Effective Diffusion Research Articles

Critical exponent to a cancer invasion model with nonlinear diffusion

This paper is concerned with a cancer invasion model that incorporates porous medium diffusion (Δum) and extracellular matrix remodeling effects [ηω(1 − u − ω)] in a bounded domain of RN (N ≥ 2). Rich achievements have been achieved for the case η = 0 in the past ten years for the nonlinear diffusion case, but there is no any progress for η > 0. In this paper, we pay our attention to the global existence of solutions of the case η > 0, and establish the critical exponent m*=2N−2N of global solvability. More precisely, if m > m*, the solution will always exist globally, while if m < m*, there exist blow-up solutions. In this system, the remodeling effect of extracellular matrix [ηω(1 − u − ω)] bring some essential difficulties to the estimation of the haptotactic term, so the main technique we used is completely different from the case of η = 0.

Terrestrial Carbon Sink and Clean Air Co‐Benefits From China's Carbon Neutrality Policy

AbstractAs the world's largest carbon emitter, China has been confronting the dual challenge of climate change and air pollution. China's quest for reducing carbon emissions will promisingly benefit the air quality, yet its impact on carbon sinks remains unclear. Here, we assess the effect of China's clean air actions and carbon neutrality policy on air quality and its associated co‐benefits for terrestrial carbon sinks by integrating multiple observations and numerical modeling. We find a quadratic response of plant photosynthesis to aerosol loading due to trade‐offs between diffuse fertilization effect and light limitations. The estimations show that China's air pollution suppresses terrestrial carbon uptake through aerosol‐induced light limitations, leading to a 7.3% decrease in plant productivity in the 2010s. In the context of carbon neutrality pledge, the associated aerosol reductions tend to alleviate the suppression and produce an additional CO2 removal of 0.39 GtCO2 year−1. Our results uncover the enhanced terrestrial carbon sinks by aerosol mitigation, highlighting the synergy between carbon neutrality and clean air.

Evaluation and quantification of diffusion wear between cutting chip and workpiece using forging press

The state of the interface between the workpiece and the cutting tool affects the cutting temperature and pressure on the tool surface during the cutting process. In particular, while cutting difficult-to-cut materials such as Ni-based alloy 718, the workpiece exhibits a high affinity for cutting tool materials and could easily adhere to them. Adhesion can, at times, adversely affect productivity. The diffusion between the cutting tool and the workpiece is a factor considered to contribute to the adhesion phenomenon during cutting. Addressing this issue involves choosing tool materials and coated materials with high resistance to diffusion and optimizing cutting conditions, particularly the cutting speed, which significantly impacts cutting temperature. However, because cutting tool wear comprises various forms, clarifying the effect of diffusion on tool wear remains open. In this study, to reproduce the diffusion phenomenon between cutting tool and workpiece, two pairs of test specimens were prepared: (1) cemented carbide-AISI 1045 and (2) cemented carbide-Alloy718, which could be held at high temperature under vacuum conditions by a forging press. The degree of diffusion phenomena was evaluated at each tool-work material interface, and the quantification of diffusion amount was performed by diffused element in each work material. Additionally, the theoretical analysis of the diffusion phenomenon using the thermodynamic and phase diagram calculation software Thermo-Calc was also performed.

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.

Research on gas-liquid interface parameters related to thermal performance of frost-free evaporator of air source heat pump

Direct spray frost-free air source heat pumps (FFASHPs) base on liquid desiccant solutions are a more promising renewable energy technology for developing net-zero emission buildings. In order to improve the thermal performance of the frost-free evaporator, a numerical mode was established based on the penetration theory and the two-film theory to reveal the interfacial heat and mass transfer mechanism of LiCl solution falling film absorption on the air side of the frost-free evaporator. The distribution characteristics of temperature, water vapor concentration, effective diffusion coefficient, morphology, velocity and pressure at the interface under different air Reynolds numbers and temperatures were analyzed. The results show that the distribution uniformity of interface parameters has a greater effect on heat transfer performance than its average value. The critical Reynolds number is 391.0 under the present study, and the distribution uniformity of interface parameters and the intensity of interface fluctuation are improved, and the thermal performance reaches the peak. The COP of FFASHP system can be improved effectively when the frost-free evaporator is operated under the critical condition matching its parameters. The purpose of the study is to provide theoretical support for the performance improvement and efficient operation of frost-free evaporators.

