Diffusive Flux Research Articles

Methane dynamics altered by reservoir operations in a typical tributary of the Three Gorges Reservoir

Substantial nutrient inputs from reservoir impoundment typically increase sedimentation rate and primary production. This can greatly enhance methane (CH4) production, making reservoirs potentially significant sources of atmospheric CH4. Consequently, elucidating CH4 emissions from reservoirs is crucial for assessing their role in the global methane budget. Reservoir operations can also influence hydrodynamic and biogeochemical processes, potentially leading to pronounced spatiotemporal heterogeneity, especially in reservoirs with complex tributaries, such as the Three Gorges Reservoir (TGR). Although several studies have investigated the spatial and temporal variations in CH4 emissions in the TGR and its tributaries, considerable uncertainties remain regarding the impact of reservoir operations on CH4 dynamics. These uncertainties primarily arise from the limited spatial and temporal resolutions of previous measurements and the complex underlying mechanisms of CH4 dynamics in reservoirs. In this study, we employed a fast-response automated gas equilibrator to measure the spatial distribution and seasonal variations of dissolved CH4 concentrations in XXB, a representative area significantly impacted by TGR operations and known for severe algal blooms. Additionally, we measured CH4 production rates in sediments and diffusive CH4 flux in the surface water. Our multiple campaigns suggest substantial spatial and temporal variability in CH4 concentrations across XXB. Specifically, dissolved CH4 concentrations were generally higher upstream than downstream and exhibited a vertical stratification, with greater concentrations in bottom water compared to surface water. The peak dissolved CH4 concentration was observed in May during the drained period. Our results suggest that the interplay between aquatic organic matter, which promotes CH4 production, and the dilution process caused by intrusion flows from the mainstream primarily drives this spatiotemporal variability. Importantly, our study indicates the feasibility of using strategic reservoir operations to regulate these factors and mitigate CH4 emissions. This eco-environmental approach could also be a pivotal management strategy to reduce greenhouse gas emissions from other reservoirs.

The cell-centered positivity-preserving finite volume scheme for 3D convection–diffusion equation on distorted meshes

PurposeThis paper aims to construct positivity-preserving finite volume schemes for the three-dimensional convection–diffusion equation that are applicable to arbitrary polyhedral grids.Design/methodology/approachThe cell vertices are used to define the auxiliary unknowns, and the primary unknowns are defined at cell centers. The diffusion flux is discretized by the classical nonlinear two-point flux approximation. To ensure the fully discrete scheme has positivity-preserving property, an improved discretization method for the convection flux was presented. Besides, a new positivity-preserving vertex interpolation method is derived from the linear reconstruction in the discretization of convection flux. Moreover, the Picard iteration method may have slow convergence in solving the nonlinear system. Thus, the Anderson acceleration of Picard iteration method is used to solve the nonlinear system. A condition number monitor of matrix is employed in the Anderson acceleration method to achieve better robustness.FindingsThe new scheme is applicable to arbitrary polyhedral grids and has a second-order accuracy. The results of numerical experiments also confirm the positivity-preserving of the discretization scheme.Originality/value1. This article presents a new positivity-preserving finite volume scheme for the 3D convection–diffusion equation. 2. The new discretization scheme of convection flux is constructed. 3. A new second-order interpolation algorithm is given to eliminate the auxiliary unknowns in flux expressions. 4. An improved Anderson acceleration method is applied to accelerate the convergence of Picard iterations. 5. This scheme can solve the convection–diffusion equation on the distorted meshes with second-order accuracy.

