Unequal Diffusion Research Articles

Dynamics of reaction–diffusion–advection system and its impact on river ecology in the presence of spatial heterogeneity

This study considers a two-species reaction–diffusion–advection (RDA) model in a heterogeneous advective environment with zero Neumann boundary conditions. We suppose that two species compete for the same food resource but have different diffusion and advection rates. The primary objective of this study is to investigate the global asymptotic stability and coexistence of steady state based on different and unequal diffusion and advection rates through theoretical and numerical analysis. We establish the local stability of two semi-trivial steady states of the competing species. Also, the non-existence of coexistence steady state is proved with the help of some non-trivial assumptions. Finally, we show the global stability with the help of monotone dynamical systems and combine the local stability and non-existence of coexistence steady state. If one species adopts a smaller diffusion and advection rate, the competition’s result depends on the advection and diffusion rate ratio. If the ratio is smaller, then the species will prevail. Also, the species with higher diffusion and smaller advection will win. Lastly, the effectiveness of the model in one and two-dimensional situations is shown by a series of numerical calculations, which is particularly important for environmental consideration.

Asymmetric Rectified Electric Fields for Symmetric Electrolytes.

In this paper, building upon the numerical discovery of asymmetric rectified electric fields (AREFs), we explore the generation of AREF by applying a sawtooth-like voltage to 1:1 electrolytes with equal diffusion coefficients confined between two planar blocking electrodes. This differs from an earlier approach based on a sinusoidal AC voltage applied to 1:1 electrolytes with unequal diffusion coefficients. By numerically solving the full Poisson-Nernst-Planck equations, we demonstrate that AREF can be generated by a slow rise and a fast drop of the potential (or vice versa), even for electrolytes with equal diffusion coefficients of the cations and anions. We employ an analytically constructed equivalent electric circuit to explain the underlying physical mechanism. Importantly, we find that the strength of AREF can be effectively tuned from zero to its maximal value by only manipulating the time dependence of the driving voltage, eliminating the necessity to modify the electrolyte composition between experiments. This provides valuable insights to control the manipulation of AREF, which facilitates enhanced applications in diverse electrochemical systems.

Microstructure evolution and mechanical properties of Sn-9Zn-2.5Bi-1.5In solder joints with aging treatment under various conditions

Sn-Zn system solder has been considered promising lead-free solder materials to replace Sn-Pb and Sn-Ag-Cu systems in various conditions, due to the performance characteristics of low melting point and high reliabilities. This study investigates the microstructure evolution and mechanical properties of Sn-9Zn-2.5Bi-1.5In (Sn-Zn) solder paste joints on Cu substrates with aging treatment, which are under various conditions of different paste thicknesses and reflow times. It is concluded that the intermetallic compounds (IMC) of Sn-Zn/Cu solder joints are Cu5Zn8 layers at all stages of aging. The microstructure of before-aging joints and evolution during aging is significantly affected by the reflow times, while slightly affected by the paste thicknesses. In all experimental conditions, the IMC layers gradually thicken and reach 4-5 μm when aging for 720 h. While Cu5Zn8 products are generated at the position of the original Zn phases or along the Sn grain boundaries in the solder matrix with the aging process. The unequal diffusion rates of Cu and Zn atoms create two types of joint voids which are accumulated by Zn vacancies in the solder and accumulated by Cu vacancies at the interface between the solder and IMC layer. The interface voids and coarsened crystal structure are identified as the main factor for joint failure during aging. Finally, the shear strength of the joints with the initial 3.5 μm thickness IMC layers can maintain at high values above 45 MPa, exhibiting satisfactory reliability, which indicates that the soldering process determines the initial IMC structure, and affects the joint reliability more than the aging process.

