Total Diffusion Flux Research Articles

Effects of dry density and porewater salinity on Eu(Ⅲ) diffusion in compacted GMZ bentonite: A perspective from triple pore structure

Compacted bentonite is microscopically characterized by a triple pore structure composed of inter-aggregate pores, inter-particle pores and interlayer pores. These three types of pores are available for diffusive transport of cations through different mechanisms: free water diffusion, surface diffusion, and interlayer diffusion. This study investigated the effects of dry density and porewater salinity on Eu(Ⅲ) diffusion in compacted GMZ bentonite from the perspective of triple pore structure. A series of through-diffusion (TD) experiments were conducted as a function of the density and porewater salinity. Then the triple pore structure was characterized using SEM and MIP tests. On this basis, a mathematical expression about the dependence of Eu(Ⅲ) diffusion on the triple pore structure was developed. Results indicated that increasing dry density inhibited the Eu(Ⅲ) diffusion, as evidenced by decreases in the effective diffusion coefficient De, capacity factor α, and apparent diffusion coefficient Da. This inhibition is attributed to the reduction in inter-aggregate pores, inter-particle pores, and interlayer pores with increased density, thereby suppressing free water diffusion, surface diffusion, and interlayer diffusion. Conversely, increasing porewater salinity facilitated the Eu(Ⅲ) diffusion. This is likely because the relatively high concentration of Eu(Ⅲ) in the TD tests makes free water diffusion as the dominant pathway. Although surface diffusion and interlayer diffusion were inhibited owning to the decrease of inter-particle pores and interlayer pores, their negative effects on total diffusion flux were less than the positive effects of enhanced free water diffusion resulting from the increase of inter-aggregate pores. Finally, by comparing the calculated total diffusion fluxes and experimental values, the applicability of the proposed expression for predicting Eu(Ⅲ) diffusion in compacted bentonite with varying dry densities and salinities was discussed.

Nucleation-Limited Kinetics of GaAs Nanostructures Grown by Selective Area Epitaxy: Implications for Shape Engineering in Optoelectronics Devices.

The growth kinetics of vertical III-V nanowires (NWs) were clarified long ago. The increasing aspect ratio of NWs results in an increase in the surface area, which, in turn, enhances the material collection. The group III adatom diffusion from the NW sidewalls to the top sustains a superlinear growth regime. In this work, we report on the growth of different GaAs nanostructures by selective area MOVPE on GaAs (111)B substrates. We show that the opening dimensions and geometry qualitatively alter the morphology and height evolution of the structures. We compare the time evolution of vertical GaAs NWs stemming from circular holes and horizontal GaAs nanomembranes (NMs) growing from one-dimensional (1D) rectangular slits on the same substrate. While NW heights grow exponentially with time, NMs surprisingly exhibit sublinear kinetics. The absence of visible atomic steps on the top facets of both NWs and NMs suggests layer-by-layer growth in the mononuclear mode. We interpret these observations within a self-consistent growth model, which links the diffusion flux of Ga adatoms to the position- and shape-dependent nucleation rate on top of NWs and NMs. Specifically, the island nucleation rate is lower on top of the NMs than that on the NWs, resulting in the total diffusion flux being directed from the top facet to the sidewalls. This gives a sublinear height evolution for the NMs. These results open innovative perspectives for shape engineering of III-V nanostructures and new avenues for the design of optoelectronics and photonic devices.

Significant inter-annual fluctuation in CO2 and CH4 diffusive fluxes from subtropical aquaculture ponds: Implications for climate change and carbon emission evaluations