Multi-component forms of the 2nd generation H1 receptor antagonist drug, Bilastine and its enhanced physicochemical characteristics

Bilastine (BIL) is a novel 2nd generation antihistamine medication is used to treat symptoms of chronic urticaria and allergic rhinitis. However, its poor solubility limits its therapeutic efficacy. In order to enhance the physicochemical characteristics of BIL, various molecular adducts of BIL (Salt, hydrate and co-crystal) were discovered in this study using two distinct salt-formers: Terephthalic acid (TA), 2,4-Dihydroxybenzoic acid (2,4-DHBA), and three nutraceuticals (Vanillic Acid (VA), Hydroquinone (HQN) and Hippuric acid (HA)). Various analytical methods were used to examine the synthesised adducts, including Powder X-Ray Diffraction (PXRD), Single Crystal X-ray Diffraction (SCXRD), and thermal analysis (Thermogravimetric analysis (TGA) and Differential Scanning Calorimetry (DSC)). Single-crystal X-ray diffraction (SCXRD) studies avowed that the architectures of the molecular adducts are maintained in the solid state by an array of strong (N+H⋯O−, NH⋯O, OH⋯O) and weak (CH⋯O) hydrogen bonds. Additionally, a solubility test was performed to establish the in vitro release characteristics of newly synthesised BIL adducts and it observed that most of the molecular adducts exhibit higher rates of dissolution in comparison to pure BIL; in particular, BIL.TA.HYD showed the highest solubility and the fastest rate of dissolution. Moreover, experiments on flux permeability and diffusion demonstrated that the BIL.TA.HYD and BIL.VA salts had strong permeability and a high diffusion rate. In addition, the synthesized adduct’s stability was assessed at 25 °C and 90 % ± 5 % relative humidity, and it was found that all the molecular salts were stable and did not undergo any phase changes or dissociation. The foregoing result leads us to believe that the newly synthesized molecular adducts’ increased permeability and solubility will be advantageous for the creation of novel BIL formulations.

Front stability of infinitely steep travelling waves in population biology

Reaction–diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many reaction–diffusion models of biological invasion are extensions of the well–known Fisher–Kolmogorov–Petrovskii–Piskunov model that describes the spatiotemporal evolution of a 1D population density, u(x,t) , as a result of linear diffusion with flux J=−∂u/∂x , and logistic growth source term, S=u(1−u) . In 2020 Fadai introduced a new reaction–diffusion model of biological invasion with a nonlinear degenerate diffusive flux, J=−u∂u/∂x , and the model was formulated as a moving boundary problem on 0<x<L(t) , with u(L(t),t)=0 and dL(t)/dt=−κu∂u/∂x at x=L(t) (Fadai and Simpson 2020 J. Phys. A: Math. Theor. 53 095601). Fadai’s model leads to travelling wave solutions with infinitely steep, well–defined fronts at the moving boundary, and the model has the mathematical advantage of being analytically tractable in certain parameter limits. In this work we consider the stability of the travelling wave solutions presented by Fadai. We provide general insight by first presenting two key extensions of Fadai’s model by considering: (i) generalised nonlinear degenerate diffusion with flux J=−um∂u/∂x for some constant m > 0; and, (ii) solutions describing both biological invasion with dL(t)/dt>0 , and biological recession with dL(t)/dt<0 . After establishing the existence of travelling wave solutions for these two extensions, our main contribution is to consider stability of the travelling wave solutions by introducing a lateral perturbation of the travelling wavefront. Full 2D time–dependent level–set numerical solutions indicate that invasive travelling waves are stable to small amplitude lateral perturbations, whereas receding travelling waves are unstable. These preliminary numerical observations are corroborated through a linear stability analysis that gives more formal insight into short time growth/decay of wavefront perturbation amplitude. Julia–based software, including level–set algorithms, is available on Github to replicate all results in this study.

Solute transport in unsaturated porous media with spatially correlated disorder

Solute transport in unsaturated porous media is of interest in many engineering and environmental applications. The interplay between small-scale, local forces and the porous microstructure exerts a strong control on the transport of fluids and solutes at the larger, macroscopic scales. Heterogeneity in pore geometry is intrinsic to natural materials across a large range of scales. This multiscale nature, and the intricate links between two-phase flow and solute transport, remain far from well understood, by and large. Here, we use high-resolution direct simulation to quantify solute mixing and dispersion behavior within correlated porous media during drainage under an unfavorable viscosity ratio. Through analysis of flow and transport at multiple realizations, we find that increasing spatial correlations in pore sizes increase the size of the required Representative Elementary Volume (REV). We show that increasing the correlation length enhances solute dispersivity through its impact on the spatial distribution of low-velocity (diffusion-dominated) and high-velocity (advection-dominated) regions. Fluid saturation is shown to directly affect diffusive mass flux among high- and low-velocity zones. Another indirect effect of correlated heterogeneity on solute transport is through its control of the drainage patterns via repeated alteration in the connectivity of flowing pathways. Our findings improve quantitative understanding of solute mixing and dispersion under two-phase conditions, highly relevant to some of our most urgent environmental problems.

