Isotherm Migration Research Articles

Diffusiophoresis of Macromolecules within the Framework of Multicomponent Diffusion.

Diffusiophoresis is the isothermal migration of a colloidal particle through a liquid caused by a cosolute concentration gradient. Although diffusiophoresis was originally introduced using hydrodynamics, it can also be described by employing the framework of multicomponent diffusion. This not only enables the extraction of diffusiophoresis coefficients from measured multicomponent-diffusion coefficients but also their theoretical interpretation using fundamental thermodynamic and transport parameters. This review discusses the connection of diffusiophoresis with the 2 × 2 diffusion-coefficient matrix of ternary liquid mixtures. Specifically, diffusiophoresis is linked to the cross-term diffusion coefficient characterizing diffusion of colloidal particles due to cosolute concentration gradient. The other cross-term, which describes cosolute diffusion due to the concentration gradient of colloidal particles, is denoted as osmotic diffusion. Representative experimental results on diffusiophoresis and osmotic diffusion for polyethylene glycol and lysozyme in the presence of aqueous salts and osmolytes are described. These data were extracted from ternary diffusion coefficients measured using precision Rayleigh interferometry at 25 °C. The preferential-hydration and electrophoretic mechanisms responsible for diffusiophoresis are examined. The connection of diffusiophoresis and osmotic diffusion to preferential-interaction coefficients, Onsager reciprocal relations, Donnan equilibrium and Nernst-Planck equations are also discussed.

Radiative Cooling, Latent Heating, and Cloud Ice in the Tropical Upper Troposphere

Abstract The radiative cooling rate in the tropical upper troposphere is expected to increase as climate warms. Since the tropics are approximately in radiative–convective equilibrium (RCE), this implies an increase in the convective heating rate, which is the sum of the latent heating rate and the eddy heat flux convergence. We examine the impact of these changes on the vertical profile of cloud ice amount in cloud-resolving simulations of RCE. Three simulations are conducted: a control run, a warming run, and an experimental run in which there is no warming but a temperature forcing is imposed to mimic the warming-induced increase in radiative cooling. Surface warming causes a reduction in cloud fraction at all upper-tropospheric temperature levels but an increase in the ice mixing ratio within deep convective cores. The experimental run has more cloud ice than the warming run at fixed temperature despite the fact that their latent heating rates are equal, which suggests that the efficiency of latent heating by cloud ice increases with warming. An analytic expression relating the ice-related latent heating rate to a number of other factors is derived and used to understand the model results. This reveals that the increase in latent heating efficiency is driven mostly by 1) the migration of isotherms to lower pressure and 2) a slight warming of the top of the convective layer. These physically robust changes act to reduce the residence time of ice at any particular temperature level, which tempers the response of the mean cloud ice profile to warming. Significance Statement Here we examine how the amount of condensed ice in part of the atmosphere—the tropical upper troposphere (UT)—responds to global warming. In the UT, the energy released during ice formation is balanced by the emission of radiation to space. This emission will strengthen with warming, suggesting that there will also be more ice. Using a model of the tropical atmosphere, we find that the increase in ice amount is mitigated by a reduction in the amount of time ice spends in the UT. This could have important implications for the cloud response to global warming, and future work should focus on how these changes are manifested across the distribution of convective cloud types.

Ocean warming compresses the three-dimensional habitat of marine life.

Vertical migration to reach cooler waters is a suitable strategy for some marine organisms to adapt to ocean warming. Here, we calculate that realized vertical isotherm migration rates averaged -6.6 + 18.8 m dec-1 across the global ocean between 1980 and 2015. Throughout this century (2006-2100), surface isotherms are projected to deepen at an increasing rate across the globe, averaging -32.3 m dec-1 under the representative concentration pathway (RCP)8.5 'business as usual' emissions scenario, and -18.7 m dec-1 under the more moderate RCP4.5 scenario. The vertical redistribution required by organisms to follow surface isotherms over this century is three to four orders of magnitude less than the equivalent horizontal redistribution distance. However, the seafloor depth and the depth of the photic layer pose ultimate limits to the vertical migration possible by species. Both limits will be reached by the end of this century across much of the ocean, leading to a rapid global compression of the three-dimensional (3D) habitat of many marine organisms. Phytoplankton diversity may be maintained but displaced toward the base of the photic layer, whereas highly productive benthic habitats, especially corals, will have their suitable 3D habitat rapidly reduced.