Microscopic mechanism of big-white-spot defect formation in hot-based galvanized strip steel: Theoretical calculation and molecular dynamics simulation

By combining experimental, thermodynamic, dynamics, and molecular dynamics simulations, the microstructure characteristics and microscopic processes generated of big-white-spot defects on the surface of hot-based galvanizing were studied. OM, LCM, FESEM, EPMA, XRD are used to characterize the microstructure of the coating surface and cross-section from different angles, and electrochemical tests are used to test corrosion mechanism of the coating. Molecular dynamics is used to calculate the atomic diffusion coefficient. The distribution of the aluminum-rich layer in the big-white-spot coating is extremely uneven. And the aluminum-rich layer loses its hindrance to the diffusion of Fe and Zn. There are many holes inside the defect coating. The fracture of aluminum-rich layer leads to a large number of Fe2Al5 particles within the defect. The defects cause the transformation of Al5Sb3 phase from interdendritic segregation to particle distribution. Nucleation theory, diffusion model, coating growth model are used to analyze the influence of temperature on coating. The nucleation rate increases exponentially with temperature and is mainly controlled by diffusion. The simulation results indicate that diffusion coefficient of Al is greater than Fe, and unequal diffusion leads to an increase in holes. The intensification of element diffusion, increase of holes, and poor adhesion between aluminum-rich layer and substrate jointly contribute the fracture of aluminum-rich layer.

Zeolite Encapsulation of Indole as an Antibacterial with Controllable Release Property.

Effective regulation of the release behavior of bactericides to avoid both too fast release and too slow release to maximize their antibacterial ability is still the face of a grand challenge. In this study, indole as a bactericide was encapsulated into three types of zeolites (denoted as indole@zeolite), including the ZSM-22 zeolite, ZSM-12 zeolite, and beta zeolite with different topologies, respectively, to obtain indole@ZSM-22, indole@ZSM-12, and indole@Beta complexes finally. Benefiting from the confinement effect of zeolites, the release rate of indole from these three zeolite encapsulation systems showed a much slower release rate than that of indole impregnated onto a counterpart zeolite (denoted as indole/zeolite), thus avoiding the too-fast and too-slow release very well. As determined by molecular dynamics simulation combined with experimental results, attributed to the unequal diffusion coefficient in these three encapsulation systems caused by different zeolite topologies, the release rate of indole within these three complexes was different from each other, hence providing an effective way to avoid a too-slow release rate through choosing different zeolite topologies. The simulation results showed that the timescale of hopping of indoles in zeolites plays an important role in the dynamics in zeolites. Taking killing Escherichia coli as an instance, compared with indole/zeolite, the corresponding indole@zeolite sample exhibited more efficient and sustainable antibacterial activity for its controlled-release behavior.

A modelling of bioconvective flow existing with tiny particles and quartic autocatalysis reaction across stratified upper horizontal surface of a paraboloid of revolution

The study considers the case of the unequal diffusion coefficients of reactant $A$ (bulk fluid) and reactant $B$ (catalyst at the wall) with the dispersion of both nanoparticles and gyrotactic microorganisms of Erying-Powell fluid flow over a surface with non-uniform thickness in the presence of variable fluid properties and stratification. The numerical solution of the transformed governing equations is obtained by using the Runge-Kutta method and shooting techniques. The outcome of this study is that the increasing values of temperature-dependent thermal conductivity parameter lead to the augmentation of the kinetic energy which thereafter causes a significant enhancement of the fluid temperature.

In English

The goal of this study is unraveling the specific features of non-stationary surface concentration distribution of electroactive and inactive species in a model electrochemical process with a preceding homogeneous first-order chemical reaction (CE mechanism). For this purpose, the exact analytical expressions for the non-stationary concentration distributions of electroactive and inactive species in the thin layer attached to a planar electrode are analyzed. The both cases of equal and unequal diffusion coefficients of species taking part in the preceding chemical reaction are considered. In the former case, the exact analytical expressions for the concentration distributions of electroactive and inactive species on a planar electrode are obtained. The peculiarities of the limiting cases of zero and infinite frequency of an applied alternating current for the both cases of equal and unequal diffusion coefficients of species are discussed. It is shown that there is a phase shift between AC and the surface concentration of species that changes under the action of this current. At low frequencies, the phase angle tends to p/2, whereas at high frequencies it decreases to p/4. The phase angle is the function of the two important measures, namely, the ratio of the Nernst diffusion layer thickness to the oscillation diffusion layer thickness, and the ratio of the Nernst diffusion layer thickness to the reaction layer one. It is shown that the phase angle depends on the diffusion coefficient of species in different manner for low and high values of the rate constants of the chemical reaction. At low values of these parameters, the phase angle shifts slightly to the range of high frequencies with an increase of diffusion coefficient. At the high rate constants, the phase angle decreases with frequency more slowly, and its dependence on diffusion coefficient is observed only at middle frequencies. The surface concentration of electroactive and inactive species decreases with an increase of frequency, but for the inactive species this process is faster than that for the electroactive species. The influence of the inactive species on the surface concentration of electroactive species decreases at high frequencies and at low rate constants of the preceding chemical reaction. The results obtained shed the light on complex dynamics at an electrode/electrolyte interface under non-stationary conditions.

