Total Diffusion Flux Research Articles

Neutrinos from failed supernovae at future water and liquid argon detectors

We discuss the diffuse flux of electron neutrinos and antineutrinos from cosmological failed supernovae, stars that collapse directly into a black hole, with no explosion. This flux has a hotter energy spectrum compared to regular, neutron-star forming collapses, and therefore it dominates the total diffuse flux from core collapses above 20-45 MeV of neutrino energy. Reflecting the features of the originally emitted neutrinos, the flux of nu_e and anti-nu_e at Earth is larger for larger survival probability of these species, and for stiffer equations of state of nuclear matter. In the energy window 19-29 MeV, the flux from failed supernovae is susbtantial, ranging from 7% to a dominant fraction of the total flux from all core collapses. It can be as large as phi = 0.38 s^{-1} cm^{-2} for anti-nu_e (phi = 0.28 s^{-1} cm^{-2} for nue), normalized to a local rate of core collapses of R_{cc}(0)=10^{-4} yr^{-1} Mpc^{-3}. In 5 years, a 0.45 Mt water Cherenkov detector should see 5-65 events from failed supernovae, while up to 160 events are expected for the same mass with Gadolinium addition. A 0.1 Mt liquid argon experiment should record 1-11 events. Signatures of neutrinos from failed supernovae are the enhancement of the total rates of events from core collapses (up to a factor of 2) and the appearance of high energy tails in the event spectra.

Strategy for predicting effective transport properties of complex porous structures

Measurements of effective transport properties of porous media, such as effective diffusivity and permeability, are well established by several experimental techniques. Effective transport properties can be also calculated from the spatially 3D reconstructed porous media, where the morphology characteristics required for the reconstruction are obtained from electron microscopy images. Here we demonstrate the reconstruction of porous alumina catalyst carrier with bimodal pore size distribution. Multi-scale concept is employed for the computation of effective diffusivity and permeability of reconstructed porous media and calculated effective transport properties are compared with transport parameters experimentally determined in Graham diffusion and simple permeation cell. The limitations of current state-of-the-art reconstruction techniques for porous media with broad pore size distribution are discussed. We show that the contribution of nano-pores towards the total diffusion flux is significant and cannot be neglected, but it is reasonable to neglect the contribution of nano-pores towards the sample permeability.

Convective diffusion from strip-like micro-probes into colloidal suspensions

Full equations of convective diffusion are solved numerically for a strip-like (2D) electrodiffusion friction probe in a stream of microdisperse liquid, assuming a non-linear near-to-wall velocity profile ranging from simple shear flow ( p = 1) to ideal slip ( p = 0). The range of generalized Peclet number H from H = 0.01 (almost pure spatial diffusion) to H = 100 (diffusion layer with negligible longitudinal diffusion) covers all cases of possible experimental relevance. The main result is expressed as a relative deviation of actual total diffusion flux N from its diffusion-layer approximation N DLA, Ψ = N/ N DLA − 1.

Diffuse Neutrino Flux from Failed Supernovae

I study the diffuse flux of electron antineutrinos from stellar collapses with direct black hole formation (failed supernovae). This flux is more energetic than that from successful supernovae, and therefore it might contribute substantially to the total diffuse flux above realistic detection thresholds. The total flux might be considerably higher than previously thought, and approach the sensitivity of Super-Kamiokande. For more conservative values of the parameters, the flux from failed supernovae dominates for antineutrino energies above 30-45 MeV, with potential to give an observable spectral distortion at megaton detectors.

Extraction into a flow of a fluid with a velocity gradient

Unsteady extraction from a system of semi-infinite capillaries to the flow of a fluid with a linear velocity gradient is studied. An assumption that the diffusion in the flow is a quasi-steady-state process is taken to obtain a linear equation for the local mass flux from the pore space, which involves fractional derivatives with respect to time and flow coordinate. Limiting solutions for the total diffusion flux at small and large times that cover the entire time interval are found.