Identification of animal behavioral strategies by inverse reinforcement learning.

Animals are able to reach a desired state in an environment by controlling various behavioral patterns. Identification of the behavioral strategy used for this control is important for understanding animals’ decision-making and is fundamental to dissect information processing done by the nervous system. However, methods for quantifying such behavioral strategies have not been fully established. In this study, we developed an inverse reinforcement-learning (IRL) framework to identify an animal’s behavioral strategy from behavioral time-series data. We applied this framework to C. elegans thermotactic behavior; after cultivation at a constant temperature with or without food, fed worms prefer, while starved worms avoid the cultivation temperature on a thermal gradient. Our IRL approach revealed that the fed worms used both the absolute temperature and its temporal derivative and that their behavior involved two strategies: directed migration (DM) and isothermal migration (IM). With DM, worms efficiently reached specific temperatures, which explains their thermotactic behavior when fed. With IM, worms moved along a constant temperature, which reflects isothermal tracking, well-observed in previous studies. In contrast to fed animals, starved worms escaped the cultivation temperature using only the absolute, but not the temporal derivative of temperature. We also investigated the neural basis underlying these strategies, by applying our method to thermosensory neuron-deficient worms. Thus, our IRL-based approach is useful in identifying animal strategies from behavioral time-series data and could be applied to a wide range of behavioral studies, including decision-making, in other organisms.

Numerical solutions for a Stefan problem

The initial version of a Stefan problem is the melting of a semi-infinite sheet of ice. This problem is described by a parabolic partial differential equation along with two bou ndary conditions on the moving boundary which are used to determine the boundary itself and complete the solution of the differenti al equation. In this paper firstly, we use variable space grid method, boundary immobilisation method and isotherm migration method to get rid of the trouble of the Stefan problem. Then, collocation finite element method based on cubic B-spline bases function s is applied to model problem. The numerical schemes of finite element methods provide a good numerical approximation for the model problem. The numerical results show that the present results are in good agreement with the exact ones.

Extending the persistent primary variable algorithm to simulate non-isothermal two-phase two-component flow with phase change phenomena

Abstract In high-enthalpy geothermal reservoirs and many other geo-technical applications, coupled non-isothermal multiphase flow is considered to be the underlying governing process that controls the system behavior. Under the high temperature and high pressure environment, the phase change phenomena such as evaporation and condensation have a great impact on the heat distribution, as well as the pattern of fluid flow. In this work, we have extended the persistent primary variable algorithm proposed by (Marchand et al. Comput Geosci 17(2):431–442) to the non-isothermal conditions. The extended method has been implemented into the OpenGeoSys code, which allows the numerical simulation of multiphase flow processes with phase change phenomena. This new feature has been verified by two benchmark cases. The first one simulates the isothermal migration of H 2 through the bentonite formation in a waste repository. The second one models the non-isothermal multiphase flow of heat-pipe problem. The OpenGeoSys simulation results have been successfully verified by closely fitting results from other codes and also against analytical solution.

The isotherm migration method in spherical coordinates with a moving heat source

An isotherm migration method is presented to track the isotherms at the surface of a semi-infinite workpiece that is being heated by a point source with a linear motion. The governing heat conduction equation is first transformed into a one-dimensional isotherm migration equation in spherical coordinates, which expresses the isotherm velocities as a function of the isotherm positions and their temperature derivatives. A finite difference formulation of this equation is then derived together with the corresponding boundary conditions. It is shown through a number of simulations that this system converges to the analytical solution when the temperature mesh is refined. The additional presence of a phase change results in a Stefan problem that can be solved approximately with some minor modifications to the method. The resulting system of equations can be used as a simple but accurate thermal model for some laser-material interaction processes such as laser heat treatments and laser cladding.