Aquaculture ponds are potential hotspots for carbon cycling and emission of greenhouse gases (GHGs) like CO2 and CH4, but they are often poorly assessed in the global GHG budget. This study determined the temporal variations of CO2 and CH4 concentrations and diffusive fluxes and their environmental drivers in coastal aquaculture ponds in southeastern China over a five-year period (2017–2021). The findings indicated that CH4 flux from aquaculture ponds fluctuated markedly year-to-year, and CO2 flux varied between positive and negative between years. The coefficient of inter-annual variation of CO2 and CH4 diffusive fluxes was 168% and 127%, respectively, highlighting the importance of long-term observations to improve GHG assessment from aquaculture ponds. In addition to chlorophyll-a and dissolved oxygen as the common environmental drivers, CO2 was further regulated by total dissolved phosphorus and CH4 by dissolved organic carbon. Feed conversion ratio correlated positively with both CO2 and CH4 concentrations and fluxes, showing that unconsumed feeds fueled microbial GHG production. A linear regression based on binned (averaged) monthly CO2 diffusive flux data, calculated from CO2 concentrations, can be used to estimate CH4 diffusive flux with a fair degree of confidence (r2 = 0.66; p < 0.001). This algorithm provides a simple and practical way to assess the total carbon diffusive flux from aquaculture ponds. Overall, this study provides new insights into mitigating the carbon footprint of aquaculture production and assessing the impact of aquaculture ponds on the regional and global scales.

Flavor composition of neutrinos from choked gamma-ray bursts

The nature of the astrophysical sources responsible for producing the observed high energy neutrinos have yet to be unveiled. Choked gamma-ray bursts (CGRBs) are sources that have been proposed as being capable of generating the flux detected by IceCube, since no accompanying gamma-ray signal is expected from them, as required by observations. We focus on obtaining the neutrino flux and flavor composition corresponding to CGRBs under different assumptions for the target photon density and the magnetic field of the emission region. We consider the injection of both electrons and protons into the internal shocks of CGRBs, and using a steady-state transport equation, we account for all the relevant cooling processes. In particular, we include as a target for pγ interactions the usually adopted background of soft photons, which is a fraction of the thermalized emission originated at the shocked jet head. Additionally, we consider the synchrotron photons emitted by the electrons co-accelerated with the protons at the internal shocks in the jet. We also obtain the distribution of charged pions, kaons, and muons using the transport equation to account for the cooling effects due not only to synchrotron emission but also interactions with the soft photons in the ambient. We integrate the total diffuse flux of neutrinos of different flavors and compute the flavor ratios to be observed on Earth. As a consequence of the losses suffered mainly by pions and muons, we find these ratios to be dependent on the energy: for energies above ∼(105 − 106) GeV (depending on the magnetic field, proton-to-electron ratio, and jet power), we find that the electron flavor ratio decreases and the muon flavor ratio increases, while the tau flavor ratio increases only moderately. Our results are sensitive to the mentioned key physical parameters of the emitting region of CGRBs. Hence, the obtained flavor ratios are to be contrasted with cumulative data from ongoing and future neutrino instruments in order to assess the contribution of these sources to the diffuse flux of astrophysical neutrinos.

Searches for Neutrinos from Gamma-Ray Bursts Using the IceCube Neutrino Observatory

Gamma-ray bursts (GRBs) are considered as promising sources of ultra-high-energy cosmic rays (UHECRs) due to their large power output. Observing a neutrino flux from GRBs would offer evidence that GRBs are hadronic accelerators of UHECRs. Previous IceCube analyses, which primarily focused on neutrinos arriving in temporal coincidence with the prompt gamma-rays, found no significant neutrino excess. The four analyses presented in this paper extend the region of interest to 14 days before and after the prompt phase, including generic extended time windows and targeted precursor searches. GRBs were selected between 2011 May and 2018 October to align with the data set of candidate muon-neutrino events observed by IceCube. No evidence of correlation between neutrino events and GRBs was found in these analyses. Limits are set to constrain the contribution of the cosmic GRB population to the diffuse astrophysical neutrino flux observed by IceCube. Prompt neutrino emission from GRBs is limited to ≲1% of the observed diffuse neutrino flux, and emission on timescales up to 104 s is constrained to 24% of the total diffuse flux.

Precipitation phase diffusion kinetics of AZ61 alloy under electrical pulse treatment

In this work, electrical pulse treatment and isothermal heat treatment are employed to tailor the microstructure of the hot-rolled AZ61 alloy. The influence of pulsed current on the crystal growth mechanism and precipitation phase diffusion was investigated. According to the findings, electrical pulses enhance the recrystallization and dissolution of Mg17Al12 precipitate in hot-rolled AZ61 alloy. The recrystallization fraction of EPTed samples is higher than that of the isothermal HTed counterparts. The amount of Mg17Al12 phase is considerably reduced with the increased EPT duration. In contrast, the Mg17Al12 phase fraction in isothermal HTed samples is just slightly changed. The Nernst–Einstein formula indicates that the electrical pulse effectively improves the total diffusion flux in the diffusion system via the coupling of athermal effect and thermal effect.