Effects of different drying methods on drying characteristics and quality of silage Broussonetia papyrifera L.

The effects of hot air drying (HAD), vacuum drying (VD) and pulsed vacuum drying (PVD) on moisture ratio, drying rate, effective diffusion coefficient, activation energy, color, ash, protein, acid detergent fiber, neutral detergent, fiber total digestible nutrients (TDN) and relative feeding value (RFV) of silage paper mulberry were investigated, and optimal drying processes were developed using entropy weight method. Results show that the drying characteristics of silage paper mulberry, which can be seen as particle packed porous media, undergoing different drying methods exhibit similarities to those of conventional hygroscopic porous media. In terms of quality, noticeable browning occurs when the silage paper mulberry is subjected to HAD at 70 °C or higher, whereas no significant color change is observed under VD at temperatures of 80 °C or lower. Increasing the material thickness leads to higher TDN and RFV after HAD, but higher pressures and drying temperatures resulting in reducing in RFV after VD or PVD. The optimal drying process for HAD is 3 cm, 70 °C, 20%, 1 m/s and it is recommended to use 3 cm, 7 kPa and 70 °C for VD. As for PVD, the conditions are same as VD and using pulsation ratio of 50:5 min.

Microwave drying characteristics and kinetics of hematite pellets

Microwave drying characteristics and kinetics of hematite pellets were investigated based on evaluation of the effects of initial mass, microwave power and pellet size during the drying process. The results showed the average drying rate increased with initial mass from 50 g to 80 g and microwave power from 600 W to 1000 W. However, it decreased with increasing pellet size from 10–12 mm to 14–16 mm. The process was successively controlled by external diffusion, internal diffusion, and chemical reaction. The Verma model was the most suitable kinetic model for describing the process. The effective diffusion coefficient of moisture ranged from 6.61 × 10−7 m2/s to 9.98 × 10−7 m2/s. The activation energy for the microwave drying process was only 2.83 W/g.

The synergistic interaction of interstitial carbon/oxygen, alloying Cr/Ni and vacancy in dilute austenitic iron alloys

The synergistic interaction of interstitial carbon (C)/oxygen (O), alloying Cr/Ni and vacancy as well as diffusion property of C/O in dilute austenitic iron (Fe) alloys were investigated using a first-principles method and the empirical model. The interactions of C-Cr/C-Ni and C-C /C-O pairs are repulsive (−0.03/−0.15 eV and −0.90/−0.28 eV), while vacancy can attract C. Simple CrmCn clusters are less stable energetically, and the tetrahedral staggered Cr4C4 configuration is the most stable compared with other ones. Furthermore, the stability of small Cr-C-O/Cr-C-N complexes and the dissociation behavior of O from Cr7C7-nOn clusters with n=1–7 were determined. The synergistic interactions stabilize the clusters and O impurities, Cr-C-O complexes are more stable than Cr-C clusters. A vacancy-Cr/vacancy-Ni can trap two C atoms and form stable complex defects, in same with pure vacancy. Finally, the dissolution and effective diffusivity of C and O were predicted by empirical formulas. These findings provide a better understanding for interstitial C/O in austenitic Fe-Cr-Ni alloys.

Impact of bacterial outer membrane and general porins on cyanide diffusion and biodegradation kinetics

The present study focuses on the analysis of the diffusion process of various cyanide compounds through general porins and outer membranes of gram-negative bacteria. We demonstrate the impact of the compound-to-porin radius ratio, the charge of cyanide ion, the Donnan potential, the intrinsic porin potential, the number and length of general porins, the fraction of open channels, and the size of bacteria on the effective diffusion coefficients and permeability coefficients of cyanide compounds. Moreover, we report, for the first time, the procedure for comparison of the rate of cyanide diffusion across the outer membrane with the rate of cyanide biodegradation that allows establishing the conditions for which the biodegradation is a diffusion-limited process or the diffusion is a significantly faster process than biodegradation. We apply this procedure to several experimental studies and predict the range of extracellular cyanide concentrations for which diffusion is a significantly faster process than biodegradation. We also demonstrate how these results affect the theoretical view of the cyanide biodegradation kinetics.

