Mushy Layer Research Articles

Mathematical modeling of solidification process near the inner core boundary of the Earth

Radially symmetric analytic solutions of the heat and mass transfer equations governing convection in the Earth’s fluid core are found in terms of deviations from the adiabatic reference state. We demonstrate that an increase of the convective velocity leads to a decrease of the light constituent mass fraction and specific entropy. Where fluid is rising/descending, convective motions decrease/increase the mass fraction and entropy at the inner core boundary (ICB). The influence of convective motions on the thermal fluxes at the core mantle boundary is studied. On the basis of exact solutions we demonstrate that the liquid is supercooled near the ICB. An important point is that an increase in the convective velocity directed to the ICB increases the constitutional supercooling. We show that the anelastic model (AM) can be used only at small supercoolings near the ICB. The most probable solidification scenario “constitutional supercooling and morphological instability” should be described by a mushy layer theory near the ICB and by the AM in the rest region of the fluid outer core. On the basis of dendritic theory and selection mechanisms of crystal growth the dendrite tip radius and interdendritic spacing in the mushy layer at the ICB are determined in the presence of convection.

Two modes of sea‐ice gravity drainage: A parameterization for large‐scale modeling

We present a new one‐dimensional parameterization of gravity drainage implemented in an all‐new thermodynamic component of the Los Alamos Sea Ice Model (CICE), based on mushy layer theory. We solve a set of coupled, nonlinear equations for sea‐ice temperature (enthalpy) and salinity using an implicit Jacobian‐free Newton‐Krylov method. Time resolved observations of gravity drainage show two modes of desalination during growth. Rapid drainage occurs in a thin region just above the ice/ocean interface, while slower drainage occurs throughout the ice. Parameterizations are designed to represent each of these modes and work simultaneously. Near the interface, desalination occurs primarily via the fast drainage, while slow drainage continues to desalinate ice above the interface. The rapid desalination is convectively driven and is parameterized based on a consideration of flow driven upward within the mush and downward in chimneys, modified by the Rayleigh number. The slow desalination is represented as a simple relaxation of bulk salinity to a value based on a critical porosity for sea‐ice permeability. It is shown that these parameterizations can adequately reproduce observational data from laboratory experiments and field measurements.

Brinicles as a Case of Inverse Chemical Gardens

Brinicles are hollow tubes of ice from centimeters to meters in length that form under floating sea ice in the polar oceans when dense, cold brine drains downward from sea ice to seawater close to its freezing point. When this extremely cold brine leaves the ice, it freezes the water it comes into contact with: a hollow tube of ice-a brinicle-growing downward around the plume of descending brine. We show that brinicles can be understood as a form of the self-assembled tubular precipitation structures termed chemical gardens, which are plantlike structures formed on placing together a soluble metal salt, often in the form of a seed crystal, and an aqueous solution of one of many anions, often silicate. On one hand, in the case of classical chemical gardens, an osmotic pressure difference across a semipermeable precipitation membrane that filters solutions by rejecting the solute leads to an inflow of water and to its rupture. The internal solution, generally being lighter than the external solution, flows up through the break, and as it does so, a tube grows upward by precipitation around the jet of internal solution. Such chemical-garden tubes can grow to many centimeters in length. In the case of brinicles, on the other hand, in floating sea ice we have porous ice in a mushy layer that filters out water, by freezing it, and allows concentrated brine through. Again there is an osmotic pressure difference leading to a continuing ingress of seawater in a siphon pump mechanism that is sustained as long as the ice continues to freeze. Because the brine that is pumped out is denser than the seawater and descends rather than rises, a brinicle is a downward-growing tube of ice, an inverse chemical garden.