Anomalous diffusion in presence of twin boundaries

After implantation of the 71Ge radiotracer in the Mg-1.8 wt% Al magnesium alloy, tracer diffusion coefficients were measured using both the serial sectioning and the residual activity technique in the temperature range from 448 to 848 K. Anomalously high diffusivities were observed at high temperatures where volume diffusion usually predominates. A contribution of high diffusivity paths to the total diffusion flux can be a possible explanation of both phenomena. Based on the high fraction of twin boundaries confirmed by electron microscopy, a simple microstructure model is proposed.

Competition effects in diffusion-controlled bulk reactions between ions

A numerical solution for competitive diffusion into two static charged sinks is presented and compared against an approximate analytical solution. It is shown that for an attractive Coulomb potential the correction to the total diffusive flux of ionic reactants due to diffusion interaction between sinks may be ignored for large enough values of the Onsager length and thus the reaction rate can be described by the classical Debye formula. On the other hand, for repulsive potentials the competition becomes more profound than in the case of uncharged sinks. However, this effect is of little interest because of a small value of the diffusive flux on the reaction surface.

Variability in abundance and fluxes of dimethyl sulphide in the Indian Ocean

Dimethyl sulphide (DMS) is a biogenic gas of climatic significance on which limited information is available from the Indian Ocean. To fill this gap, we collected data on DMS and total dimethylsulphoniopropionate (DMSPt) by participating in a dozen cruises. Here, we discuss the variability in DMS and DMSPt in the north and central Indian Ocean in terms of their spatial and temporal variation. DMS and DMSPt exhibited significant spatial and temporal variability. Apart from the concentration gradients in DMS within the Arabian Sea, Bay of Bengal and Central Indian Ocean basins, differences in average abundances were conspicuous between these basins. The Arabian Sea contained more DMS (mixed layer average was 7.8 nM) followed by the Bay of Bengal (2.8 nM) and the Central Indian Ocean (2.7 nM). The highest concentrations of DMS and DMSPt (525 nM and 916 nM, respectively) were found in upwelling regimes along the west coast of India during the Southwest monsoon and fall intermonsoon seasons. Average surface DMS was the highest in the Arabian Sea. On the other hand observed sea-to-air fluxes of DMS were higher in the Bay of Bengal due to the prevalence of turbulent conditions. In the Arabian Sea wind speeds were low and hence the sea-to-air fluxes. The total diffusive flux of DMS from the study area to atmosphere is estimated to be about 1.02 × 1012 g S y−1, which contributes to 4.1–6.3% of the global DMS emission

Ostwald ripening under conditions of mixed-type diffusion

The Ostwald ripening in metallic alloys and quasi-zero-dimensional semiconductor structures is investigated under conditions of mixed dislocation-matrix diffusion, when none of the terms jd and jv in the expression for the total diffusion flux can be ignored. The size distribution functions and time dependences of the maximum size rg and critical (average) size rk(〈r〉) of particles for different ratios x between the fluxes are obtained. It is demonstrated that mixed dislocation-matrix diffusion can occur in the course of the formation of CdS quantum dots prepared through chemical deposition.

The color of the Martian sky and its influence on the illumination of the Martian surface

The dust in the atmosphere above the Mars Pathfinder landing site produced a bright, red sky that increases in redness toward the horizon at midday. There is also evidence for an absorption band in the scattered light from the sky at 860 nm. A model of the sky brightness has been developed [Markiewicz et al., this issue] and tested against Imager for Mars Pathfinder (IMP) observations of calibration targets on the lander. The resulting model has been used to quantify the total diffuse flux onto a surface parallel to the local level for several solar elevation angles and optical depths. The model shows that the diffuse illumination in shadowed areas is strongly reddened while areas illuminated directly by the Sun (and the blue forward scattering peak) see a more solar‐type spectrum, in agreement with Viking and IMP observations. Quantitative corrections for the reddening in shadowed areas are demonstrated. It is shown quantitatively that the unusual appearance of the rock Yogi (the east face of which appeared relatively blue in images taken during the morning but relatively red during the afternoon) can be explained purely by the changing illumination geometry. We conclude that any spectrophotometric analysis of surfaces on Mars must take into account the diffuse flux. Specifically, the reflectances of surfaces viewed under different illumination geometries cannot be investigated for spectral diversity unless a correction has been applied which removes the influence of the reddened diffuse flux.