MOF-derived Ni3Fe/Ni/NiFe2O4@C for enhanced hydrogen storage performance of MgH2

Magnesium hydride (MgH2) is an important material for hydrogen (H2) storage and transportation owing to its high capacity and reversibility. However, its intrinsic properties have considerably limited its industrial application. In this study, the NiFe-800 catalyst as metal-organic framework (MOF) derivative was first utilized to promote the intrinsic properties of MgH2. Compared to pure MgH2, which releases 1.24 wt% H2 in 60 min at 275 °C, the MgH2-10 NiFe-800 composite releases 5.85 wt% H2 in the same time. Even at a lower temperature of 250 °C, the MgH2-10 NiFe-800 composite releases 3.57 wt% H2, surpassing the performance of pure MgH2 at 275 °C. Correspondingly, while pure MgH2 absorbs 2.08 wt% H2 in 60 min at 125 °C, the MgH2-10 NiFe-800 composite absorbs 5.35 wt% H2 in just 1 min. Remarkably, the MgH2-10 NiFe-800 composite absorbs 2.27 wt% H2 in 60 min at 50 °C and 4.64 wt% H2 at 75 °C. This indicates that MgH2-10 NiFe-800 exhibits optimum performance with excellent kinetics at low temperatures. Furthermore, the capacity of the MgH2-10 NiFe-800 composite remains largely stable after 10 cycles. Moreover, the Mg2Ni/Mg2NiH4 acts as a “hydrogen pump”, providing effective diffusion channels that enhance the kinetic process of the composite during cycling. Additionally, Fe0 facilitates electron transfer and creates hydrogen diffusion channels and catalytic sites. Finally, carbon (C) effectively prevents particle agglomeration and maintains the cyclic stability of the composites. Consequently, the synergistic effects of Mg2Ni/Mg2NiH4, Fe0, and C considerably improve the kinetic properties and cycling stability of MgH2. This work offers an effective and valuable approach to improving the hydrogen storage efficiency in the commercial application of MgH2.

Experimental analysis and development of novel drying kinetics model for drying grapes in a double slope solar dryer

This experimental study aimed to evaluate the efficacy of natural and forced convective drying techniques in reducing the moisture content of the grapes in comparison with the conventional open sun drying method. Moisture effective diffusivity and activation energy were graphically determined using the Arrhenius equation. In the initial three-day period, forced convection drying significantly reduced moisture from 2000 g to 353 g, with a minimum loss of 14 g. In the next three days, natural convection reduced moisture from 2787 g to 468 g, with a minimum loss of 11 g. These outcomes were then compared to the results of open-sun drying. The investigation showed that open drying and natural convection methods eliminated 25.05 % and 82.35 % of the moisture content, respectively. However, for three days, open-sun drying removed 30.5 % of grape moisture, while forced convection achieved an impressive 83.21 % reduction. The study's innovative mathematical model explained drying curve characteristics, supported by correlation coefficients and parity plots. The comparison shows that the experimental moisture ratios and those predicted by the new correlation exhibit R2 values ranging from 0.984 to 0.994.

Tayler Instability Revisited

Tayler instability of toroidal magnetic fields B ϕ is broadly invoked as a trigger for turbulence and angular momentum transport in stars. This paper presents a systematic revision of the linear stability analysis for a rotating, magnetized, and stably stratified star. For plausible configurations of B ϕ , instability requires diffusive processes: viscosity, magnetic diffusivity, or thermal/compositional diffusion. Our results reveal a new physical picture, demonstrating how different diffusive effects independently trigger instability of two types of waves in the rotating star: magnetostrophic waves and inertial waves. It develops via overstability of the waves, whose growth rate sharply peaks at some characteristic wavenumbers. We determine instability conditions for each wave branch and find the characteristic wavenumbers. The results are qualitatively different for stars with magnetic Prandtl number Pm ≪ 1 (e.g., the Sun) and Pm ≫ 1 (e.g., protoneutron stars). The parameter dependence of unstable modes suggests a nonuniversal scaling of the possible Tayler–Spruit dynamo.

