The charge effect on the hindrance factors for diffusion and convection of a solute in pores II

The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e.the Debye-Hückel equation. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Charge effects on hindrance factors for diffusion and convection of solute in pores I

The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.

Effect of aspect ratio on thermal convection in open and closed systems

Internally heated fluids are found across the nuclear fuel cycle. In certain situations the motion of the fluid is driven by the decay heat (i.e. corium melt pools in severe accidents, the shutdown of liquid metal reactors, molten salt and the passive control of light water reactors) as well as normal operation (i.e. intermediate waste storage and generation IV reactor designs). This can in the long-term affect reactor vessel integrity or lead to localized hot spots and accumulation of solid wastes that may prompt local increases in activity. Two approaches to the modeling of internally heated convection are presented here. These are based on numerical analysis using codes developed in-house and simulations using widely available computational fluid dynamics solvers. Open and closed fluid layers at around the transition between conduction and convection of various aspect ratios are considered. We determine optimum domain aspect ratio (1:7:7 up to 1:24:24 for open systems and 5:5:1, 1:10:10 and 1:20:20 for closed systems), mesh resolutions and turbulence models required to accurately and efficiently capture the convection structures that evolve when perturbing the conductive state of the fluid layer. Note that the open and closed fluid layers we study here are bounded by a conducting surface over an insulating surface. Conclusions will be drawn on the influence of the periodic boundary conditions on the flow patterns observed. We have also examined the stability of the nonlinear solutions that we found with the aim of identifying the bifurcation sequence of these solutions en route to turbulence.

Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios. © 2008 American Institute of Physics.

Bistable attractors in a model of convection-driven spherical dynamos

The range of existence and the properties of two essentially different chaotic attractors found in a model of nonlinear convection-driven dynamos in rotating spherical shells are investigated. A hysteretic transition between these attractors is established as a function of the rotation parameter t. The width of the basins of attraction is also estimated. © 2012 The Royal Swedish Academy of Sciences.

Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells

Bistability and hysteresis of magnetohydrodynamic dipolar dynamos generated by turbulent convection in rotating spherical fluid shells is demonstrated. Hysteresis appears as a transition between two distinct regimes of dipolar dynamos with rather different properties including a pronounced difference in the amplitude of the axisymmetric poloidal field component and in the form of the differential rotation. The bistability occurs from the onset of dynamo action up to about 9 times the critical value of the Rayleigh number for onset of convection and over a wide range of values of the ordinary and the magnetic Prandtl numbers including the value unity. Copyright © EPLA, 2009.

Convection induced by instabilities in the presence of a transverse seepage

The transition of laterally heated flows in a vertical layer and in the presence of a streamwise pressure gradient is examined numerically for the case of different values Prandtl number. The stability analysis of the basic flow for the pure hydrodynamic case ( Pr = 0 ) was reported in [1]. We find that in the absence of transverse pumping the previously known critical parameters are recovered [2], while as the strength of the Poiseuille flow component is increased the convective motion is delayed considerably. Following the linear stability analysis for the vertical channel flow our attention is focused on a study of the finite am- plitude secondary travelling-wave (TW) solutions that develop from the perturbations of the transverse roll type imposed on the basic flow and temperature profiles. The linear stability of the secondary TWs against three-dimensional perturbations is also examined and it is shown that the bifurcating tertiary flows are phase-locked to the secondary TWs.

Geochemical variation among small eruptive centers in the central SVZ of the Andes: An evaluation of subduction, mantle and crustal influences