Constitutive equations for viscoelastic surface diffusion: Effects of deformation and thermal history

In this paper we derive constitutive equations for surface diffusion in a non-isothermal fluid–fluid interface, consisting of a mixture of linear viscoelastic components with fading memory. The constitutive equation contains three main contributions to the total diffusive flux: thermal diffusion, diffusion resulting from the thermal history of the components, and mechanical diffusion. The mechanical diffusion term incorporates the effects of ordinary diffusion, forced diffusion, and diffusion arising from surface tension gradients. It also incorporates diffusion caused by inertial effects, diffusion resulting from hydrostatic normal stresses, diffusion arising from hydrodynamic viscous stresses, and contributions arising from the deformation history of the individual components. The history terms in the constitutive equation are all expressed in terms of memory integrals. In addition to an equation for the surface mass flux vector, the analysis also provides constitutive equations for the surface thermal energy flux vector, and the surface stress tensor. All these constitutive equations are derived using the jump entropy inequality.

Carbon dioxide and helium emissions from a reservoir of magmatic gas beneath Mammoth Mountain, California

Carbon dioxide and helium with isotopic compositions indicative of a magmatic source ( δ13C = −4.5 to −5‰, 3He/ 4He = 4.5 to 6.7 RA) are discharging at anomalous rates from Mammoth Mountain, on the southwestern rim of the Long Valley caldera in eastern California. The gas is released mainly as diffuse emissions from normal‐temperature soils, but some gas issues from steam vents or leaves the mountain dissolved in cold groundwater. The rate of gas discharge increased significantly in 1989 following a 6‐month period of persistent earthquake swarms and associated strain and ground deformation that has been attributed to dike emplacement beneath the mountain. An increase in the magmatic component of helium discharging in a steam vent on the north side of Mammoth Mountain, which also began in 1989, has persisted until the present time. Anomalous CO2 discharge from soils first occurred during the winter of 1990 and was followed by observations of several areas of tree kill and/or heavier than normal needlecast the following summer. Subsequent measurements have confirmed that the tree kills are associated with CO2 concentrations of 30–90% in soil gas and gas flow rates of up to 31,000 g m−2 d−1 at the soil surface. Each of the tree‐kill areas and one area of CO2 discharge above tree line occurs in close proximity to one or more normal faults, which may provide conduits for gas flow from depth. We estimate that the total diffuse CO2 flux from the mountain is approximately 520 t/d, and that 30–50 t/d of CO2 are dissolved in cold groundwater flowing off the flanks of the mountain. Isotopic and chemical analyses of soil and fumarolic gas demonstrate a remarkable homogeneity in composition, suggesting that the CO2 and associated helium and excess nitrogen may be derived from a common gas reservoir whose source is associated with some combination of magmatic degassing and thermal metamorphism of metasedimentary rocks. Furthermore, N2/Ar ratios and nitrogen isotopic values indicate that the Mammoth Mountain gases are derived from sources separate from those that supply gas to the hydrothermal system within the Long Valley caldera. Various data suggest that the Mammoth Mountain gas reservoir is a large, low‐temperature cap over an isolated hydrothermal system, that it predates the 1989 intrusion, and that it could remain a source of gas discharge for some time.

The Maxwell–Stefan equations for diffusion in multiphase systems with intersecting dividing surfaces

In this paper, the Maxwell–Stefan theory for diffusion is extended to multiphase systems with intersecting dividing surfaces. The general Maxwell–Stefan equation is separated into equations for bulk diffusion, surface diffusion and (common) line diffusion. Expressions for the driving forces in these equations are derived using the jump entropy inequality and the entropy inequality at the common line. The resulting equations for surface and line diffusion are more general than previously reported extensions of Fick’s law. They incorporate contributions from forced diffusion, and diffusion resulting from surface tension and line tension gradients into the total diffusive flux.