Stability analysis of compositional convection in a mushy layer in the time-dependent solidification system

Instabilities of convection in a mushy layer with a permeable interface underlying a liquid layer are studied in the time-dependent solidification system in which a binary melt cooled from below. The self-similar stability equations in the liquid and mushy layers are derived by propagation theory. The onset of mushy-layer-mode convection is examined considering the variation of permeability with porosity in the mushy layer. The numerical results show that the critical Darcy-Rayleigh number defined in terms of the mean permeability increases with increasing the concentration ratio and decreases with increasing the superheat. When the concentration ratio is small, a small convective cell appears in the vicinity of the liquid-mush interface. The influences of various non-uniform permeability models on the stability of compositional convection are discussed.

Nonlinear evolution analysis and stability for convection in a mushy layer with permeable interface

We consider the problem of two- and three-dimensional nonlinear buoyant flows in horizontal mushy layers during the solidification of binary alloys. We study the nonlinear evolution of such flow based on a recently developed realistic model for the mushy layer with permeable interface. The evolution approach is based on a Landau type equation for the amplitude of the secondary nonlinear solution, which can be in the form of rolls, squares, rectangles or hexagons. Using both analytical and computational methods, we calculate the solutions to the evolution equation near the onset of motion for both subcritical and supercritical regimes and determine the stable solutions. We find, in particular, that for several investigated cases with different parameter regimes, secondary solution in the form of subcritical down-hexagons or supercritical up-hexagons can be stable. However, the preferred solution for smallest values of the Rayleigh number and the amplitude of motion is in the form of subcritical down-hexagons. This result appears to agree with the experimental observation on the form of the convective flow near the onset of motion.

Sea Ice Dynamics Induced by External Stochastic Fluctuations

The influence of stochastic fluctuations in the atmosphere and in the ocean caused by different occasional phenomena (noises) on dynamic processes of sea ice growth with a mushy layer is studied. It is shown that atmospheric temperature variances substantially increase the sea ice thickness, whereas dispersion variations of turbulent flows in the ocean to a great extent decrease the ice content produced by false bottom evolution.

Water content of primitive low-K tholeiitic basalt magma from Iwate Volcano, NE Japan arc: implications for differentiation mechanism of frontal-arc basalt magmas

The water content of low-K tholeiitic basalt mag- ma from Iwate volcano, which is located on the volcanic front of the NE Japan arc, was estimated using multi- component thermodynamic models. The Iwate lavas are moderately porphyritic, consisting of ~8 vol.% olivine and ~20 vol.% plagioclase phenocrysts. The olivine and plagioclase phenocrysts show significant compositional variations, and the Mg# of olivine phenocrysts (Mg#78-85) correlates positively with the An content of coexisting plagioclase phenocrysts (An85-92). The olivine phenocrysts with Mg# > ~82 do not form crystal aggregates with plagioclase phenocrysts. It is inferred from these observations that the phenocrysts with vari- able compositions were primarily derived from mushy boundary layers along the walls of a magma chamber. By using thermodynamic calculations with the observed petrological features of the lavas, the water content of the Iwate magma was estimated to be 4-5 wt.%. The high water content of the magma supports the recent consensus that frontal-arc magmas are remarkably hydrous. Using the estimated water content of the Iwate magma, the water content and temperature of the source mantle were estimated. Given that the Iwate magma was derived froma primarymagmasolelybyolivinefractionation, the water content and temperature were estimated to be ~0.7 wt.% and ~1,310 °C, respectively. Differentiation mech- anisms of low-K frontal-arc basalt magmas were also exam- ined by application of a thermodynamics-based mass balance model to the Iwate magma. It is suggested that magmatic differentiation proceeds primarily through fractionation of crystals from the main molten part of a magma chamber when it is located at <~200 MPa, whereas magma evolves through a convective melt exchange between the main magma and mushy boundary layers when the magma body is located at

Quantitative field constraints on the dynamics of silicic magma chamber rejuvenation and overturn