Homogeneous–Heterogeneous Reactions Within Magnetic Sisko Nanofluid Flow Through Stretching Sheet Due to Convective Conditions Using Buongiorno’s Model

The flow due to stretching sheet has key role in many engineering fields such as making rubber sheets and plastic, wire drawing, glass-fiber manufacture and hot rolling etc. The Sisko fluid has its significant role in drilling fluids, blood, cement slurry, liquid polymers, paint and mud, synovial fluid and water-borne coating. Here, we examined the magnetic Sisko fluid flow via stretching sheet with convective conditions using Buongiorno’s model and flow problem occurring due to homogeneous–heterogeneous reactions. Influence of pertinent flow parameters viz. magnetic field, material index, Brownian motion parameter, thermophoresis parameter, Brownian diffusivity, Lewis number, ratio of diffusion coefficient, strength of homogeneous reaction, strength of heterogeneous reaction and Biot number are revealed by graphs for both shear thinning (n < 1) and shear thickening (n > 1) cases. The existing model has considered the case of unequal diffusion coefficients of chemical species. Hence, accounting the interaction of both homogeneous–heterogeneous reactions. One of the important outcomes of this work is concentration of auto-catalyst of Sisko fluid decreased due to rise in material index parameter.

Assessment of flame height of two unequal turbulent diffusion flames: Experimental interpretation and quantification

Multiple fires burning is a fairly common phenomenon in wildland fires and urban process industries. The burning of multiple fires is much more dangerous than single fire due to the merging of flames. This work aims to study the flame height of two unequal buoyant turbulent diffusion flames, which has not been well revealed. Total 168 experimental tests were performed using two square gas burners with different side lengths of 10 cm and 15 cm as the fire sources. The heat release rates (HRRs) in fire group and burner spacing (S) were changed. Results showed that for a given HRRs group, with the increase of S, the flame height presents a decay trend first, followed by a rise trend, and finally it maintains unchanged. This non-monotonic trend is explained from the view of interaction mechanisms. Three states of fully merging, intermittent merging and non-merging of two flames are divided to illustrate and quantify the flame height. By introducing a normalized parameter λ to characterize the air entrainment difference, a correlation for flame height of intermittent merging is developed. For the fully merging and non-merging, the equations for flame heights are respectively established based on the assumed equivalent single flame. The accuracy of the proposed model for flame height is validated using experimental data of this work and in literatures. And the application scope of model is expanded to the flame height in merging state of two identical fires.

Diffusive majority-vote model

We define a stochastic reaction-diffusion process that describes a consensus formation in a nonsedentary population. The process is a diffusive version of the majority-vote model, where the state update follows two stages: In the first stage, spins are allowed to jump to a random neighbor node with probabilities D_{+} and D_{-} for the respective spin orientations, and in the second stage, the spins in the same node can change its values according to the majority-vote update rule. The model presents a consensus formation phase when the concentration is greater than a threshold value and a paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining the inversion symmetry. Setting unequal diffusion probabilities for the respective spin orientations is the same as applying an external magnetic field. The system undergoes a discontinuous phase transition for concentrations higher than the critical threshold on the external field. The individuals that diffuse more dominate the stationary collective opinion.