Flame-ball drift in the presence of a total diffusive heat flux

For a one-component reaction model, the total diffusive heat flux (TDHF) is—∇( λT+pDQY ) where λ and pD are diffusive transport coefficients, T is the temperature, Y is the reactant mass-fraction, and Q is the heat of reaction. We show that a flame ball exposed to a weak TDHF will drift, and we derive an explicit formula for the drift speed. The key mathematical feature is that the flux generates a flametemperature perturbation that varies as cos φ , where φ is the polar angle measured from the axis parallel to the flux vector, and this is unacceptable as it leads to a simple boundary-value problem for a harmonic function (a temperature perturbation) that has no solution. Drift generates a like perturbation and the drift speed must be chosen so that the two cancel. If the TDHF is generated by a second flame ball whose far-temperature-field is suppressed by radiation, so that only ∇ Y contributes to the flux, the balls will drift apart with a separation distance that grows as the one-third power of time. Observations made during recent space shuttle flights are presented and are consistent with this prediction. We also formulate the problem of drift in a weak gravitational field and solve it in an approximate fashion.

Revisiting the thermal-spike concept in ion-surface interactions

In recent years many groups have advocated a thermal-spike model to explain a variety of experimental results in ion-irradiation of solids, as for example sputtering, mixing, compositional change, structural change, and track formation. The latter include crystal-to-amorphous transitions as well as track formation due to MeV/u particles. In this paper we reconsider the phenomena occurring during ion impact of solids looking at the time scale generally indicated as relevant for thermal-spike effects, namely a picosecond scale as shown by molecular dynamics. Sputtering, mixing, and track formation, however, will be analyzed in more detail. We consider first ion-beam sputtering and reiterate (as is already well-known) that yields which increase with the bulk temperature most often indicate merely the onset of normal vaporization. Indeed, only simulations appear to be capable of giving insight even if the information is sometimes tentative. In mixing, ballistic transport is important but not dominant. It is often argued that the additional transport is provided by thermal spikes but it is noted that such an assumption is normally not required by the experimental results. What is more relevant is a role for residual defects such that the total diffusion flux includes (if the defects are chemically guided) a modified Darken factor, or (if the defects are not chemically guided) simply an increased diffusivity. The time scale (min), distances (well beyond the collision cascade), temperature sensitivity (changes of as little as 75 K are relevant), and correlation with vacancy properties (thence with the solid rather than liquid state) which are relevant to these residual defects are not understandable in terms of thermal spikes. We finally consider track formation. Recent work claiming that track formation in solids, irradiated with heavy ions, may be understood in terms of thermal spikes is reconsidered to show that the thermal-spike model is utilized without considering all the relevant phenomena included in irradiation-induced heating and phase transitions. For example, a comparison of fs-laser pulse irradiation of Si with swift heavy-ion irradiation, shows that melting is possible in the first case since the excited electrons have a low and more or less restricted energy while in the case of swift ion-irradiation, the motion of the excited electrons includes a ballistic component which does not favour the localization of the thermal energy necessary to induce lattice melting. It is concluded that track formation is better understandable in a more general framework of defect-induced processes in solids.

Two- and three-dimensional analysis of diffusion through a dense membrane supported on a porous material

Two- and three-dimensional diffusive flow behavior in a coated dense layer of a composite membrane or in a dense polymer membrane placed adherently on a mechanical porous support in a permeation test cell was analyzed and compared to clarify the extent of decrement in flux compared with the case without support. By solving two- and three-dimensional models proposed to describe the flow in the coated dense layer, steady-state concentration profiles of fluid and total diffusive flux were calculated. As a result, the flux decreased with decreasing ratio of membrane thickness to width of unit porous support, t m w u , and with decreasing porosity of support, ϵ. The three-dimensional analysis was found to better realize the flow in the dense layer supported on porous material. Such a decrease in flux could be represented by flux ratio, f, which was found to be approximated by the following semi-empirical formula as a function of t m w u ratio and ϵ. f=ϵ+ (1−ϵ)(1−10 − ϵt m w u )

Impact of microsensor-caused changes in diffusive boundary layer thickness on O2 profiles and photosynthetic rates in benthic communities of microorganisms