Total diffuse CO2 flux from Yellowstone caldera incorporating high CO2 emissions from cold degassing sites

Previous calculations of total diffuse carbon dioxide (CO2) emissions from Yellowstone National Park have been based on flux measurements from thermally active, altered basins. However, our recent measurements show that thermally inactive, cold degassing sites can emit more diffuse CO2 per km2 than thermally active basins. The contribution of these cold degassing sites must be included in calculations of total diffuse CO2 flux for adequate quantification of Yellowstone's role as a major contributor within the global CO2 budget.We acquired 1342 diffuse CO2 flux point measurements across 19 different sites in Yellowstone National Park during summer 2018 and 2019. Eleven of the measured sites are thermally active with heat flux elevated above background, four sites are vegetation sites, and four sites are thermally inactive, cold degassing sites outside the caldera. Our measurements of diffuse CO2 flux agree with previous findings that the highest average flux occurs in acid sulfate soils (706 ± 79 gm−2 day−1, average for both thermally active and cold degassing sites) with lower diffuse CO2 flux in travertine (189 ± 98 gm−2 day−1) and neutral-chloride (19 ± 8 gm−2 day−1) soils. All cold degassing sites measured were in acid sulfate dominated soil chemistries. The average diffuse CO2 flux for these cold degassing sites was higher (840 ± 163 gm−2 day−1) than the average flux through acid sulfate soils in thermally active basins (625 ± 79 gm−2 day−1). We also measured the carbon isotope composition of diffuse CO2 soil gas samples from most sites to characterize the potential source(s) of these emissions. The majority of carbon isotope values from cold degassing sites are within the typical range of values for Yellowstone fumaroles. This suggests that cold degassing sites have a similar magmatic source for diffuse CO2.Previous calculations of the total daily diffuse CO2 emitted through Yellowstone National Park use the arithmetic average flux per soil chemistry and extrapolate that value across the entire park using only thermally active altered soils. Instead, we calculate the total CO2 flux per site in tons CO2 per km2 per day using Gaussian Geostatistical Simulations through the Geostatistical Analyst toolbox in ArcGIS. To account for the large component of cold degassing CO2, we extrapolate the average emission rate per soil chemistry to all hydrothermally altered soils rather than only thermally active soils across the entire area of Yellowstone National Park. We calculate a total deeply sourced (biogenic flux removed) CO2 flux of 24 ± 12 kt CO2 per day, with nearly two-thirds of that flux estimated to be from cold degassing acid sulfate soils. Cold diffuse degassing sites can be significant sources of magmatic carbon emissions and this has implications for the relationship between the flux of CO2 and heat as well as for global contributions from mantle CO2 emissions.

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

We present a theory for the self-propulsion of symmetric, half-spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air–water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion–advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient along the air–water–swimmer contact line and Marangoni flow forces. We unravel whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occur for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.Graphic abstract

Modeling of pore formation in phase inversion processes: analysis of pore formation mechanism

The phase inversion process is the most important preparation process of porous polymer membranes. Recently, a numerical model based on first principles to predict pore structures has been proposed (Hopp-Hirschler and Nieken in J Membr Sci 564:820–831, 2018). This model enables a detailed investigation of the mechanism of pore formation in porous polymer membranes. This follow-up presents investigations of the mechanism of nucleation of pores during the phase inversion process in 1D. Pores originate due to accumulation of over-saturated mixtures inside a diffuse interface between homogeneous and demixed polymer solutions behind the precipitation front. This is caused by an expansion of the width of the diffuse interface and time-dependent concentration profiles which finally lead to a change of sign of total diffusive mass flux inside of the diffuse interface. As a result, oscillating compositions behind the precipitation front lead to formation of pores. It is concluded that large surface tension leads to initially small pore sizes. In the second part, a detailed discussion of directional diffusion behind the precipitation front is presented in 2D, which is responsible for different pore structures, e.g., finger or sponge pores. Depending on the dominant direction of diffusion finger pores, lamella structures or sponge pores are formed. This picture can straightforwardly be extended to 3D structures.

