Dynamic model of dehydration melting motivated by a natural analogue: applications to the Ivrea–Verbano zone, northern Italy

1996 ◽  
Vol 87 (1-2) ◽  
pp. 23-31 ◽  
Author(s):  
Scott A. Barboza ◽  
George W. Bergantz
Keyword(s):  
Numerical Model ◽  
Mixture Theory ◽  
Mafic Magma ◽  
Northern Italy ◽  
Porous Media Flow ◽  
Theory Approach ◽  
Dehydration Melting ◽  
Porous Flow ◽  
Crustal Rocks ◽  
Switching Functions

ABSTRACT:Dehydration melting of crustal rocks may commonly occur in response to the intrusion of mafic magma in the mid- or lower crust. However, the relative importance of melt buoyancy, shear or dyking in melt generation and extraction under geologically relevant conditions is not well understood. A numerical model of the partial melting of a metapelite is presented and the model results are compared with the Ivrea-Verbano Zone in northern Italy. The numerical model uses the mixture theory approach to modelling simultaneous convection and phase change and includes special ramping and switching functions to accommodate the rheology of crystal-melt mixtures in accordance with the results of deformation experiments. The model explicitly includes both porous media flow and thermally and compositionally driven bulk convection of a restitecharged melt mass. A range of melt viscosity and critical melt fraction models is considered. General agreement was found between predicted positions of isopleths and those from the Ivrea-Verbano Zone. Maximum melt velocities in the region of porous flow are found to be 1 × 10−7 and 1 × 10−1m per year in the region of viscous flow. The results indicate that melt buoyancy alone may not be a sufficient agent for melt extraction and that extensive, vigorous convection of partially molten rocks above mafic bodies is unlikely, in accord with direct geological examples.

Water–mineral interaction in hygromechanics of clays exposed to environmental loads: a mixture-theory approach

1992 ◽  
Vol 29 (6) ◽  
pp. 1071-1086 ◽  
Author(s):  
Tomasz A. Hueckel
Keyword(s):  
Mass Transfer ◽  
Mixture Theory ◽  
Adsorbed Water ◽  
Theory Approach ◽  
Environmental Loads ◽  
Fluid Fraction ◽  
Effects Of Temperature ◽  
Dynamics Simulations ◽  
Experimental Findings ◽  
Mineral Interaction

Water–mineral interaction in narrow interstices (<30 Å (1 Å = 0.1 nm)) in dense, saturated clays is discussed in view of recent experimental findings and molecular dynamics simulations. Consequences to the macroscopic behavior are considered. A mixture theory for two interacting constituents is developed. Effects of temperature and chemicals are discussed. A postulate of mass transfer of adsorbed water from solid to fluid fraction caused by thermal or chemical load is then discussed. Theory of plasticity of clays affected by heat or chemicals is developed to deal with the effects of thermal and chemical consolidation. Key words : hydraulic conductivity, effective stress, environmental loads, thermo-chemo-plasticity.

scholarly journals Fertility of crustal rocks during anatexis

1996 ◽  
Vol 87 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Alan Bruce Thompson
Keyword(s):  
Experimental Investigations ◽  
Crustal Rock ◽  
Dehydration Melting ◽  
Specific Pressure ◽  
Crustal Rocks ◽  
Rock Types ◽  
Increasing Temperature ◽  
Low Pressures ◽  
Kbar Pressure ◽  
Melting Relations

ABSTRACT:After many years of systematic experimental investigations, it is now possible to quantify the conditions for optimum fertility to melt production of most common crustal rock types as functions of temperature and to about 30 kbar pressure. Quartzo-feldspathic melting produces steady increases in melt proportion with increasing temperature. The exact melt fraction depends on the mineral mode relative to quartz-feldspar eutectics and the temperatures of mica dehydration melting reactions. Mica melting consumes SiO2 from residual quartz during the formation of refractory Al2SiO5, orthopyroxene, garnet or cordierite.A simple graphical interpretation of experimental results allows a deduction of the proportions of mica and feldspar leading to optimum fertility. In effect, the mica dehydration melting reactions, at specific pressure and are superimposed on quartz-feldspar melting relations projected onto Ab-An-Or. Fertility to melt production varies with the mica to feldspar ratio and pressure. Pelites are more fertile than psammites at low pressures (e.g. 5 kbar), especially if they contain An40 to An50 plagioclase. At higher pressure (e.g. 10-20 kbar) and for rocks containing albitic plagioclase, psammites are more fertile than pelites. For a typical pelite (e.g. with An25 at 20 kbar), the cotectic with muscovite lies at higher (≍·) and XAb (≍0·42) than with biotite :≍0·35; XAb(≍·), thus dehydration melting of muscovite requires 10% more plagioclase for fertility than does biotite.The first melts from dehydration melting of muscovite (with Plg + Qtz) are more sodic and form at lower temperatures than the first melts from Bio + Plg + Qtz. With increasing pressure, to at least 30 kbar, granite minimum and mica dehydration melts become more sodic. This indicates that of such melts is greater than 0·3.