Assessment of Runoff Sensitivity in the Upper Indus Basin to Interannual Climate Variability and Potential Change Using MODIS Satellite Data Products

The Upper Indus Basin (UIB) covers an area of more than 200,000 km2 and has an elevation range from below 1000 to over 8000 m above sea level. Its water resources underpin Pakistan's food security and energy supply. Vertical and horizontal variations in key climate variables govern the runoff contributions of the UIB's various elevation zones and subcatchments. Remote sensing climatic data products from NASA's Moderate Resolution Imaging Spectrometer (MODIS) instrument platform provide an opportunity to develop a spatial characterization of the climatology of remote and rugged regions such as the UIB. Specifically, snow-covered area (SCA) and land surface temperature (LST) have been shown to provide good analogues, respectively, for precipitation and air temperature. As such, SCA and LST quantify regional variations in mass and energy inputs to runoff generation processes. Although the 10-year (2000–2010) MODIS observational record is not adequate to evaluate long-term trends, it does provide a consistent depiction of annual cycles and a preliminary assessment of interannual variability. This study presents a summary of the period means and interannual variability found in remotely sensed SCA and LST products for the UIB. It then provides an update of locally observed recent climate trends for the 1962 to 2007 period. Nonparametric trend tests are applied both to the local observations and to remote sensing records to assess patterns in recent variability. The climatic noise (intense variability) of the past decade, however, renders conclusions on nascent trends in SCA and LST premature. Finally, runoff sensitivity to temperature change—spatially applied as summer (JJA) nighttime 0°C LST isotherm migration—is assessed for a range of potential scenarios. Results indicate that changes in mean summer (JJA) runoff could range from −30 to 35% or more, depending on whether recent locally observed changes continue or scenarios derived from current regional climate model (RCM) simulations unfold.

Caesium isothermal migration behaviour in sintered titanium nitride: New data and comparison with previous results on iodine and xenon

Titanium nitride has been proposed as a fission product barrier in fuel structures for gas cooled fast reactor (GFR) systems. The thermal migration of Cs was studied by implanting 800keV 133Cs++ ions into sintered samples of TiN at an ion fluence of 5×1015cm−2. Thermal treatments at temperatures ranging from 1500 to 1650°C were performed under a secondary vacuum. Concentration profiles were determined by 2.5MeV 4He+ elastic backscattering. The results reveal that the global mobility of caesium in the host matrix is low compared to xenon and iodine implanted in the same conditions. Nevertheless, the evolution of caesium depth profile during thermal treatment presents similarities with that of xenon. Both species are homogeneously transported towards the surface and the transport rate increases with the temperature. In comparison, iodine exhibits singular migration behaviour. Several assumptions are proposed to explain the better retention of caesium in comparison with both other species. The potential role played by the oxidation is underlined since even a slight modification of the surface stoichiometry may modify species mobility. More generally, the apparition of square-like shapes on the surface of the samples after implantations and thermal treatments is discussed.

Iodine isothermal migration behaviour in titanium nitride

Titanium nitride is one of the inert matrixes proposed to surround the fuel in gas cooled fast reactor (GFR) systems. These reactors will operate at high temperature and refractory materials with a high chemical stability and good mechanical properties are required. Furthermore, a total retention of the most volatile fission products, such as I, Xe or Cs, by the inert matrix is needed during the in-pile process. The isothermal migration of iodine in TiN was studied by implanting 800 keV I ++ ions in sintered samples at an ion fluence of 5 × 10 15 cm −2. Thermal treatments were performed under secondary vacuum at temperatures ranging from 1200 to 1700 °C. Iodine concentration profiles were determined by 2.5 MeV α-particle elastic backscattering. The migration of iodine seems to be correlated with point defects created by implanted ions near the surface. The Arrhenius plot corresponding to iodine detrapping is curved with possibly two straight-line regions which could indicate either the presence of two types of traps, or a strong dependence of trap’s concentration on temperature above 1500 °C. The activation energies associated with each linear region of the Arrhenius plot were found to be: E a = 2.4 ± 0.2 eV below 1500 °C and E a ′ = 11.4 ± 0.2 eV above 1500 °C. Nitrogen evaporation from TiN surface under secondary vacuum was proposed as a contributing factor to the enhanced mobility of iodine at high temperature.