Computational fluid dynamic model for the prediction of the unsteady operation process of a non-dispersive gold extraction from wastewater

The current study tries to investigate gold extraction in a membrane extractor in unsteady mode. The model was successfully validated using experimental results. The results showed that the diffusive flux on the zone close to the membrane surface is dominant in the first minutes of extraction but later the convective flux is the main flux, particularly at the centre of the shell side. The extraction time of one hour was not ample to extract all gold from the aqueous solution when the volume of solutions was 2000 mL and 3000 mL. Finally, the change in feed flow rate in the range of 30–55 cm3/min did not have a significant influence on the gold extraction time. However, the outlet dimensionless concentration of gold after one hour was increased from 0.24 to 44 with the increase of feed flow rate from 30 cm3/min to 55 cm3/min.

A new approach to explaining nano-bubbles paradoxical longevity

It has been established experimentally that nano-bubbles exist in water for weeks, even months. This contradicts the theory that predicts life span for such small bubbles being on the scale of milliseconds. Nano-bubbles are charged due to adsorption of OH- ions, which creates electric double layers (EDL) at their interfaces. Suggestion has been made that EDL could be responsible for nano-bubbles longevity, but the mechanism remains unknown. We propose such a mechanism here. There is one overlooked feature of the EDL – water molecules in the first layer at interface are oriented, which is supported by many experiments and theory overviewed here. EDL electric field has a gradient component, which exerts force on these oriented molecules dipole moments. We show that it is practically equal to the Young-Laplace force but opposite in direction. It ensures balance of normal forces at interface and creates a pressure gradient that prevents leakage diffusion flux from the stable bubble. In addition, oriented water dipole moments repel each other. This effect is similar to the repulsion of surfactant polar groups, which are known to counterbalance surface tension in tangential direction and stabilize bubbles. Oriented water molecules should cause the same effect. Balance of forces acting on the bubble interface leads to the equation for the stable bubble size that agrees with experimental trends.

Breakthrough-induced loop formation in evolving transport networks

Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They usually contain loops whose significance for the stability and robustness of the network is well documented. However, the dynamics of their formation is usually not considered. Such structures often grow in response to the gradient of an external field. During evolution, extending branches compete for the available flux of the field, which leads to effective repulsion between them and screening of the shorter ones. Yet, in remarkably diverse processes, from unstable fluid flows to the canal system of jellyfish, loops suddenly form near the breakthrough when the longest branch reaches the boundary of the system. We provide a physical explanation for this universal behavior. Using a 1D model, we explain that the appearance of effective attractive forces results from the field drop inside the leading finger as it approaches the outlet. Furthermore, we numerically study the interactions between two fingers, including screening in the system and its disappearance near the breakthrough. Finally, we perform simulations of the temporal evolution of the fingers to show how revival and attraction to the longest finger leads to dynamic loop formation. We compare the simulations to the experiments and find that the dynamics of the shorter finger are well reproduced. Our results demonstrate that reconnection is a prevalent phenomenon in systems driven by diffusive fluxes, occurring both when the ratio of the mobility inside the growing structure to the mobility outside is low and near the breakthrough.

Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids

The prototypical diffuse-interface model for incompressible fluid mixtures is the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model. Despite its foundation in continuum mixture theory, it is not fully compatible with this theory due to the diffusive flux approximation. This paper introduces a class of thermodynamically consistent diffuse-interface incompressible fluid mixture models that is fully compatible with the continuum theory of mixtures. The proposed models can be formulated in either constituent or mixture quantities, enabling a direct comparison with the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model with non-matching densities. This comparison reveals the key modelling simplifications employed in the latter.