An Effective Photocatalytic Degradation of Industrial Pollutants through Converting Titanium Oxide to Magnetic Nanotubes and Hollow Nanorods by Kirkendall Effect.

Controlling of morphology from nanoparticles to magnetic nanotubes and hollow nanorods are interesting for developing the photo-active materials and their applications in the field of photocatalysis and decontamination of aquatic effluents. In the current study, titanium dioxide nanoparticles and nanocomposites were prepared by different techniques to produce various morphologies. The nanoparticles of pure titanium dioxide were prepared by sol-gel technique. Magnetic nanotubes and hollow nanorods were prepared by combining titanium with di- and tri-valent iron through two stages: urea hydrolysis and solvent thermal technique. According to the Kirkendall effect, magnetic nanotubes were fabricated by unequal diffusion of Fe2+, Fe3+ and Ti4+ inside the nanocomposite to produce maghemite-titanian phase. In the same trend, hollow nanorods were synthesized by limited diffusion of both trivalent iron and tetravalent titanium producing amorphous structure of titanium iron oxides. The magnetic and optical properties showed that these nanotubes and hollow nanorods are magnetically active and optically more effective compared with titanium dioxide nanoparticles. Therefore, the Naphthol green B dye completely disappeared after 45 min of UV light irradiation in presence of the hollow nanorods. The kinetic study confirmed the high performance of the hollow nanorods for the photocatalytic degradation of Naphthol green B compared with titanium dioxide nanoparticles.

The Idea of Justice in Innovation: Applying Non-Ideal Political Theory to Address Questions of Sustainable Public Policy in Emerging Technologies

Justice as such is not a new idea. Since the time of Plato and Aristotle, justice has been conceived as a moral and political standard of how people ought to conduct themselves and relate to one another in a fair society and institutions. However, even though principles of justice and related theories have been used to provide guidance to social and political actions, technological innovation remains an area of policy and practice in which justice cannot be easily applied. This is not only due to the complex process of generating new technologies and their unpredictable impact on social relations and institutions but also to perceptions of value neutrality in the innovation process. Such perceptions make public policy difficult to sustain. Nevertheless, innovation is a human action that is guided by both ethical norms and interests and is significant for justice. Emerging technologies create opportunities for promoting justice, but at the same time, they also pose risks to injustice. This paper is of theoretical nature and aims to explain why justice needs to provide the normative direction of innovation systems and related public policy in the 21st century. Through a critical review of the literature, the paper argues that justice as such is a non-ideal standard which is significant for the legitimacy of emerging technologies and related developmental change. The normative direction of innovation systems in the 21st century depends on non-ideal principles of equity, participation, and recognition. These principles embody sustainable public-policy solutions to problems of unequal generation and diffusion of emerging technologies.

Cuticular hydrocarbon profiles differ between ant body parts: implications for communication and our understanding of CHC diffusion.

Insect cuticular hydrocarbons (CHCs) serve as communication signals and protect against desiccation. They form complex blends of up to 150 different compounds. Due to differences in molecular packing, CHC classes differ in melting point. Communication is especially important in social insects like ants, which use CHCs to communicate within the colony and to recognize nestmates. Nestmate recognition models often assume a homogenous colony odor, where CHCs are collected, mixed, and redistributed in the postpharyngeal gland (PPG). Via diffusion, recognition cues should evenly spread over the body surface. Hence, CHC composition should be similar across body parts and in the PPG. To test this, we compared CHC composition among whole-body extracts, PPG, legs, thorax, and gaster, across 17 ant species from 3 genera. Quantitative CHC composition differed between body parts, with consistent patterns across species and CHC classes. Early-melting CHC classes were most abundant in the PPG. In contrast, whole body, gaster, thorax, and legs had increasing proportions of CHC classes with higher melting points. Intraindividual CHC variation was highest for rather solid, late-melting CHC classes, suggesting that CHCs differ in their diffusion rates across the body surface. Our results show that body parts strongly differ in CHC composition, either being rich in rather solid, late-melting, or rather liquid, early-melting CHCs. This implies that recognition cues are not homogenously present across the insect body. However, the unequal diffusion of different CHCs represents a biophysical mechanism that enables caste differences despite continuous CHC exchange among colony members.

