Formation of the Lunar Primary Crust From a Long-Lived Slushy Magma Ocean.

Classical fractional crystallization scenarios of early lunar evolution suggest crustal formation by the flotation of light anorthite minerals from a liquid magma ocean. However, this model is challenged by the > 200 Myr age range of primitive ferroan anorthosites, their concordance with Mg-suite magmatism and by the compositional diversity observed in lunar anorthosites. Here, we propose a new model of slushy magma ocean crystallization in which crystals remain suspended in the lunar interior and crust formation only begins once a critical crystal content is reached. Thereafter crustal formation occurs by buoyant melt extraction and magmatism. The mixture viscosity strongly depends on temperature and solid fraction driving the development of a surface stagnant lid where enhanced solidification and buoyant ascent of melt lead to an anorthite-enriched crust. This model explains lunar anorthosites heterogeneity and suggests a crustal formation timescale of 100s Ma, reconciling anorthosite ages with an early age of the Moon.

Crystal settling and convection in the Shiant Isles Main Sill.

The 168 m-thick Shiant Isles Main Sill is a composite body, dominated by an early, 24 m-thick, picrite sill formed by the intrusion of a highly olivine-phyric magma, and a later 135 m-thick intrusion of olivine-phyric magma that split the earlier picrite into a 22 m-thick lower part and a 2 m-thick upper part, forming the picrodolerite/crinanite unit (PCU). The high crystal load in the early picrite prevented effective settling of the olivine crystals, which retain their initial stratigraphic distribution. In contrast, the position of the most evolved rocks of the PCU at a level ~80% of its total height point to significant accumulation of crystals on the floor, as evident by the high olivine mode at the base of the PCU. Crystal accumulation on the PCU floor occurred in two stages. During the first, most of the crystal load settled to the floor to form a modally and size-sorted accumulation dominated by olivine, leaving only the very smallest olivine grains still in suspension. The second stage is recorded by the coarsening-upwards of individual olivine grains in the picrodolerite, and their amalgamation into clusters which become both larger and better sintered with increasing stratigraphic height. Large clusters of olivine are present at the roof, forming a foreshortened mirror image of the coarsening-upwards component of the floor accumulation. The coarsening-upwards sequence records the growth of olivine crystals while in suspension in a convecting magma, and their aggregation into clusters, followed by settling over a prolonged period (with limited trapping at the roof). As olivine was progressively lost from the convecting magma, crystal accumulation on the (contemporaneous) floor of the PCU was increasingly dominated by plagioclase, most likely forming clusters and aggregates with augite and olivine, both of which form large poikilitic grains in the crinanite. While the PCU is unusual in being underlain by an earlier, still hot, intrusion that would have enhanced any driving force for convection, we conclude from comparison with microstructures in other sills that convection is likely in tabular bodies >100 m thickness.

Viscous control of peeling an elastic sheet by bending and pulling.

Propagation of a viscous fluid beneath an elastic sheet is controlled by local dynamics at the peeling front, in close analogy with the capillary-driven spreading of drops over a precursor film. Here we identify propagation laws for a generic elastic peeling problem in the distinct limits of peeling by bending and peeling by pulling, and apply our results to the radial spread of a fluid blister over a thin prewetting film. For the case of small deformations relative to the sheet thickness, peeling is driven by bending, leading to radial growth as t(7/22). Experimental results reproduce both the spreading behavior and the bending wave at the front. For large deformations relative to the sheet thickness, stretching of the blister cap and the consequent tension can drive peeling either by bending or by pulling at the front, both leading to radial growth as t(3/8). In this regime, detailed predictions give excellent agreement and explanation of previous experimental measurements of spread in the pulling regime in an elastic Hele-Shaw cell.

Ultimate regime of high Rayleigh number convection in a porous medium.

Well-resolved direct numerical simulations of 2D Rayleigh-Bénard convection in a porous medium are presented for Rayleigh numbers Ra≤4×10(4) which reveal that, contrary to previous indications, the linear classical scaling for the Nusselt number, Nu~Ra, is attained asymptotically. The flow dynamics are analyzed, and the interior of the vigorously convecting system is shown to be increasingly well described as Ra→∞ by a simple columnar "heat-exchanger" model with a single horizontal wave number k and a linear background temperature field. The numerical results are approximately fitted by k~Ra(0.4).

Stable and unstable miscible displacements in layered porous media.

The effect of permeability heterogeneities and viscosity variations on miscible displacement processes in porous media is examined using high-resolution numerical simulations and reduced theoretical modelling. The planar injection of one fluid into a fluid-saturated, two-dimensional porous medium with a permeability that varies perpendicular to the flow direction is studied. Three cases are considered, in which the injected fluid is equally viscous, more viscous or less viscous than the ambient fluid. In general it is found that the flow in each case evolves through three regimes. At early times, the flow exhibits the concentration evolves diffusively, independent of both the permeability structure and the viscosity ratio. At intermediate times, the flow exhibits different dynamics including channelling and fingering, depending on whether the injected fluid is more or less viscous than the ambient fluid, and depending on the relative magnitude of the viscosity and permeability variations. Finally, at late times, the flow becomes independent of the viscosity ratio and dominated by shear-enhanced (Taylor) dispersion. For each of the regimes identified above, we develop reduced-order models for the evolution of the transversely averaged concentration and compare them to the full numerical simulations.