The catastrophic eruption of large-volume, crystal-rich silicic magmas is often proposed to be a consequence of reheating, melting and overturn of partially molten, buoyant silicic material following repeated injection of dense, hot mafic magma. To test this “rejuvenation hypothesis”, we analyze at high spatial resolution 33 examples of deformed interfaces between intrusive mafic and silicic layers in two plutons of the Coastal Maine Magmatic Province, USA. These deformed interfaces are thought to record the buoyant overturn of silicic crystal mush layers, apparently in response to the injection and cooling of hot, dense mafic magmas. We use spectral analysis and scaling theory along with petrologic and textural data to identify, characterize, and understand periodic deformations from the scale of individual crystals (≈1 cm) to the thicknesses of mafic and silicic layers. Deformations at the largest scale lengths (>100 m) are at wavelengths comparable to, or greater than, silicic layer thicknesses and support a conjecture that mafic recharge can cause large-scale Rayleigh–Taylor-type overturning of silicic mushy layers. By contrast, the smallest scales of individual crystals probably record effects related to production and buoyancy-driven rise of melt from the tops of silicic mushes in contact with overlying hot basalt, whereas intermediate scales are explained by compaction. Our results constrain the evolution of a thermal rejuvenation event and potentially identify a condition for a large-scale overturn of the magma chamber that may lead to eruption. This work provides the first quantitative field-based constraints on some of the key physical processes inherent to the rejuvenation hypothesis.

Analytical Solution of Mushy Zone under Directional Solidification

Based on the general mathematical formulation under unidirectional solidification with mushy layer developed in Ref.[13], leading approximation of solution in mushy layer is obtained for the case that the inverse Lewis number is small parameter. For the steady state of solidification, concentration field in the mushy region is given as function of a solid volume fraction. Mushy layer width and solid volume fraction at the solid-mush interface are obtained. Effects of temperature gradient on mushy layer width and solid volume fraction at solid-mush interface are presented.

Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes

AbstractWe model buoyancy-driven convection with chimneys – channels of zero solid fraction – in a mushy layer formed during directional solidification of a binary alloy in two dimensions. A large suite of numerical simulations is combined with scaling analysis in order to study the parametric dependence of the flow. Stability boundaries are calculated for states of finite-amplitude convection with chimneys, which for a narrow domain can be interpreted in terms of a modified Rayleigh number criterion based on the domain width and mushy-layer permeability. For solidification in a wide domain with multiple chimneys, it has previously been hypothesized that the chimney spacing will adjust to optimize the rate of removal of potential energy from the system. For a wide variety of initial liquid concentration conditions, we consider the detailed flow structure in this optimal state and derive scaling laws for how the flow evolves as the strength of convection increases. For moderate mushy-layer Rayleigh numbers these flow properties support a solute flux that increases linearly with Rayleigh number. This behaviour does not persist indefinitely, however, with porosity-dependent flow saturation resulting in sublinear growth of the solute flux for sufficiently large Rayleigh numbers. Finally, we consider the influence of the porosity dependence of permeability, with a cubic function and a Carman–Kozeny permeability yielding qualitatively similar system dynamics and flow profiles for the optimal states.

Fluxes through steady chimneys in a mushy layer during binary alloy solidification

AbstractSolute transport within solidifying binary alloys occurs predominantly by convection from narrow liquid chimneys within a porous mushy layer. We develop a simple model that elucidates the dominant structure and driving forces of the flow, which could be applied to modelling brine fluxes from sea ice, where a cheaply implementable approach is essential. A horizontal density gradient within the mushy layer in the vicinity of the chimneys leads to baroclinic torque which sustains the convective flow. In the bulk of the mushy layer, the isotherms are essentially horizontal. In this region, we impose a vertically linear temperature field and immediately find that the flow field is a simple corner flow. We determine the strength of this flow by finding a similarity solution to the governing mushy-layer equations in an active region near the chimney. We also determine the corresponding shape of the chimney, the vertical structure of the solid fraction and the interstitial flow field. We apply this model first to a periodic, planar array of chimneys and show analytically that the solute flux through the chimneys is proportional to a mush Rayleigh number. Secondly we extend the model to three dimensions and find that an array of chimneys can be characterized by the average drainage area alone. Therefore we solve the model in an axisymmetric geometry and find new, sometimes nonlinear, relationships between the solute flux, the Rayleigh number and the other dimensionless parameters of the system.