Reversible reactions controlled by surface diffusion on a sphere.

We study diffusion of particles on the surface of a sphere toward a partially reactive circular target with partly reversible binding kinetics. We solve the coupled diffusion-reaction equations and obtain the exact expressions for the time-dependent concentration of particles and the total diffusive flux. Explicit asymptotic formulas are derived in the small target limit. This study reveals the strong effects of reversible binding kinetics onto diffusion-mediated reactions that may be relevant for many biochemical reactions on cell membranes.

Extraction of Material from a Porous Body into a Moving Liquid

In this paper, we study the nonstationary process of extracting material from a porous body simulated by a system of semi-infinite capillaries into a moving liquid in which the transfer rate of the material in the flow is a linear function of the cross-flow coordinate. The case where the liquid velocity at the interface becomes zero is considered. It is assumed that the diffusion in the flow is quasi-stationary. Analytical dependences at the interface between the porous material and the flow region are found for mass transfer characteristics of practical interest (concentration, diffusion flow, total diffusion flux, and the total yield of the target component extracted through the cross section of the porous body).

Methane dynamics in a large river: a case study of the Elbe River

We conducted multiple small (2011–2012) and one large sampling campaign (2013) at selected profiles along the Elbe River. With the data we were able to outline spatial and temporal variability of methane concentration, oxidation and emissions in one of the major rivers of Central Europe. The highest methane concentrations were found in human-altered riverine habitats, i.e., in a harbor (1,888 nmol L−1), in a lock and weirs (1409 ± 1545 nmol L−1), and in general in the whole “impounded” river segment (383 ± 215 nmol L−1). On the other hand, the lowest methane concentrations were found in the “lowland” river segment (86 ± 56 nmol L−1). The methane oxidation rate was more efficient in the “natural” segment (71 ± 113 nmol L−1day−1, which means a turnover time of 49 ± 83 day−1) than in the “lowland” segment (4 ± 3 nmol L−1day−1, which means a turnover time of 39 ± 45 day−1). Methane emissions from the surface water into the atmosphere ranged from 0.4 to 11.9 mg m−2 day−1 (mean 2.1 ± 0.6 mg m−2 day−1) with the highest CH4 emissions at the Meissen harbor (94 kg CH4 year−1). Such human-altered riverine habitats (i.e., harbors and similar) have not been taken into consideration in the CH4 budget before, despite them being part of the river ecosystems, they may be significant CH4 hot-spots. The total CH4 diffusive flux from the whole Elbe was estimated to be approximately 97 t CH4 year−1.

Transportation and Transformation of Arsenic Species at the Intertidal Sediment-Water Interface of Bohai Bay, China

Arsenic species including arsenite As(III), arsenate As(V), monomethylarsenate (MMA), dimethylarsenate (DMA), and some diagenetic constituents (Fe, Mn, and S2−) in porewaters along with the unstable arsenic species in sediments collected from a typical intertidal zone of Bohai Bay in China were measured. Their vertical distributions were subsequently obtained to reveal the transportation and transformation characteristics of arsenic at the intertidal sediment-water interface (SWI). Results show that the reduction of As(V) by microorganisms occurred in sediments, but the methylation of arsenic by microorganisms was weak in the intertidal zone. The distribution of As(V) was mainly controlled by Mn, whereas As(III) appeared to be more likely controlled by Fe. Arsenic in sediments mainly existed in a stable state, so that only little arsenic could be released from sediments when the environmental conditions at the SWI are changed. As(III) diffused from porewaters to the overlying water while the opposite was true for As(V) at that time when the samples were collected. The total diffusion direction for arsenic across the SWI was from porewaters to the overlying water with a total diffusive flux estimated at 1.23 mg·m−2·a−1.

Characterising the VHE diffuse emission in the central 200 parsecs of our Galaxy with H.E.S.S.