Modeling of the dynamics of transient liquid films in ternary systems

The presence of a concentration gradient across a thin liquid film leads to the phenomenon of isothermal liquid film migration (LFM). In most cases, the concentration gradient is due to coherency stresses, and the migration of the liquid film results in the relaxation of these stresses. It is also possible to envisage cases in which LFM occurs as a result of chemical solubility differences between stable and metastable phases. Both situations are examined in this contribution with special emphasis on the effect of adding a second solute element to the liquid phase. The kinetics of LFM is examined as a function of the initial liquid concentration and the ratio of the solute diffusion coefficients in a model coherency-driven ternary system. The growth of the Γ2 inside δ particles in the Zn-Fe-Al system is presented as a possible example of chemically driven LFM.

An isotherm migration formulation for one-phase Stefan problem with a time dependent Neumann condition

In this paper, we present a numerical scheme based on an isotherm migration formulation for one-dimensional, one-phase Stefan problem with a time dependent Neumann condition on the fixed boundary and a constant Dirichlet condition on the moving boundary. The numerical results obtained by the present method have been compared with exact one and also those obtained by earlier authors, and are found to be in very good agreement with each other. It is also shown that the numerical solution displays the expected convergence to the exact one as the mesh size is refined.

Migration of a van der Waals bubble: Lattice Boltzmann formulation

A numerical study of the isothermal migration of a two-dimensional bubble in Poiseuille flow is reported here for vapor–liquid density and dynamic viscosity ratios of 1/8, Red=1, and Ca=2. A lattice Boltzmann model with a van der Waals equation of state is employed to simulate the diffuse interface for three interface thickness to bubble diameter ratios, 1/5, 1/10, and 1/20. Point-by-point comparisons with the sharp-interface incompressible counterpart (reported in the literature) reveal velocity discrepancies which are more evident on the vapor side. These differences are a manifestation of a finite mass flux through the interface, associated with driven finite–thickness interfaces. An analytical study of the one-dimensional analog of the traveling diffuse interface problem explains this phenomenon and shows that this flux vanishes as a result of viscous dissipation as the interface thickness tends to zero. This trend is corroborated by the two-dimensional lattice Boltzmann results.

Natural gas hydrates on the continental slope off Pakistan: constraints from seismic techniques

In October 1997, new vertical-incidence, wide-angle reflection and refraction data were obtained on the convergent continental margin off Pakistan. The most prominent feature across the entire margin into the Gulf of Oman is a bottom simulating reflector (BSR). This reflection generally coincides with the depth predicted for the base of the gas hydrate stability field. On the accretionary prism the BSR is a clear reflection with inverse polarity, and strata beneath the BSR show enhanced reflectivities, suggesting that gas is trapped between stratigraphic layers. Joint inversion of wide-angle and refraction data yielded a ∼200 m thick low-velocitiy zone at BSR depth. Using the Born expansion, band-limited impedance logs were calculated from deconvolved and scaled single-channel data, suggesting that velocity at the BSR drops by ∼200 m s−1. Some 40 km towards the coast, CDP4400 of Minshull & White (1989) yielded a velocity inversion of about 600 m s−1, indicating that BSR characteristics vary significantly across the continental margin off Pakistan. Beneath the Gulf the BSR was sampled at a similar subbottom depth, where seismic bright spots occur. However, its reflection amplitude is unusually low and seismic stratigraphy beneath the BSR did not show enhanced reflectivities. Joint traveltime inversion of wide-angle and refraction data revealed continuously increasing velocities, suggesting that an adequate supply of methane for forming free gas and gas hydrate is mainly confined to sediments incorporated into the accretionary prism. We believe that these variations are related to an evolutionary process due to tectonic uplift and ongoing sedimentation as sediments are incorporated into the accretionary prism. Sedimentation and uplift produce an upward migration of isotherms and therefore lead to a dissociation of gas hydrates, which releases methane gas and thus causes an enhancement of the BSR. Our survey imaged BSR properties of the abyssal plain and within the first slope basin at water depths of 3300 m and 2490 m, respectively. CDP4400 was located farther landwards at a depth of 1730 m within a buried and uplifted and hence more evolved slope basin. We therefore suggest that, in the accretionary wedge, tectonic uplift and ongoing sedimentation cause hydrate recycling by upward migration of the stability field. In addition, tectonic dewatering may accumulate hydrate at the base of the stability field by advection of methane from depth.