Subduction zone magmatism is an important and extensively studied topic in igneous geochemistry. Recent studies focus on from where arc magmas are generated, how subduction components (fluids or melts) are fluxed into the source of the magmas, and whether or how the subduction components affect partial melting processes beneath volcanic arcs at convergent boundaries. ^ At 39.5°S in the Central Southern Volcanic Zone of the Andes, Volcano Villarrica is surrounded by a suite of Small Eruptive Centers (SEC). The SECs are located mostly to the east and northeast of the stratovolcano and aligned along the Liquine-Ofqui Fault Zone, the major fracture system in this area. Former studies observed the geochemical patterns of the SECs differ distinctively from those of V. Villarrica and suggested there may be a relationship between the compositions of the volcanic units and their edifice sizes. This work is a comprehensive geochemical study on the SECs near V. Villarrica, using a variety of geochemical tracers and tools including major, trace and REE elements, Li-Be-B elements, Sr-Nd-Pb isotopes and short-lived isotopes such as U-series and 10Be. In this work, systematic differences between the elemental and isotopic compositions of the SECs and those of V. Villarrica are revealed and more importantly, modeled in terms of magmatic processes occurring at continental arc margins. Detailed modeling calculations in this work reconstruct chemical compositions of the primary magmas, source compositions, compositions and percentages of different subduction endmembers mixed into the source, degrees of partial melting and different time scales of the SECs and V. Villarrica, respectively. Geochemical characteristics and possible origins of the two special SECs—andesitic Llizan, with crustal signatures, and Rucapillan, to the northwest toward the trench, are also discussed in this work. ^

An investigation into the Hawaiian mantle from a xenolithic perspective

Salt Lake Crater (SLC), on the island of Oahu, Hawaii, is best known for its wide variety of crustal and mantle xenoliths. SLC is only the second locality in oceanic regimes where deeper portions of the upper mantle (i.e., garnet-bearing xenoliths) have been sampled. These garnet-bearing xenoliths, that contain clinopyroxene (cpx), orthopyroxene (opx), olivine, and garnet, are the focus of this study Opx is present in small amounts. Cpx has exsolved opx, spinel, and garnet. In addition, many xenoliths contain spinel-cored garnets. In some xenoliths, opx crystals contain exsolved cpx and spinel. Olivine, cpx, and garnet are in chemical equilibrium with each other. Opx is not in chemical equilibrium with the other dominant minerals. ^ The origin of these xenoliths is interpreted on the basis of liquidus phase relations in the simplified system CaO-MgO-Al2O3-SiO 2 (CMAS) system at 3.0 and 5.0 GPa. The occurrence of spinel-cored garnets and the Ol-Cpx-Gt assemblage suggests that the depth of crystallization of the SLC xenoliths examined was ∼100–110 km (i.e., uppermost asthenosphere). ^ The experimental study is concerned with the equilibrium melting of garnet clinopyroxenite at 2.0–2.5 GPa and it explores the role of such melting process in the generation of tholeiitic and alkalic lavas in ocean island basalts (OIBs). The starting material is a tholeiitic picrite in terms of its normative composition. Its solidus temperature is 1295 ± 15°C and 1332 ± 15°C at 2.0 and 2.5 GPa, respectively. At 2.0 GPa, the liquidus phase is opx that is in reaction relation with the melt. It reacts out at ∼40°C below the liquidus as cpx and spinel appear. Garnet appears long after opx disappearance. Opx is absent in runs at 2.5 GPa. Cpx and garnet appear simultaneously on the liquidus at 2.5 GPa, and are the only assemblage throughout the melting interval. At both the pressures, the partial melts are olivine-hypersthene normative at high melt fraction ( F), becoming moderately to strongly nepheline-normative, as F decreases. It is concluded that the involvement of CO 2 (and perhaps H2O) is necessary for the generation of alkalic melts in most OIBs. ^

Investigation of Mantle Dynamics from Platinum Group Elements and Rhenium-Osmium Isotope Systematics of Mantle Xenoliths from Oahu, Hawaii