Reactive bulk assimilation: A model for crust-mantle mixing in silicic magmas

Geology ◽  
2005 ◽  
Vol 33 (8) ◽  
pp. 681-684 ◽  
Author(s):  
James S. Beard ◽  
Paul C. Ragland ◽  
Maria Luisa Crawford
Keyword(s):  
Dehydration Melting ◽  
Crustal Rocks ◽  
Host Magma ◽  
Ti Oxides ◽  
Energy Penalty ◽  
Magma Crystallization ◽  
Hydrous Melt ◽  
Silicic Magmas ◽  
Solid Form ◽  
Hydrous Magma

Abstract Bulk assimilation of small (millimeters to ∼1 km) fragments of crust—driven and (ultimately) masked by reactions during xenolith melting and magma crystallization—is an important mechanism for crust-mantle mixing. Xenoliths containing mica or amphibole undergo dehydration melting when incorporated into a host magma, yielding mainly plagioclase, pyroxene, Fe-Ti oxides, and hydrous melt. The xenolith is physically compromised by partial melting and begins to disintegrate; xenolithic melt and crystals are mixed into the host magma. Xenocrystic zircon is liberated at this stage. The cryptic character of assimilation is greatly enhanced in any hydrous magma by hydration crystallization reactions (the reverse of dehydration melting). All pyroxenes and oxides (phenocrysts, xenocrysts, or crystals having a hybrid signature) will be subject to these reactions, producing feldspars, amphiboles, and micas that incorporate material from several sources, a particularly effective mixing mechanism. Implicit in the model is a reduced energy penalty for bulk assimilation—much of the assimilant remains in solid form—compared to melt-assimilation models. A large role for bulk assimilation supports stoping as a credible mechanism for the ascent of magmas. While the assimilation of low-density crust and concomitant fractionation provide the isostatic impetus for ascent, the wholesale incorporation and processing of crustal rocks in the magma chamber helps create the room for ascent.

EFFECT OF STENOSIS SEVERITY ON SHEAR-INDUCED DIFFUSION OF RED BLOOD CELLS IN CORONARY ARTERIES

2019 ◽  
Vol 19 (05) ◽  
pp. 1950034 ◽  
Author(s):  
ABDULRAJAK BURADI ◽  
SUMANT MORAB ◽  
ARUN MAHALINGAM
Keyword(s):  
Red Blood Cells ◽  
Blood Cells ◽  
Mixture Theory ◽  
Theory Approach ◽  
Newtonian Viscosity ◽  
Maximum Fluctuation ◽  
Stenosis Severity ◽  
Flux Model ◽  
First Time ◽  
Arterial Endothelial Cells

In large blood vessels, migration of red blood cells (RBCs) affects the concentration of platelets and the transport of oxygen to the arterial endothelial cells. In this work, we investigate the locations where hydrodynamic diffusion of RBCs occurs and the effects of stenosis severity on shear-induced diffusion (SID) of RBCs, concentration distribution and wall shear stress (WSS). For the first time, multiphase mixture theory approach with Phillips shear-induced diffusive flux model coupled with Quemada non-Newtonian viscosity model has been applied to numerically simulate the RBCs macroscopic behavior in four different degrees of stenosis (DOS) geometries, viz., 30%, 50%, 70% and 85%. Considering SID of RBCs, the calculated average WSS increased by 77.70% which emphasises the importance of SID in predicting hemodynamic parameters. At the stenosis throat, it was observed that 85% DOS model had the lowest concentration of RBCs near the wall and highest concentration at the center. For the stenosis models with 70% and 85% DOS, the RBC lumen wall concentration at the distal section of stenosis becomes inhomogeneous with the maximum fluctuation of 1.568%. Finally, the wall regions with low WSS and low RBC concentrations correlate well with the atherosclerosis sites observed clinically.

Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory

2006 ◽  
Vol 52 (5) ◽  
pp. 571-594 ◽  
Author(s):  
Greg Lemon ◽  
John R. King ◽  
Helen M. Byrne ◽  
Oliver E. Jensen ◽  
Kevin M. Shakesheff
Keyword(s):  
Mathematical Modelling ◽  
Mixture Theory ◽  
Tissue Growth ◽  
Porous Flow ◽  
Engineered Tissue

scholarly journals Modeling of Tumor Occurrence and Growth – II

2021 ◽  
pp. 72-83
Author(s):  
S.N. Antontsev ◽  
А.А. Papin ◽  
M.A. Tokareva ◽  
E.I. Leonova ◽  
E.A. Gridushko
Keyword(s):  
Blood Vessel ◽  
Blood Vessels ◽  
Cellular Proliferation ◽  
Tumor Tissue ◽  
Mixture Theory ◽  
Theory Approach ◽  
Cancer Disease ◽  
Cylindrical Structures ◽  
The Mathematical Model ◽  
Oxidation Of Glucose

This paper considers the mathematical model of tumor growth along a blood vessel. The model employs the mixture theory approach to describe a tissue that consists of cells, extracellular matrix, and liquid. The growing tumor tissue is supposed to be surrounded by the host tissue. Tumors, where complete oxidation of glucose prevails, are considered. Special attention is paid to consistent descriptions of oxygen consumption and growth processes based on the energy balance. The level set method is used to track an interface between the tissues. The simulations show localization of the tumor within a limited distance from the vessels and constant expansion speed along the vessels. Cancer disease manifests itself as abnormally excessive cell proliferation. This is the result of dysregulation of normal constraints on cellular proliferation. This fact has serious implications on the morphology of the growth. The intensive proliferation of tumor cells creates cell populations distant from blood vessels and deprived of nutrient and oxygen supply while most of the cells in the human body are within few cell diameters from a blood vessel. This leads to the formation of cylindrical structures around blood vessels.

Forced Convection Flow Through an Unsaturated Wellbore

2003 ◽  
Author(s):  
Maria Laura Martins-Costa ◽  
Roge´rio M. Saldanha da Gama
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Operator Splitting ◽  
Mixture Theory ◽  
Porous Matrix ◽  
Convection Flow ◽  
Theory Approach ◽  
Splitting Technique ◽  
Nonlinear Hyperbolic System ◽  
Implicit Finite Difference Scheme ◽  
Flow Through

This work studies the dynamics of the filling up of a rigid cylindrical shell porous matrix by a Newtonian fluid and the heat transfer associated phenomenon. A mixture theory approach is employed to obtain a preliminary local model for nonisothermal flows through a wellbore. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas included to account for the compressibility of the mixture as a whole. Assuming the convection flow on radial direction only, a set of four nonlinear partial differential equations describes the problem. Its hydrodynamic part — a nonlinear hyperbolic system — is approximated by means of a Glimm’s scheme, combined with an operator splitting technique, while an implicit finite difference scheme is used to simulate the thermal part.

scholarly journals Interaction between Crustal-Scale Darcy and Hydrofracture Fluid Transport: A Numerical Study

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Tamara de Riese ◽  
Paul D. Bons ◽  
Enrique Gomez-Rivas ◽  
Till Sachau
Keyword(s):  
Fluid Flow ◽  
Numerical Model ◽  
Transport Mechanism ◽  
Large Scale ◽  
Fluid Transport ◽  
Numerical Study ◽  
Ballistic Transport ◽  
Accretionary Prism ◽  
Small Scale ◽  
Porous Flow

Crustal-scale fluid flow can be regarded as a bimodal transport mechanism. At low hydraulic head gradients, fluid flow through rock porosity is slow and can be described as diffusional. Structures such as hydraulic breccias and hydrothermal veins both form when fluid velocities and pressures are high, which can be achieved by localized fluid transport in space and time, via hydrofractures. Hydrofracture propagation and simultaneous fluid flow can be regarded as a “ballistic” transport mechanism, which is activated when transport by diffusion alone is insufficient to release the local fluid overpressure. The activation of a ballistic system locally reduces the driving force, through allowing the escape of fluid. We use a numerical model to investigate the properties of the two transport modes in general and the transition between them in particular. We developed a numerical model in order to study patterns that result from bimodal transport. When hydrofractures are activated due to low permeability relative to fluid flux, many hydrofractures form that do not extend through the whole system. These abundant hydrofractures follow a power-law size distribution. A Hurst factor of ~0.9 indicates that the system self-organizes. The abundant small-scale hydrofractures organize the formation of large-scale hydrofractures that ascend through the whole system and drain fluids in large bursts. As the relative contribution of porous flow increases, escaping fluid bursts become less frequent, but more regular in time and larger in volume. We propose that metamorphic rocks with abundant veins, such as in the Kodiak accretionary prism (Alaska) and Otago schists (New Zealand), represent regions with abundant hydrofractures near the fluid source, while hydrothermal breccias are formed by the large fluid bursts that can ascend the crust to shallower levels.

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