The top-down solidification of iron asteroids driving dynamo evolution.

The cores of some small planetesimals, such as asteroid (16) Psyche, are thought to have been exposed through collisions during the early solar system that removed their mantles. These small bodies likely solidified from the top down representing a fundamentally different solidification regime to that of Earth's core. Here we derive simplified models of the downwards solidification of the metallic crust, and consider thermal convection and the potential for viscous delamination of the weak, warm base of the crust to provide a buoyancy flux sufficient to drive a dynamo. Thermal buoyancy is very short lived (~1000 years), and therefore cannot be the source of measured paleomagnetic remanence. In contrast, viscous delamination is found to provide a long-lasting buoyancy flux sufficient to generate an intense, multipolar magnetic field, while not greatly affecting the crustal solidification time. Our results suggest that a Psyche-sized (150 km radius) body solidified in roughly 6.7 - 20 Myr, and that delamination produced a strong magnetic field over much of this time. Finally, including light, insoluble impurities, such as sulfur, results in a partially solid mushy zone at the base of the crust. This further weakens the base of the crust and results in smaller scale delamination events. Despite a significant change in the dynamics of delamination, the time to total solidification and the predicted properties of the magnetic field are broadly comparable to the sulfur-free case, though we argue this may result in observable compositional stratification of the body.

Indentation of a floating elastic sheet: geometry versus applied tension.

The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth. For small indentation depths, we find that the force-indentation curve is linear with a stiffness that we characterize in terms of the applied tension and bending stiffness of the sheet. At larger indentations, the force-indentation curve becomes nonlinear and the sheet is subject to a wrinkling instability. We study this wrinkling instability close to the buckling threshold and calculate both the number of wrinkles at onset and the indentation depth at onset, comparing our theoretical results with experiments. Finally, we contrast our results with those previously reported for very thin, highly bendable membranes.

Maximal liquid bridges between horizontal cylinders.

We investigate two-dimensional liquid bridges trapped between pairs of identical horizontal cylinders. The cylinders support forces owing to surface tension and hydrostatic pressure that balance the weight of the liquid. The shape of the liquid bridge is determined by analytically solving the nonlinear Laplace-Young equation. Parameters that maximize the trapping capacity (defined as the cross-sectional area of the liquid bridge) are then determined. The results show that these parameters can be approximated with simple relationships when the radius of the cylinders is small compared with the capillary length. For such small cylinders, liquid bridges with the largest cross-sectional area occur when the centre-to-centre distance between the cylinders is approximately twice the capillary length. The maximum trapping capacity for a pair of cylinders at a given separation is linearly related to the separation when it is small compared with the capillary length. The meniscus slope angle of the largest liquid bridge produced in this regime is also a linear function of the separation. We additionally derive approximate solutions for the profile of a liquid bridge, using the linearized Laplace-Young equation. These solutions analytically verify the above-mentioned relationships obtained for the maximization of the trapping capacity.

Flow-induced compaction of a deformable porous medium.

Fluid flowing through a deformable porous medium imparts viscous drag on the solid matrix, causing it to deform. This effect is investigated theoretically and experimentally in a one-dimensional configuration. The experiments consist of the downwards flow of water through a saturated pack of small, soft, hydrogel spheres, driven by a pressure head that can be increased or decreased. As the pressure head is increased, the effective permeability of the medium decreases and, in contrast to flow through a rigid medium, the flux of water is found to increase towards a finite upper bound such that it becomes insensitive to changes in the pressure head. Measurements of the internal deformation, extracted by particle tracking, show that the medium compacts differentially, with the porosity being lower at the base than at the upper free surface. A general theoretical model is derived, and the predictions of the model give good agreement with experimental measurements from a series of experiments in which the applied pressure head is sequentially increased. However, contrary to theory, all the experimental results display a distinct and repeatable hysteresis: the flux through the material for a particular applied pressure drop is appreciably lower when the pressure has been decreased to that value compared to when it has been increased to the same value.

Interface pinning of immiscible gravity-exchange flows in porous media.

We study the gravity-exchange flow of two immiscible fluids in a porous medium and show that, in contrast with the miscible case, a portion of the initial interface remains pinned at all times. We elucidate, by means of micromodel experiments, the pore-level mechanism responsible for capillary pinning at the macroscale. We propose a sharp-interface gravity-current model that incorporates capillarity and quantitatively explains the experimental observations, including the x~t(1/2) spreading behavior at intermediate times and the fact that capillarity stops a finite-release current. Our theory and experiments suggest that capillary pinning is potentially an important, yet unexplored, trapping mechanism during CO(2) sequestration in deep saline aquifers.