Multigrid Methods for Incompressible Heat Flow Problems with an Unknown Interface

Finite-volume/multigrid methods are presented for solving incompressible heat flow problems with an unknown melt/solid interface, mainly in solidification applications, using primitive variables on collocated grids. The methods are implemented based on a multiblock and multilevel approach, allowing the treatment of a complicated geometry. The inner iterations are based on the SIMPLE scheme, in which the momentum interpolation is used to prevent velocity/pressure decoupling. The outer iterations are set up for interface update through the isotherm migration method. V-cycle and full multigrid (FMG) methods are tested for both two- and three-dimensional problems and are compared with a global Newton's method and a single-grid method. The effects of Prandtl and Rayleigh numbers on the performance of the schemes are also illustrated. Among these approaches, FMG has proven to be superior on performance and efficient for large problems. Sample calculations are also conducted for horizontal Bridgman crystal growth, and the performance is compared with that of traditional single-grid methods.

Prograde metamorphism, strain evolution, and collapse of footwalls of thick thrust sheets: a case study from the Mesozoic Sevier hinterland U.S.A.

Analysis of prograde metamorphic fabrics in the exhumed footwall of the Mesozoic Windermere thrust, northeast Nevada, reveals fabrics and style of ductile flow developed during tectonic burial metamorphism of a sedimentary footwall of a thick thrust sheet. In response to structural burial, footwall strata underwent Barrovian metamorphism synchronous with development of bedding-parallel or near parallel S and S– L tectonites. Footwall rocks range from unmetamorphosed at high structural levels and progressively increase in metamorphic grade to upper amphibolite facies at deep levels. Attenuation of footwall stratigraphic units accompanied tectonite development whereby the amount of attenuation varies with metamorphic grade from ∼0% in lower greenschist facies to ∼30–50% in upper amphibolite facies rocks. Microstructures in metacarbonate, metapsammite, and metapelite, and analysis of crystallographic preferred orientations of quartz c-axes in quartzite, suggest a dominantly coaxial strain path with flattening strain predominating at lower metamorphic grade and plane strain more dominant at higher metamorphic grade. The microstructural data indicate that dominantly coaxial deformation during metamorphism accommodated extension of the footwall. Ductile extension most likely records footwall collapse induced by a loss of strength due to relative upward migration of isotherms during and or following burial. Extension may act as a mechanism that in part facilitates isostatic accommodation or sinking of the overlying load resulting in a reduction of topography. Attenuation of footwalls of thick thrust sheets and production of predominantly coaxial layer-parallel or near parallel fabrics may be an intrinsic process once sufficient structural overburden is developed and thermal relaxation and prograde metamorphism ensues.

Simultaneous drying and pyrolysis of solid fuel particles

Drying and devolatilization are studied at combustion temperatures. The surface temperature of particles at the end of drying can significantly exceed the temperature when devolatilization starts, implying that drying and pyrolysis may partly overlap. Devolatilization is controlled by heat transfer, when the particle size is large. The critical particle size at which heat transfer dominates chemical kinetics is discussed. A model for calculating the intrinsic rate of generation of volatiles in the regime of heat transfer control is presented. A novel isotherm migration method is used for the computation of simultaneous drying and pyrolysis inside a fuel particle. It applies to the study of heat transfer in a one-dimensional geometry with moving phase-change boundaries, internal fluid flow and mass generation, including steep temperature and density profiles, as frequently encountered in combustion.