Intraplate volcanism that has created the Hawaiian-Emperor seamount chain is generally thought to be formed by a deep-seated mantle plume. While the idea of a Hawaiian plume has not met with substantial opposition, whether or not the Hawaiian plume shows any geochemical signal of receiving materials from the Earth’s Outer Core and how the plume may or may not be reacting with the overriding lithosphere remain debatable issues. In an effort to understand how the Hawaiian plume works I report on the first in-situ sulfides and bulk rock Platinum Group Element (PGE) concentrations, together with Os isotope ratios on well-characterized garnet pyroxenite xenoliths from the island of Oahu in Hawaii. The sulfides are Fe-Ni Monosulfide Solid Solution and show fractionated PGE patterns. Based on the major elements, Platinum Group Elements and experimental data I interpret the Hawaiian sulfides as an immiscible melt that separated from a melt similar to the Honolulu Volcanics (HV) alkali lavas at a pressure-temperature condition of 1530 ± 100OC and 3.1±0.6 GPa., i.e. near the base or slightly below the Pacific lithosphere. The 187Os/188Os ratios of the bulk rock vary from subchondritic to suprachondritic (0.123-0.164); and the 187Os/188Os ratio strongly correlates with major element, High Field Strength Element (HFSE), Rare Earth Element (REE) and PGE abundances. These correlations strongly suggest that PGE concentrations and Os isotope ratios reflect primary mantle processes. I interpret these correlations as the result of melt-mantle reaction at the base of the lithosphere: I suggest that the parental melt that crystallized the pyroxenites selectively picked up radiogenic Os from the grain boundary sulfides, while percolating through the Pacific lithosphere. Thus the sampled pyroxenites essentially represent crystallized melts from different stages of this melt-mantle reaction process at the base of the lithosphere. I further show that the relatively low Pt/Re ratios of the Hawaiian sulfides and the bulk rock pyroxenites suggest that, upon ageing, such pyroxenites plus their sulfides cannot generate the coupled 186Os- 187Os isotope enrichments observed in Hawaiian lavas. Therefore, recycling of mantle sulfides of pyroxenitic parentage is unlikely to explain the enriched Pt-Re-Os isotope systematics of plume-derived lavas.

Numerical Investigation of the Effect of Magnetic Field on Natural Convection in a Curved-Shape Enclosure

This investigation reports the magnetic field effect on natural convection heat transfer in a curved-shape enclosure. The numerical investigation is carried out using the control volume-based-finite element method (CVFEM). The numerical investigations are performed for various values of Hartmann number and Rayleigh number. The obtained results are depicted in terms of streamlines and isotherms which show the significant effects of Hartmann number on the fluid flow and temperature distribution inside the enclosure. Also, it was found that the Nusselt number decreases with an increase in the Hartmann number.

Espessura da zona de transição do manto sob a Província Borborema, NE Brasil, através de conversões Ps telessísmicas

The mantle transition zone is defined by two seismic discontinuities, nominally at 410 and 660 km depth, which result from transformations in the mineral olivine. The topography of these discontinuities provides information about lateral temperature changes in the transition zone. In this work, P-to-S conversions from teleseismic events recorded at 32 broadband stations in the Borborema Province were used to determine the transition zone thickness beneath this region and to investigate whether there are lateral temperature changes within this depth range. For this analysis, stacking and migration of receiver functions was performed. In the Borborema Province, geophysical studies have revealed a geoid anomaly which could reflect the presence of a thermal anomaly related to the origin of intraplate volcanism and uplift that marked the evolution of the Province in the Cenozoic. Several models have been proposed to explain these phenomena, which include those invoking the presence of a deep-seated mantle plume and those invoking shallower sources, such as small-scale convection cells. The results of this work show that no thermal anomalies are present at transition zone depths, as significant variations in the transition zone thickness were not observed. However, regions of depressed topography for both discontinuities (410 and 660 km) that approximately overlap in space were identified, suggesting that lower-thanaverage, lateral variations in seismic velocity above 410 km depth may exist below the the Borborema Province. This is consistent with the presence of a thermally-induced, low-density body independently inferred from analysis of geoid anomalies. Therefore, the magma source responsible for the Cenozoic intraplate volcanism and related uplift in the Province, is likely to be confined above the upper mantle transition zone.

Lasting mantle scars lead to perennial plate tectonics

R.N.P. and P.J.H. are grateful for funding from an NSERC Discovery Grant. Computations were performed on the GPC supercomputer at the SciNet HPC Consortium. SciNet is funded by the Canada Foundation for Innovation under the auspices of Compute Canada, the Government of Ontario, Ontario Research Fund—Research Excellence and the University of Toronto. Numerical calculations were done using a modified version of the SOPALE (2000) software. The SOPALE modelling code was originally developed by Philippe Fullsack at Dalhousie University with Chris Beaumont and his Geodynamics group.

Controls of mantle potential temperature and lithospheric thickness on magmatism in the North Atlantic Igneous Province.

FUNDING This study was funded by University of Aberdeen. SUPPLEMENTARY DATA Supplementary data for this paper are available at Journal of Petrology online. ACKNOWLEDGEMENTS The authors wish to thank Claude Herzberg, Estaban Gazel and an anonymous reviewer for thoughtful and constructive reviews.