused in time to produce elongated high‐porosity fingers that act as conduits for transport of fast flowing melt. This instability arises due to a positive feedback mechanism in which a region of slightly higher than average porosity causes increased influx of unsaturated flow, leading to increased dissolution which further reduces the Porosity. Even in the presence of matrix compaction and chemical diffusion the instability is demonstrated to be robust. Our analysis also indicates the existence of growing, traveling waves which transport and amplify porosity and concentration perturbations.

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We numerically model two-dimensional systems of granular aggregates confined between two rough walls and demonstrate that at a critical grain volume fraction nu(c) an abrupt rigidity transition occurs. The transition has first-order characteristics, although the elastic constants undergo a second-order transition. Densely packed grains, with a volume fraction nu>nu(c), display an elastic-plastic rheology. Loose packings, with nu

We present results from two-dimensional computer simulations of shearing granular layers, using a discrete element code, and applying a wide range of boundary conditions. We specifically investigate the distribution of shear within the granular layer and find two different modes of localization depending on the applied shear velocity, pressure, and layer thickness: (1) granular layers that develop a persistent shearing boundary region ("fluidlike" behavior) and (2) layers that switch between diffuse deformation and randomly positioned internal shear bands ("solidlike" behavior). The two end-member deformation modes can be found in laboratory experiments performed under low and high confining pressure, respectively. Micromechanical investigation reveals two different statistical distributions of the grain contacts correlating with the two different shearing modes. These results imply that rehological transitions in granular flow modes are linked to quantifiable microtstructural organization.

[1] Two-dimensional numerical simulations of shear in a gravity-free layer of circular grains were conducted to illuminate the basic mechanics of shear of granular layers (such as layers of fault gouge). Our simulated granular layers exhibit either stable (steady state) or unstable (stick slip) motion. The transition from steady to stick-slip sliding depends on loading velocity and applied confining stress in a way similar to a simple model of a block on a frictional surface. We investigate the conditions which lead to naturally occurring stick-slip behavior and study in detail the systems behavior prior to and during slip events. Matching our numerical results to a spring block model, the system of grains was found to have bulk static and dynamic coefficients of friction that differ by about 0.1. This differing static and dynamic friction emerged spontaneously, from the collective behavior of grains, and was not prescribed a priori via a frictional rule between grain contacts. Results show that the micromechanics of contact forces is responsible for stick-slip behavior: During the ''stuck'' phase, and in preparation for slip, more and more grain contacts which carry low forces slide, resulting in accelerating internal stress release. When enough of the low-force contacts frictionally slide, the granular layer weakens and losses rigidity, leading to motion of contacts that carry larger forces and large-scale slip. Our results may have implications to the understanding of the stability of gouge layers and are thus related to the underlying physics of earthquakes.

Understanding the mechanical properties of glasses remains elusive since the glass transition itself is not fully understood, even in well studied examples of glass formers in two dimensions. In this context we demonstrate here: (i) a direct evidence for a diverging length scale at the glass transition (ii) an identification of the glass transition with the disappearance of fluid-like regions and (iii) the appearance in the glass state of fluid-like regions when mechanical strain is applied. These fluid-like regions are associated with the onset of plasticity in the amorphous solid. The relaxation times which diverge upon the approach to the glass transition are related quantitatively.