40Ar/ 39Ar and 18O/ 16O studies of the Chegem ash-flow caldera and the Eldjurta Granite: Cooling of two late Pliocene igneous bodies in the Greater Caucasus Mountains, Russia

Volcanic and intrusive rocks of the Chegem caldera and the nearby Eldjurta (Eldzhurtinskiy) Granite record a late Pliocene episode of silicic magmatism in the north-central Caucasus Mountains. Surface exposures, created by the recent rapid uplift and erosion of the Caucasus Mountains, span a 2 km vertical section of Chegem caldera fill and 1150 m of the Eldjurta Granite; cored mineral-exploration drillholes in the Eldjurta Granite extend the sampling to a depth of 4 km. The unique sampling range available in these two young igneous bodies affords an excellent opportunity to study their denudation and cooling histories, which we examine by means of 40Ar/ 39Ar and 18O/ 16O measurements on an extensive sample suite. Total-fusion biotite and sanidine ages from eight Chegem Tuff samples, both intracaldera and outflow, are analytically indistinguishable with a weighted mean of 2.82 ± 0.02 Ma. A cross-cutting granodiorite porphyry intrusion has a sanidine total fusion age of 2.84 ± 0.03 Ma, and whole-rock incremental heating of a post-caldera andesite flow, which caps the caldera fill, yields an age of 2.82 ± 0.02 Ma. Thus, caldera formation and post-caldera resurgence and volcanism all occurred within a very short time (< 50,000 yr). Biotite total-fusion ages of ten Eldjurta Granite samples, including seven from ∼ 500 m intervals in the 4 km deep drillhole, show a systematic linear decrease in age with depth from 1.90 Ma near the roof contact of the granite to 1.56 Ma at a depth of 3700 m. Assuming these ages were set at the same temperature, this age/depth gradient implies an isotherm migration rate of 13 mm/yr between 1.90 and 1.56 Ma. This migration rate is due to a combination of rapid denudation and downward relaxation of isotherms, with cooling rates between 200 and 500°C/Ma during this period. Oxygen isotopic compositions of quartz, K-feldspar, plagioclase and biotite from the drillhole samples below the 800 m depth are fairly uniform and record primary igneous δ 18O values with little evidence for subsolidus hydrothermal activity. However, in surface outcrop samples and in the shallowest drillhole sample, mineral δ 18O values have been lowered by up to 3‰ by interaction with an external (meteoric-hydrothermal?) fluid. The primary mineral δ 18O values of the Eldjurta Granite are distinctly higher than the corresponding phenocryst δ 18O values in the Chegem volcanic rocks, indicating that the two bodies evolved as separxate magma batches.

Adaptive finite element analysis of axisymmetric freezing

The paper describes an adaptive finite element analysis of the transient axisymmetric freezing process. Adaptivity schemes are applied to both space and time tessellations. Error equidistribution adjusts the nodal positions and Taylor series analysis of time truncation error selects the time step. In implicit time integration, the location of the freezing front and the nodal temperatures at the next time is solved by full Newton all at once. The method appears to be accurate; in cases for which closed-form solutions are available, it agrees well with them. It also avoids the problem found in the Modified Isotherm Migration Method where the freezing front tends to retrogress when solid just forms on the outer surface cooled by convection.

A note on the use of the isotherm migration method

In this note we present some simple modifications of the isotherm migration method (IMM) so that a broader class of conduction problems (than the usual Stefan problems) can be effectively tackled by its use. Some numerical illustrations, based on finite differences, are presented which show that, for heat flow problems with arbitrary conditions, an accurate numerical process can be based on the IMM formulation.