Chronoamperometry for reversible charge transfers at cylindrical wire electrodes: Theory for DO ≠ DR, and a highly accurate computation of the current

Abstract Semi-analytical modelling of transient experiments at cylindrical wire or fiber electrodes is hindered by the unavailability of numerical procedures for calculating special functions arising in the models. A theory is developed, of the chronoamperometric Faradaic current for a reversible charge transfer reaction at a cylindrical electrode. Arbitrary potential steps and unequal diffusion coefficients (δ = DO/DR ≠ 1) are assumed. Two procedures (written in C++) are designed, for computing a special function occurring in the theory. One procedure is computationally inexpensive, but has a low accuracy (relative error moduli close to 2% in the worst case, when −0.5 ≤ log (δ) ≤ 0.5). The second is more expensive, but highly accurate (relative error moduli close to 4 × 10−14 in the worst case, when −3 ≤ log (δ) ≤ 3). Numerical experiments demonstrate that the effect of δ ≠ 1 on the current is not negligible, even for δ not much different from unity. Therefore, the theory presented should be taken into account in experimental investigations. The code for the procedures is freely available.

Experimental and numerical study on combustion characteristics of super lean H2–O2 premixed laminar flame in argon atmosphere

This paper presents an experimental and numerical research on super lean premixed H2–O2 flames under argon atmosphere in a combustion bomb with constant volume, and applied CHEMKIN to perform simulation for the flames. The high-speed schlieren photography is employed to record the development process of expanding spherical flame, and laminar burning velocities of super lean premixed H2–O2–Ar flames with different back pressures under argon atmosphere are calculated, and the influence of equivalence ratio and initial pressure on flame instability is analyzed, and the mass burning fluxes are calculated by simulation and flame structure and rate of elementary reactions is analyzed. The results show that, with equivalence ratio decrease, laminar flame velocity and mass burning flux will decline; with initial pressure increase, laminar flame speed will decline and mass burning flux will increase. For flame stability, when initial pressure rises, the hydrodynamic instability on hydrogen flame surface is enhanced, more easily resulting in cellular instability. As pressure rises, Lewis number and density ratio under each pressure will approximate to constant values, therefore, flame thickness is the main factor influencing flame instability when initial pressure rises. When equivalence ratio decreases, unequal diffusion instability often occurs easily under leaner conditions during flame development. According to simulation results, the laminar flame velocity is the result of interaction between the chain branching reaction and the chain termination reaction and the changes of equivalence ratio will affect above two reactions. For flame structure, the results show that when equivalence ratio is small, chemical reaction velocity of hydrogen gas burning will decline and reaction zone will enlarge, besides, H and OH concentration will also decline. As equivalence ratio decreases, the maximum H mole fraction constantly declines, which is consistent with the changing trend of laminar flame velocity with equivalence ratio.

Social Distancing, Internet Access and Inequality

This paper measures how high-speed internet affects an individual's ability to self-isolate during a global pandemic. Our data track the movements of 19 million mobile devices and whether a mobile device leaves its home that day. We examine compliance with state-level directives to remain at home. In general, the presence of a combination of high income and high-speed internet was a larger driver in households staying at home than state directives. Devices in regions with either high-income or high-speed internet were also more likely to stay at home after such a directive. Furthermore, the combination of higher income and high-speed internet has a self-reinforcing effect. This appears to be mainly driven by telecommuting rather than the ability of higher-income households to use the internet to avoid store visits. Our results suggest that the digital divide explains much of the inequality we observe in an individual's ability to self-isolate.

Electrophoretic origin of long-range repulsion of colloids near water/Nafion interfaces.