Mathematical Model of Unidirectional Solidification with Mushy Layer

The general mathematical formulation under unidirectional solidification with mushy layer is developed. For the steady state of solidification, concentration and temperature fields in the mushy region are given as functions of a solid volume fraction. The nonlinear model of solidification in mushy zone is changed into system of the second order ordinary differential equation with free boundary conditions, which is solved using numerical calculating method. Solid volume fraction at the solid-mush interface is also obtained. For fixed control conditions, mushy layer width of Fe-Ni alloy in unidirectional solidification is predicted.

Nonlinear model of the mushy layer in the time-dependent crystallization of sea water in ice cracks

In this paper we’ll focus on the phenomena of crystallization of sea water in the cracks of ancient ice. Rapidly occurring processes of ice formation in a divorce can have a signicant impact on the pattern of heat transfer in a local area isothermal between the ocean and atmosphere. In this paper we consider a model of a mushy layer.

Nonlinear model of the mushy layer in the time-dependent crystallization. II Calculations

In this paper we’ll focus on the phenomena of crystallization of sea water in the cracks of ancient ice. Rapidly occurring processes of ice formation in a divorce can have a signicant impact on the pattern of heat transfer in a local area isothermal between the ocean and atmosphere. In this paper we consider a model of a mushy layer.

Mushy-layer dynamics in micro and hyper gravity

We describe the results of experiments on mushy layers grown from aqueous ammonium chloride solution in normal, micro, and hyper gravity environments. In the fully developed chimney state, the chimney plume dynamics differ strikingly when conditions change from micro to hyper gravity. In microgravity, we find fully arrested plume motion and suppressed convection. As gravity exceeds Earth conditions, we observe a host of phenomena, ranging from arched plumes that undergo forced Rayleigh-Taylor instabilities to in-phase multiple plume oscillatory behavior. For the same initial solute concentrations and fixed boundary cooling temperatures, we find that, in runs of over two hours, the averaged effects of microgravity and hypergravity result in suppressed growth of the mushy layers, a phenomenon caused by a net enhancement of convective heat and solute transport from the liquid to the mushy layers. These behaviors are placed in the context of the theory of convecting mushy layers as studied under normal laboratory conditions.

A study on the snowing phenomenon in binary alloy solidification

The snowing phenomenon has been observed in some studies where seed crystals formed near the bottom of the test cell during solidification are carried up flow above the mushy layer by thermo-solutal convection flow, and they fall down on it just like atmospheric snow occurring in nature. In this study, snowing phenomenon was studied by varying parameters which could affect the thermal as well as solutal gradients, at six weight % concentrations of ammonium chloride solutions, from 23% to 26%, with temperatures −24 °C, −20 °C and −16 °C, and at volume of solution either full or half-full. Results show that increase in concentration decreases the onset of snowing, does not lengthen the period of the observed phenomenon, but increases the size of ejected crystals. Increase in temperature does not significantly affect the onset of snowing, but lengthens the period of snowing. Similarly, an increase in volume does not affect the onset of snowing but lengthens the process based on the ratio of the volumes. While concentration and temperature affects the final mush profile in the study, different volumes of solution does not. The combined Rayleigh number is calculated but found to produce no conclusive critical Rayleigh number to predict the onset of snowing.