Effect of laser remelting on the microstructures and properties of NiCoCrAlY-based coatings prepared by high-speed air fuel supersonic flame (HVAF)

In order to improve the oxidation resistance of the coating, laser remelting technology was used to remelt the HVAF multi-component modified coating. The influence of laser remelting technology on the phase state, microstructure characteristics, and isothermal oxidation behavior of coatings was studied. The experimental results indicate that a coating with complete morphology and no defects was obtained on the surface. There is a significant amount of metallurgical bonding and partial mechanical interlocking between the remelted layer and the substrate. The remelted layer is mainly composed of β-NiAl phase, accompanied by a small amount of γ′ phase and oxide phase. The microhardness test results show that the average hardness of the remelted layer is 1.1–1.42 times that of the prepared coating, and the bonding strength has increased by 23 %. After 100 h of high-temperature oxidation, the oxidation rate of the 4N3T4H remelted layer is the lowest, at 1.5 × 10−15 cm2/s, which is one order of magnitude lower than that of the as-sprayed coating. This is because after laser remelting, the remelted layer has the inherent hysteresis diffusion effect of HEA, which can improve the high-temperature oxidation resistance of the remelted layer and basically eliminate many pores and cracks contained in the HVAF coating. The coating density is significantly increased, which is conducive to hindering the diffusion of oxygen. Meanwhile, the oxide of HVAF coating mainly accumulates at pores and cracks, and there is no or late formation of uniform and dense oxide film on the surface. The surface of the remelted coating after oxidation forms a relatively uniform and dense oxide film, providing more effective protection for the substrate.

The effect of diffusion on multistability and stochastic sensitivity in spatially extended systems

A spatially-extended reaction-diffusion model is considered. The work is focused on self-organization mechanisms of diffusion instability and Turing pattern formation. Pattern generation and multistability of the system is demonstrated for varying diffusion intensity. In the stochastic variant of the model, the sensitivity of coexisting patterns to noise is studied. The stochastic sensitivity function technique is used for the analysis of noise-induced transitions between patterns. Application of stochastic sensitivity functions is discussed on examples.

Soil gas gradient method for estimating natural source zone depletion rates of LNAPL and specific chemicals of concern

This paper presents a simplified approach for the soil gas gradient method for estimating natural source zone depletion (NSZD) rates of specific contaminants of concern (COCs) at sites contaminated by light non-aqueous phase liquids (LNAPL). Traditional approaches to quantify COC-specific NSZD rates often rely on numerical or analytical reaction-transport models that require detailed site-specific data. In contrast, the proposed method employs simple analytical solutions, making it more accessible to practitioners. Specifically, it requires only the maximum soil gas concentration, the effective diffusion coefficient, and the diffusive reaction length calculated from vertical soil gas concentration profiles. The simplified approach was validated against a reactive transport numerical model reported in the literature, showing consistent results within the same order of magnitude for BTEX NSZD rates at a gasoline spill site in South Carolina. Further validation using a larger dataset involved comparing NSZD rate estimates for benzene and total petroleum hydrocarbons (TPH) against those obtained using BioVapor, utilizing empirical soil gas data from the USEPA Petroleum Vapor Intrusion Database. Results demonstrated a strong correlation between NSZD rates and maximum soil gas concentrations, allowing the development of a rapid screening approach based only on the measured soil gas concentrations and literature values for diffusion coefficients and diffusive reaction lengths. This approach aligned well with previous modeling studies and was consistent with literature values for TPH NSZD rates. Overall, both the simplified and screening approaches offer practical, easy-to-use tools for evaluating temporal variability in natural attenuation rates, supporting baseline assessments and ongoing performance evaluations of remediation at LNAPL sites.

RADIATION AND THERMAL DIFFUSION EFFECTS ON VISCO-ELASTIC FLUID PAST A POROUS PLATE WITH CHEMICAL REACTION AND HEAT GENERATION

A free convective two dimensional MHD boundary layer flow of a non-Newtonian (visco-elastic) fluid past a vertical porous plate have been thoroughly researched in this paper. The thermal diffusion Effects are also analyzed in presence of chemical reaction and radiation. A steady suction pressure is maintained at the plate. A singular perturbation method has been used to solve the problem. The analytical results are obtained for different values of the various dimensionless parameters entering into the flow problem and discussed quantitatively.