The diffuse very high-energy (VHE; &gt;100 GeV) γ-ray emission observed in the central 200 pc of the Milky Way by H.E.S.S. was found to follow dense matter distribution in the central molecular zone (CMZ) up to a longitudinal distance of about 130 pc to the Galactic centre (GC), where the flux rapidly decreases. This was initially interpreted as the result of a burst-like injection of energetic particles 104 yr ago, but a recent more sensitive H.E.S.S. analysis revealed that the cosmic-ray (CR) density profile drops with the distance to the centre, making data compatible with a steady cosmic PeVatron at the GC. In this paper, we extend this analysis to obtain, for the first time, a detailed characterisation of the correlation with matter and to search for additional features and individual γ-ray sources in the inner 200 pc. Taking advantage of 250 h of H.E.S.S. data and improved analysis techniques, we perform a detailed morphology study of the diffuse VHE emission observed from the GC ridge and reconstruct its total spectrum. To test the various contributions to the total γ-ray emission, we used an iterative 2D maximum-likelihood approach that allows us to build a phenomenological model of the emission by summing a number of different spatial components. We show that the emission correlated with dense matter covers the full CMZ and that its flux is about half the total diffuse emission flux. We also detect some emission at higher latitude that is likely produced by hadronic collisions of CRs in less dense regions of the GC interstellar medium. We detect an additional emission component centred on the GC and extending over about 15 pc that is consistent with the existence of a strong CR density gradient and confirms the presence of a CR accelerator at the very centre of our Galaxy. We show that the spectrum of full ridge diffuse emission is compatible with that previously derived from the central regions, suggesting that a single population of particles fills the entire CMZ. Finally, we report the discovery of a VHE γ-ray source near the GC radio arc and argue that it is produced by the pulsar wind nebula candidate G0.13−0.11.

Chaoborus spp. Transport CH4 from the Sediments to the Surface Waters of a Eutrophic Reservoir, But Their Contribution to Water Column CH4 Concentrations and Diffusive Efflux Is Minor.

Chaoborus spp. (midge larvae) live in the anoxic sediments and hypolimnia of freshwater lakes and reservoirs during the day and migrate to the surface waters at night to feed on plankton. It has recently been proposed that Chaoborus take up methane (CH4) from the sediments in their tracheal gas sacs, use this acquired buoyancy to ascend into the surface waters, and then release the CH4, thereby serving as a CH4 "pump" to the atmosphere. We tested this hypothesis using diel surveys and seasonal monitoring, as well as incubations of Chaoborus to measure CH4 transport in their gas sacs at different depths and times in a eutrophic reservoir. We found that Chaoborus transported CH4 from the hypolimnion to the lower epilimnion at dusk, but the overall rate of CH4 transport was minor, and incubations revealed substantial variability in CH4 transport over space and time. We calculated that Chaoborus transport ∼0.1 mmol CH4 m-2 yr-1 to the epilimnion in our study reservoir, a very low proportion (<1%) of total CH4 diffusive flux during the summer stratified period. Our data further indicate that CH4 transport by Chaoborus is sensitive to water column mixing, Chaoborus density, and Chaoborus species identity.

Total Exchange Flow, Entrainment, and Diffusive Salt Flux in Estuaries

AbstractThe linkage among total exchange flow, entrainment, and diffusive salt flux in estuaries is derived analytically using salinity coordinates, revealing the simple but important relationship between total exchange flow and mixing. Mixing is defined and quantified in this paper as the dissipation of salinity variance. The method uses the conservation of volume and salt to quantify and distinguish the diahaline transport of volume (i.e., entrainment) and diahaline diffusive salt flux. A numerical model of the Hudson estuary is used as an example of the application of the method in a realistic estuary with a persistent but temporally variable exchange flow. A notable finding of this analysis is that the total exchange flow and diahaline salt flux are out of phase with respect to the spring–neap cycle. Total exchange flow reaches its maximum near minimum neap tide, but diahaline salt transport reaches its maximum during the maximum spring tide. This phase shift explains the strong temporal variation of stratification and estuarine salt content through the spring–neap cycle. In addition to quantifying temporal variation, the method reveals the spatial variation of total exchange flow, entrainment, and diffusive salt flux through the estuary. For instance, the analysis of the Hudson estuary indicates that diffusive salt flux is intensified in the wider cross sections. The method also provides a simple means of quantifying numerical mixing in ocean models because it provides an estimate of the total dissipation of salinity variance, which is the sum of mixing due to the turbulence closure and numerical mixing.