Dissolution of Oxide Particles in Multi-component Slags Governed by Diffusive and Convective Fluxes

Dissolution of Oxide Particles in Multi-component Slags Governed by Diffusive and Convective Fluxes

Study of salt free-diffusion by 1D transport numerical simulations and shadowgraph experiments

Applying the Nernst-Planck formalism of 1D diffusive flux equations for ionic species of salts dissolved in water, Pitzer formalism for activity coefficients and PHREEQC software for species diffusion coefficients, with ionic strength-dependence coefficients optimized, we obtained expressions for apparent diffusion coefficients of sodium chloride, calcium chloride, and sodium sulphate, prevalent in deep aquifers. PHREEQC 1D transport simulations of free-diffusion experiments yielded temporal evolution of the concentration and gradient vertical profiles. The dynamics of concentrations non-equilibrium fluctuations during the free-diffusion experiments have been recorded by shadowgraphy. Thanks to the calculated gradient profiles the thickness of the sample has been integrated in the analysis equations of the structure functions. From the earliest stages of the diffusion process we measured the diffusion coefficients for the three salts, in very good agreement with reference measurements, validating the technique and method of analysis for studying free-diffusion in reservoirs targeted for CO2 and energy vectors storage.

Characterization of the astrophysical diffuse neutrino flux using starting track events in IceCube

Characterization of the astrophysical diffuse neutrino flux using starting track events in IceCube

HTO and selenate diffusion through compacted Na-, Na–Ca-, and Ca-montmorillonite

Radionuclide transport in smectite clay barrier systems used for nuclear waste disposal is controlled by diffusion, with adsorption significantly retarding transport rates. While a relatively minor component of spent nuclear fuel, 79Se is a major driver of the safety case for spent fuel disposal due to its long half-life (3.3 × 105 yr) and its low adsorption to clay (KD < 10 L/kg), thus a thorough understanding of Se diffusion through clay is critical for understanding the long-term safety of spent fuel disposal systems. Through-diffusion experiments with tritiated water (HTO, conservative tracer) and Se(VI) were conducted with a well-characterized, purified montmorillonite source clay (SWy-2) under a constant ionic strength (0.1 M) and three different electrolyte compositions: Na+, Ca2+, and a Na + -Ca2+ mixture at pH 6.5 in order to probe the effects of electrolyte composition and interlayer cation composition on clay microstructure, Se(VI) aqueous speciation, and ultimately diffusion. The results were modeled using a reactive transport modeling approach to determine values of porosity (ε), De (effective diffusion coefficient), and KD (distribution coefficient for adsorption). HTO diffusive flux was higher in Ca-montmorillonite (De = 1.68 × 10−10 m2 s−1) compared to Na-montmorillonite (De = 7.83 × 10−11 m2 s−1). This increase in flux is likely due to a greater degree of clay layer stacking in the presence of Ca2+ compared to Na+, which leads to larger inter-particle pores. Overall, the Se(VI) flux was much lower than the HTO flux due to anion exclusion, with Se(VI) flux following the order Ca (De = 1.03 × 10−11 m2 s−1) > Na–Ca (De = 2.12 × 10−12 m2 s−1) > Na (De = 1.28 × 10−12 m2 s−1). These differences in Se(VI) flux are due to a combination of factors, including (1) larger accessible porosity in Ca-montmorillonite due to clay layer stacking and smaller electrostatic effects compared to Na-montmorillonite, (2) larger accessible porosity for neutral-charge CaSeO4 species which makes up 32% of aqueous Se(VI) in the pure Ca system, and (3) possibly higher Se(VI) adsorption for Ca-montmorillonite. Through a combination of experimental and modeling work, this study highlights the compounding effects that electrolyte and counterion compositions can have on radionuclide transport through clay. Diffusion models that neglect these effects are not transferable from laboratory experimental conditions to in situ repository conditions.