One of the most striking properties of Nafion is the formation of a long-range solute exclusion zone (EZ) in contact with water. The mechanism of formation of this EZ has been the subject of a controversial and long-standing debate. Previous studies by Schurr et al. and Florea et al. root the explanation of this phenomenon in the ion-exchange properties of Nafion, which generates ion diffusion and ion gradients that drive the repulsion of solutes by diffusiophoresis. Here we have evaluated separately the electrophoretic and chemiphoretic contributions to multi-ionic diffusiophoresis using differently charged colloidal tracers as solutes to identify better their contribution in the EZ formation. Our experimental results, which are also supported by numerical simulations, show that the electric field, built up due to the unequal diffusion coefficients of the exchanged ions, is the dominant parameter behind such interfacial phenomenon in the presence of alkali metal chlorides. The EZ formation depends on the interplay of the electric field with the zeta potential of the solute and can be additionally modulated by changing ion diffusion coefficients or adding salts. As a consequence, we show that not all solutes can be expelled from the Nafion interface and hence the EZ is not always formed. This study thus provides a more detailed description of the origin and dynamics of this phenomenon and opens the door to the rational use of this active interface for many potential applications.

Homogeneous–heterogeneous reactions in flow past a horizontal circular cylinder with an induced magnetic field and nonlinear thermal radiation

AbstractIn this study, we investigate the steady, two‐dimensional, incompressible viscous boundary layer flow of an electrically conducting Casson fluid over a horizontal circular cylinder. The cylinder is impermeable and the flow is assumed to be subject to homogeneous–heterogeneous reactions. The homogeneous–heterogeneous reactions are also assumed to have unequal diffusion coefficients. The novelty in this study is in the consideration of a nonlinear radiative flux together with Joule heating and an induced magnetic field. The magnetodynamic pressure gradient in induced magnetic flows is important as it gives insights into the boundary layer characteristics. The flow velocity and the magnetic field in the free stream are assumed to be uniform and directed vertically over the cylinder. The partial differential equations are solved using the bivariate spectral quasi‐linearization method. An analysis and comparison of results with existing literature are provided. Among the findings, we show, inter alia, that the reactants dominate while the autocatalysts have a negligible impact on the flow progression. The skin friction coefficient decreases with an increase in the Casson parameter and increases when the Joule heating parameter is increased. The rate of heat transfer increases with increasing the Casson parameter and decreases when the Joule heating parameter is increased.

Mathematical modeling for the measurement of the competitiveness index of Brazil south urban sectors for installation of photovoltaic systems

In recent years, photovoltaic (PV) solar energy has become the most growing form of renewable electricity generation in the world. Due to its vast tropical territorial area, Brazil is one of the countries with the most significant potential for PV implementation. However, by the end of 2018, the distributed generation of Brazil by PV source had only 2.4 W/inhabitant, while many countries have more than 100 W/inhabitant. In order to identify opportunities for advancing PV participation in the country, this paper proposes mathematical modeling based on 18 performance indicators capable of measuring the level of competitiveness of municipalities for the PV installation. The methodology proposes the use of the multicriteria Analytic Hierarchy Process technique. Through consultation in 100% of the 497 municipalities in the state of Brazil with higher penetration of PV per capita, it was possible to generate a ranking with the level of competitiveness for PV installations. With this, one can identify the 20 most competitive urban sectors for investment in photovoltaic installations connected to the grid. The results explain the unequal diffusion patterns in southern Brazil and propose actions to disseminate distributed generation.

Visualization of Kirkendall Voids at Cu-Au Interfaces by In Situ TEM Heating Studies

Gold-plated copper alloys are used extensively in electrical contacts where diffusional processes are known to cause contact degradation. An in situ transmission electron microscopy (TEM) heating study was carried out to provide fundamental understanding of the aging phenomena in reasonable timescales. Samples to visualize the interface in TEM were prepared by focused ion beam (FIB) microscopy and heated in situ up to 350°C while holding at intermediate temperatures to enable imaging. The grain boundaries in Au coatings, specifically the columnar boundaries, provided rapid pathways for diffusion of Cu all the way to the Au surface. This unequal diffusion created vacancies in Cu which coalesced into Kirkendall voids. This in situ technique has been applied to visualize the diffusion pathways in electroplated and sputtered Au films deposited directly on Cu, as well the role of Ni and NiP as barrier layers for mitigating Cu diffusion.