Analysis of fractionalized Brinkman flow in the presence of diffusion effect

A vertical plate experiences a dynamic flow of fractionalized Brinkman fluid governed by fluctuating magnetic forces. This study considers heat absorption and diffusion-thermo effects. The novelty of model is the fractionalized Fourier’s and Fick’s laws. The problem is solved using the constant proportional Caputo derivative and Laplace transform method. The resulting non-dimensional equations for temperature, mass, and velocity fields are solved and compared visually. We explore the influence of various parameters like the fractional order, heat absorption/generation (Q), chemical reaction rate (R), and magnetic field strength (M) through informative graphs. Additionally, we contrast the velocity fields of fractionalized and regular fluids. The visualizations reveal that diffusion-thermo and mass Grashof number enhance fluid velocity, while chemical reaction and magnetic field tend to suppress it. For the interest of engineering, physical quantities such as Sherwood number, skin friction, and Nusselt number are computed. The present study satisfying all initial and boundary condition can be reduced to to previous published work which shows the validity of present work.

Understanding of Water Transport through Membrane Electrode Assembly in PEFC

In a polymer electrolyte fuel cell (PEFC), water generation, electroosmosis drag, and back diffusion change the humidity, which affects transport properties such as proton conductivity, effective oxygen diffusion coefficient, and permeance of the feed gas through a membrane. Since the sorption and desorption of water in the electrolyte membrane is slower than other processes such as the oxygen reduction reaction, the proton transport, and the oxygen diffusion, dynamic water behavior should be considered to estimate the cell performance precisely. In this study, the water permeation flux through a membrane electrode assembly (MEA) was measured, and the effective water diffusion coefficients in a membrane and catalyst layer (CL) were formulated as a function of temperature and the moisture content respectively. Dynamic moisture content change in MEA was simulated with the measured effective diffusion coefficients. The experimental results showed that desorption was slower than sorption in the identical moisture content range particularly at the beginning, and this tendency was successfully reproduced using the moisture content distribution obtained by numerical simulation.

Resilience strategies in an intertwined supply network: Mitigating the vulnerability under disruption ripple effects

Intertwined supply network (ISN) is a complex system consisting of multiple interconnected supply chains orchestrated by different focal firms. The inherent interconnectedness of an ISN makes it vulnerable to localized disruptions, which can propagate through intricate supplier-buyer relationships, causing unpredictable disruption ripple effects that exacerbate vulnerabilities. While existing literature provides valuable insights into the vulnerability of supply networks with a single focal firm, less attention has been given to ISN comprising multiple competing focal firms. This study proposes an agent-based model to simulate the diffusion of disruption ripple effects in a realistic ISN. The model is used to assess the relative effects of firms' structural and operational attributes on vulnerability and to compare the effectiveness of three mainstream resilience strategies—resistance, adaptation, and recovery—in mitigating the overall vulnerability of ISN. Furthermore, the interaction of resilience strategies initiated by different focal firms in the ISN is explored. The results suggest that focal firms should prioritize their own structural attributes and those of their neighboring firms to address vulnerabilities effectively. Moreover, focal firms can identify partners with higher reciprocity and engage in cooperation for resilience investment. This study contributes to the understanding of ISN vulnerability and provides practical insights for developing effective resilience strategies in complex supply networks.

High-Entropy Materials for Application: Electricity, Magnetism, and Optics.

High-entropy materials (HEMs) have recently emerged as a prominent research focus in materials science, gaining considerable attention because of their complex composition and exceptional properties. These materials typically comprise five or more elements mixed approximately in equal atomic ratios. The resultant high-entropy effects, lattice distortions, slow diffusion, and cocktail effects contribute to their unique physical, chemical, and optical properties. This study reviews the electrical, magnetic, and optical properties of HEMs and explores their potential applications. Additionally, it discusses the theoretical calculation methods and preparation techniques for HEMs, thereby offering insights and prospects for their future development.