Internal heat source in the vadose zone: A comprehensive exploration through theoretical spectral analysis and practical application into thermal diffusivity and hydraulic flux in a Quaternary soil water layer

AbstractThis groundbreaking study introduces a scientifically robust method for assessing internal heat generation in shallow, unsaturated aquifers, highlighting the intricate interplay between internal heat, thermal diffusivity, and hydraulic flux. The research pioneers a novel approach employing time‐frequency spectral analysis to address challenges posed by conventional methods that rely solely on prescribed thermal diffusivity and hydraulic flux for evaluating internal heat over time. Rooted in a solid theoretical framework supported by meticulous temperature and heat flux observations, the method adeptly incorporates the concept of an unknown internal heat. The study systematically explores three distinct boundary conditions, showcasing versatility: one with fixed temperatures at the inlet and outlet, another with known temperature at the inlet and no heat flux at the outlet, and a third with a prescribed inlet temperature and constrained outlet heat flux. The estimation of internal heat, coupled with prescribed thermal diffusivity and hydraulic flux, harnesses in‐situ temperature and heat flux spectra through an innovative inverse stochastic spectral approach. A notable feature of this research lies in its ability to strategically handle various parameters, including prescribed thermal diffusivity, hydraulic flux, variations in target depth, significant frequency components, and boundary conditions. The variation assessment findings emphasize the diverse range when predicting internal heat generation based on prescribed thermal diffusivity and hydraulic flux. This study facilitates the determination of potential internal heat magnitudes at different depths and provides profound insights into in‐situ conditions within the vadose zone.

Neutrino Fluxes from Different Classes of Galactic Sources

We estimate the neutrino flux from different kinds of galactic sources and compare it with the recent diffuse neutrino flux detected by IceCube. We find that the flux from these sources may contribute to ∼20% of the IceCube neutrino flux. Most of the sources selected in this work populate the southern hemisphere, therefore a detector like KM3NeT could help in resolving the sources out of the observed diffused galactic neutrino flux.

Choked Precessing Jets in Tidal Disruption Events and High-energy Neutrinos

It has been suggested that relativistic jets might have been commonly formed in tidal disruption events (TDEs), but those with relatively weak power could be choked by the surrounding envelope. The discovery of high-energy neutrinos possibly associated with some normal TDEs may support this picture in the hypothesis that the neutrinos are produced by choked jets. Recently, it was noted that disrupted stars generally have misaligned orbits with respect to the supermassive black hole spin axis, and highly misaligned precessing jets are more likely to be choked. Here we revisit the jet breakout condition for misaligned precessing jets by considering that the jet could be collimated by the cocoon pressure while propagating in the disk wind envelope. The jet head opening angle decreases as the jet propagates in the envelope, but the minimum power of a successful jet remains unchanged in terms of the physical jet power. We further calculate the neutrino flux from choked precessing jets, assuming that the cocoon energy does not exceed the kinetic energy of the disk wind. We find that neutrino flux from highly misaligned choked jets is sufficient to explain the neutrinos from AT2019aalc, while it is marginal to explain the neutrinos from AT2019dsg and AT2019fdr. The latter could be produced by weakly misaligned choked jets, since the duty cycle that the jet sweeps across increases as the misaligned angle decreases. We also show that the population of choked TDE jets could contribute to ∼10% of the observed diffuse neutrino flux measured by IceCube.

Micro-scale experimental investigations of CO2-WAG injection and Ostwald ripening analysis in carbonate rocks with different pore structures

Carbonate reservoirs are rich in hydrocarbon resources. However, carbonate reservoirs usually have strong pore structure heterogeneity, and thus it is necessary to understand the effect of heterogeneity on pore-scale fluid distributions during CO2 enhanced oil recover (CO2-EOR) process. We thus conducted water-alternating-gas (CO2-WAG) injection in the three carbonate samples with strong to weak heterogeneity. The 15 sets of images showed that the fractured-vuggy carbonate with the strongest heterogeneity had the highest additional oil recovery. CO2-WAG injection significantly changed the residual oil distribution, and further oil production can be achieved by increasing the number of CO2-WAG cycles. For CO2 geological storage, with the increase of carbonate heterogeneity, CO2 capillary-trapping capacity decreased, CO2 dissolution trapping potentiality decreased, but the stability of CO2 capillary trapping enhanced. These key parameters related to CO2 storage were described through the saturation of trapped gas, the types of trapped gas, and the surface area-volume relationship of CO2 clusters. For example, the higher amount of network gas is detrimental to the stability of CO2 capillary trapping because the network gas is easily displaced when the hydrodynamic force is enhanced. The specific surface area of CO2 cluster determines dissolution dynamics, and a higher specific surface area is beneficial for CO2 dissolution. Another interesting phenomenon - Ostwald ripening, is related to long-term CO2 transport. The CO2 concentration gradient in aquifer generates a vertically upward diffusive flux, causing CO2 remobilization. By calculating the height of the transition zone and the time to reach gravity-capillary pressure equilibrium, we found that as carbonate heterogeneity increased, the height of transition zone (the area where CO2 is trapped by capillary pressure) increased, while equilibrium time shortened. By comparing the results of previous gas-water two-phase flow experiments, we believe that the relationship between CO2 storage characteristics and carbonate heterogeneity summarized in this paper are universally applicable.