Prediction of the diffuse neutrino flux from cosmic ray interactions near supernova remnants

In this paper, we present high-energy neutrino spectra from 21 Galactic supernova remnants (SNRs), derived from gamma-ray measurements in the GeV–TeV range. We find that only the strongest sources, i.e. G40.5-0.5 in the north and Vela Junior in the south could be detected as single point sources by IceCube or KM3NeT, respectively. For the first time, it is also possible to derive a diffuse signal by applying the observed correlation between gamma-ray emission and radio signal. Radio data from 234 supernova remnants listed in Green’s catalog are used to show that the total diffuse neutrino flux is approximately a factor of 2.5 higher compared to the sources that are resolved so far. We show that the signal at above 10TeV energies can actually become comparable to the diffuse neutrino flux component from interactions in the interstellar medium. Recently, the IceCube collaboration announced the detection of a first diffuse signal of astrophysical high-energy neutrinos. Directional information cannot unambiguously reveal the nature of the sources at this point due to low statistics. A number of events come from close to the Galactic center and one of the main questions is whether at least a part of the signal can be of Galactic nature. In this paper, we show that the diffuse flux from well-resolved SNRs is at least a factor of 20 below the observed flux.

Thermodynamic evaluation of mass diffusion in ionic mixtures

The thermodynamic technique of Landau and Lifshitz originally developed for inter-species diffusion in a binary neutral gas mixture is extended to a quasi-neutral plasma with two ion species. It is shown that, while baro- and electro-diffusion coefficients depend on the choice of the thermodynamic system, prediction for the total diffusive mass flux is invariant.

Interstitial diffusion in systems with multiple sorts of traps

The role of several sorts of traps for one diffusing interstitial component is investigated. The site fraction of this component in each trap is calculated due to the local thermodynamic equilibrium condition with its site fraction in the lattice. Combining Fick's first law for diffusive fluxes of individual site fractions with the equilibrium condition and the mass balance allows deriving an extended nonlinear diffusion equation. If the molar volumes of the trap positions are constant with respect to time, then a generalized chemical diffusion coefficient can be derived, which allows performing the diffusion study in terms of the total concentration of the interstitial component. As an alternative way, the total diffusion flux can also be treated as the sum of diffusion fluxes of individual fractions combined with local redistribution of individual fractions based on the thermodynamic local equilibrium condition. Both concepts are presented in simulations for the diffusion of hydrogen in the system with traps as immobile dislocations, substitutional impurities and interfaces of incoherent carbide nanoprecipitates. Both concepts provide equivalent results and exhibit an asymmetric behaviour with respect to a charging/discharging process.

Equivalent diffusion coefficient of clay-rich geological formations: comparison between numerical and analytical estimates

Laboratory experiments in rock samples collected from clay-rich formations indicate that the effective molecular diffusion coefficient (D) is a heterogeneous and anisotropic property. Since laboratory measurements of D are representative of a very small volume, upscaling is necessary in order to incorporate these data in large-scale numerical models of diffusive transport. In this work we address the problem of the estimating the equivalent diffusion coefficient (D eq ), in terms of total diffusive flux, in a three-dimensional domain characterized by a heterogeneous and anisotropic spatial distribution of D. D eq was estimated from the results of steady-state diffusive transport simulations through several realizations of the D field. The ensemble averages of D eq from fields with different degrees of heterogeneity and anisotropy were then compared with estimates from analytical upscaling expressions based on stochastic as well as power-averaging approaches. These expressions are largely based on similar expressions developed for calculating the effective hydraulic conductivity in heterogeneous and anisotropic domains. Comparisons showed that stochastic expressions provide accurate estimates of D eq only for fields characterized by low heterogeneity. Within the range of heterogeneity and anisotropy considered, our results showed that a power-averaging expression is very accurate in predicting D eq especially when the parameter p i is estimated through fitting of the numerical results. Nonetheless, the relationship between this parameter and the anisotropy ratio is linear.