Finite-sample-size effects on convection in mushy layers

AbstractWe report theoretical and experimental investigations of the flow instability responsible for mushy-layer convection with chimneys, drainage channels devoid of solid, during steady-state solidification of aqueous ammonium chloride. Under certain growth conditions a state of steady mushy-layer growth with no flow is unstable to the onset of convection, resulting in the formation of chimneys. We present regime diagrams to quantify the state of the flow as a function of the initial liquid concentration, the porous-medium Rayleigh number, and the sample width. For a given liquid concentration, increasing both the porous-medium Rayleigh number and the sample width drove a transition from a weakly convecting chimney free state to a state of mushy-layer convection with fully developed chimneys. Increasing the concentration ratio stabilized the system and suppressed the formation of chimneys. As the initial liquid concentration increased, onset of convection and formation of chimneys occurred at larger values of the porous-medium Rayleigh number, but the critical cell widths for chimney formation are far less sensitive to the liquid concentration. At the highest liquid concentration, the mushy-layer mode of convection did not occur in the experiment. The formation of multiple chimneys and the morphological transitions between these states are discussed. The experimental results are interpreted in terms of a previous theoretical analysis of finite amplitude convection with chimneys, with a single value of the mushy-layer permeability consistent with the liquid concentrations considered in this study.

Initial stages of solidification during semisolid processing of a transparent model material

Growth morphology of succinonitrile crystals under different cooling and stirring conditions was experimentally investigated by real time microscopic observation of the solidifying melt. It was found that under laminar fluid flow conditions, the solidified crystals exhibited equiaxed dendritic morphology immediately after the beginning of solidification. On the other hand, under turbulent fluid flow conditions the growth of solid particles followed a spherical mode with a high growth velocity from the initial stages of solidification. When the stirring was combined with rapid heat extraction from the rotor, a mushy layer was observed to form around the rotating chill. Under turbulent conditions, detachment of dendrite arms from this layer of rapidly coarsened dendrites is suggested to be the origin of the spherical particles in the microstructure. Formation of the layer was experimentally confirmed for an Al–Si alloy. The new findings can be used for more effective refinement of rheocast microstructures.

Numerical Modeling of One-Dimensional Binary Solidification with a Mushy Layer Evolution

The numerical modeling of a binary solidification with a mushy layer mechanism is considered in this manuscript. The nonlinear coupled system of equations describes the heat and mass diffusions of a one-dimensional spatial variable in the semi-infinite interval. Also formulated is a transformed system in a finite interval. We propose numerical methods for solving the nonlinear system using a threshold strategy based on fixed computation-domain approach. Our calculated results and those from the LeadEx field experiment are well-matched in their tendencies.

Experimental constraints on permeable gas transport in crystalline silicic magmas

The gas and fluid transport in magmas via permeable flow through interconnected bubble networks controls the rate of outgassing from magmas ascending in volcanic conduits and the fluid transport in the mushy boundary layer of magma reservoirs. Hence, clarifying its mechanism and rate is crucial to understanding the explosivity of volcanic eruptions and the evolution and dynamics of a magma reservoir. Recent experimental studies have determined the gas permeabilities in crystal-free rhyolite and basalt. However, no experimental study has investigated the effect of the crystal contents on the permeable gas transport in magmas. In this study, we performed decompression experiments for hydrous rhyolitic melts having crystallinities of 30 and 50 vol% to examine the effect of crystals on the bubble microstructure and gas permeability during magma vesiculation. Size-controlled (100-meshed) corundum crystals were used as an analog of the phenocrysts in silicic magmas. Microstructural analyses using X-ray CT showed that bubbles coalesce and their connectivity increases with a decrease in the final pressure after the decompression, that is, an increase in the vesicularity. As long as the vesicularities of melt part in the crystal-free basis (melt vesicularity) were similar, no clear effect of the crystallinity on the degree of bubble coalescence and connectivity was observed at melt vesicularities 68 vol%). This result indicates that the permeable fluid transport through a deep volcanic conduit, which has been proposed on the basis of the observations of volcanic gases and natural products, is so slow that other processes, like shear deformation or magma convection, may be needed to explain the observations.