A Mini Review on the Influence of Different Intermediate Mass Transfer Effects on the Chemical Pretreatment of Lignocellulosic Biomass

ABSTRACTChemical pretreatment of lignocellulosic biomass (LCB) in the presence of an alkaline catalyst is one of the major pretreatment processes that recover cellulose, hemicellulose, and lignin at effective process conditions and also for the production of bioethanol. Replacement of conventional catalysts with waste‐derived catalysts in the pretreatment process will be helpful for the development of low‐cost biorefinery. The continuous impact of different mass transfer properties during the chemical pretreatment of LCB will affect the final yield of products at a high reaction time and has been reviewed in the current study. Intraparticle diffusion of an alkaline catalyst into LCB is going to determine the diffusion of the selected catalyst within the porous biomass structure, which helps in the enhancement of the final yield of the product recovery at low‐process conditions. The diffusion of the synthesized catalyst within the selected biomass during the chemical pretreatment process is a rate‐limiting step that influences the final recovery yield of desired products. Enhancement of the biomass pretreatment reaction through the assessment of the diffusivity using the modified Nernst–Einstein relation is also discussed. Determination of different unique mass transfer properties rate of diffusion, diffusivity flux, and mass transfer coefficient are also to be analyzed to advance the reaction rate of the pretreatment process.

Karst cave, a seasonal carbon dioxide exchanger: an example of Sloup-Šošůvka Caves (Moravian Karst)

Part of the gaseous carbon dioxide (CO2) produced in karst soils / epikarst is transported into underground cavities / caves during the growing season by advective flux, diffusive flux, and flux associated with degassing of seeping water. In dynamic caves, accumulated CO2 is released into the outside atmosphere during the autumn-winter period through advective flux associated with ventilation of the cave in the upward airflow mode. This case study from the Moravian Karst (MK) showed that the net weight of CO2 released annually from the Sloup-Šošůvka Caves (total volume of 131,580 m3 and a total area of 17,950 m2) into the external atmosphere was 348 kg. Extrapolating this value to all known MK caves (area about 352,080 m2) yielded a total of CO2 flux of 6820 kg yr−1. This flux is representing only 0.024‰ of the annual soil respiration from entire MK area (about 2.81 × 108 kg CO2 yr−1).

Numerical study of electrode permeability influence on planar SOFC performance

A solid oxide fuel cell (SOFC) is a clean and very efficient electrochemical conversion device, which generates electricity directly from fuel electrochemical oxidation. In this paper, a three dimensional numerical model has been developed in order to analyse the role of some thermophysical and morphological parameters on the performance of the SOFC cell. In particular, we studied the effect of the variation of permeability of the electrodes: fuel distribution, ionic and electric current density, pressure and diffusion flux are analyzed and compared. The volume fraction of the ionic and electronic phase in the electrodes is studied using a parametric study. It was shown that the current density enhanced by decreasing the permeability, up to a defined value, and it diminished with very small permeability. A remarkable influence of pressure and diffusion of species on the performance of the cell, with the variation of permeability, has been recognized. Varying the permeability in the active layer of electrodes has a large impact on the current density, connected to the volume fraction of ionic phase. This study permits to comprehend the relationship between the performance and microstructure of SOFCs. Meanwhile, it furnishes theoretical guidance for an optimum design of the electrode permeability.