Although O2 microsensors used for study of benthic photosynthesis have tip diameters of less than 10 pm and stem diameters of about 150 pm at a distance of 0.5 cm from the tip, they do change the local flow pattern in the overlying water and thereby reduce the thickness of the diffusive boundary layer (DBL). The reduced DBL resulted in a lower diffusional resistance towards export of 0, from communities with a net production of Oa, and insertion of a microsensor in such a community therefore resulted in lowered O2 concentrations. The total diffusion flux out of the photosynthetic layer was not significantly dffected by the presence of the microsensor. The higher upward flux into the water phase was counterbalanced by a reduced downward flux into the sediment. The O2 profiles and diffusion fluxes were only affected when the surface was smooth, while the effect of microsensor insertion was undetectable when the surface was made irregular by small tufts, bubbles, etc. In the investigated cyanobacteria-dominated mats, the gross photosynthetic rates as measured by the light/dark shift technique were unaffected by the presence of a microsensor.

Ion-beam mixing with chemical guidance IV. Thermodynamic effects without invoking thermal spikes

Various studies on ion-beam mixing suggest that the extent of mixing is sensitive to the sign and magnitude of the heat of mixing Δ H m. This suggests a role, not only for random motion, but also for chemical driving forces such that the total diffusion flux includes a modified Darken factor: 1 −α i(1−α i)[ 2h mp RT(1 +p) ]  1− α i(1 − α i)q . Here α i, is the atomic fraction of component i, α i (1 − α i ) h m is the heat of mixing of a regular solution, and p is the ratio of the diffusivities for chemically guided defect motion to those for random motion of all types. We wish to evaluate the parameter p from a variety of recent experiments. We first consider the work of Marton, Fine, and Chambers on profiling multilayers of Ni-Ag and conclude that the narrowing of the Ag profiles, as temperature increases, is connected to a strongly reduced solubility. By fitting the profiles to solutions of the continuity equation corresponding to the above total diffusion flux, values of q are obtained. Provided T can be taken as the ambient temperature, values of p then follow: 0.04 ± 0.01 at 300 K, 0.15 ± 0.02 at 400 K, and 0.24 ± 0.04 at 600 K. We then consider ion-beam mixing experiments based in some cases on solubility changes (11 examples), in some cases on interface broadening versus Δ H m (40 examples), and in still other cases on interface broadening in the presence and in the supposed absence of defect-induced transport (5 examples). Considering all results, reasonably consistent values of p are obtained for temperatures ranging from 77 to 603 K. It is thus possible to understand a variety of experimental results relating to profiling and to ion-beam mixing in terms of chemical driving forces and, moreover, to do so without invoking thermal spikes. In our opinion this approach constitutes a more satisfactory framework for describing mixing (and related bombardment-induced solid-state processes) than that in which thermal spikes are assumed.

Thermodynamic effects in depth profiling and ion-beam mixing without invoking thermal spikes

Various studies on ion-beam mixing suggest that the extent of mixing is sensitive to the sign and magnitude of the heat of mixing, ΔHm. This implies a role, not only for random motion, but also for chemical driving forces of the type where the total diffusion flux is modified by the factor [1−αi(1−αi) 2hmp/RT(1+p)]. Here α1 is the atomic fraction of component i, αi(1−αi)hm is the heat of mixing of a regular solution, and p is the ratio of the diffusivities for chemically guided defect motion to those for random motion of all types. The parameter p has never been evaluated for any system and we wish to evaluate it first by analyzing the profiling experiments of Marton, Fine, and Chambers on multilayers of Ni-Ag. We then obtain further values of p from ion-beam mixing experiments on bilayers and multilayers. It is shown that it is possible to understand a variety of experimental results relating to profiling and to ion-beam mixing in terms of chemical driving forces and, moreover, to do so without invoking thermal spikes.

A simple way of describing the diffusion phase growth in cylindrical and spherical samples

It is shown that during diffusional growth of the intermediate phase between substances A and B for cylindrical and spherical samples, the total diffusion flux relative to the center, −S(r)D̃∂c/∂r, where S is the area of the interface, varies by a small amount in the radial direction, despite the concentration dependence of the interdiffusion coefficient D̃(c). In this context we propose a constant-flux method which allows the kinetics of the diffusional phase growth in cylindrical and spherical samples to be described in a rather simple way. Deviations from the parabolic law of phase growth in cylindrical and spherical samples are analyzed.