Steady-state Diffusion Research Articles

Revealing the functional relationship between manganese dissolution potentials and lithium concentrations with diffusion coefficient for lithium intercalation in λ-MnO2 electrode

Electrochemical redox lithium extraction (ELE) with LiMn2O4/λ-MnO2 redox couple, stands out as the most prospective technology for efficient and selective lithium extraction from the salt lake brines owing to the high lithium intercalation capacity, selectivity, and recovery rate. However, the decreasing Li+ concentration induced electrode polarization, especially, at low concentrations, and inappropriately applied potentials can significantly accelerate manganese dissolution (MD). While no correlational research has established the relationship between the manganese dissolution potential (EMD) and Li+ concentration gradient. Herein, the inversely proportional relationship between EMD and the lithium concentration is first revealed through steady-state diffusion coefficients. This research sheds light on the MD mechanism at different lithium concentration gradients and lays the foundation for the industrial application of electrochemical lithium extraction with LiMn2O4/λ-MnO2 redox couple from salt lake brines.

Investigation of steady-state gas diffusion through angled metallised polymer films for applications in fibre reinforced pressure vessels as barrier membranes

Pressure vessels used for the storage of hydrogen gas, particularly carbon-fibre reinforced pressure vessels (CPVs), must demonstrate sufficient leak tightness. Currently, this is achieved by costly metallic liners which come at a weight disadvantage compared to CPVs. Therefore, novel concepts for designing CPVs with low permeation characteristics are of high interest for various industrial applications. In this paper, a new concept is proposed based on overlapping intersections of metallised polymer films. Manufacturing trials are carried out on a laboratory scale to demonstrate the feasibility of a new barrier membrane design that can also be integrated into the winding process of CPVs. An efficient analytical model, as well as finite element simulations, are compared against experimental findings for the permeation of Helium. The findings indicate significant promise for implementing the barrier concept in CPVs, with tests and models demonstrating an over 1000 - fold decrease in the permeability of the barrier membrane compared to pure polymer, even when utilizing unoptimized tape materials. Reductions by a factor of over 10 000 are possible with material optimisation.

A hybrid interpolating element-free Galerkin method for 3D steady-state convection diffusion problems

This study investigates a hybrid interpolating element-free Galerkin (HIEFG) method for solving 3D convection diffusion problems. The HIEFG approach divides a 3D solution domain into a sequence of interconnected 2D sub-domains, and in these 2D sub-domains, the interpolating element-free Galerkin (IEFG) method is applied to form the discretized equations. The improved interpolating moving least-squares (IMLS) method is used to obtain the shape function of the IEFG method for 2D problems. The finite difference method is employed to combine the discretized equations in 2D sub-domains in the splitting direction. Then, the HIEFG method's formulas are derived for steady-state convection diffusion problems in 3D solution domain. Three numerical examples are used to discuss the impacts of the number of nodes, the number of split layers, and the scaling parameters of the influence domain on the computational precision and CPU time of the HIEFG technique. Imposing boundary conditions directly and the dimension splitting technique in this method significantly improves the computational speed greatly.

Exploiting locality in sparse polynomial approximation of parametric elliptic PDEs and application to parameterized domains

This work studies how the choice of the representation for parametric, spatially distributed inputs to elliptic partial differential equations (PDEs) affects the efficiency of a polynomial surrogate, based on Taylor expansion, for the parameter-to-solution map. In particular, we show potential advantages of representations using functions with localized supports. As model problem, we consider the steady-state diffusion equation, where the diffusion coefficient and right-hand side depend smoothly but potentially in a highly nonlinear way on a parameter y ∈ [−1, 1]N. Following previous work for affine parameter dependence and for the lognormal case, we use pointwise instead of norm-wise bounds to prove ℓp-summability of the Taylor coefficients of the solution. As application, we consider surrogates for solutions to elliptic PDEs on parametric domains. Using a mapping to a nominal configuration, this case fits in the general framework, and higher convergence rates can be attained when modeling the parametric boundary via spatially localized functions. The theoretical results are supported by numerical experiments for the parametric domain problem, illustrating the efficiency of the proposed approach and providing further insight on numerical aspects. Although the methods and ideas are carried out for the steady-state diffusion equation, they extend easily to other elliptic and parabolic PDEs.

Methodology of integrated measurements with radon diffusion chamber

Calibration of Solid-State Nuclear Track Detectors - SSNTD in the diffusion chamber in most cases assumes a constant radon concentration outside the diffusion chamber and a steady state. Although this has been proven to be a valid approximation in most cases, the fact is that the radon concentration outside the chamber is not constant. In this way, the detectors are calibrated to measure the mean radon concentration. For this reason, there is doubt if the time-dependent concentration in dwellings results in the same number of tracks on the detector as the time-averaged radon concentration for the same exposure period. To obtain an answer, time-dependent and steady-state diffusion equations for radon and its progeny were solved. Then the number of tracks on the detector was calculated for these two cases and compared. For that goal, software for solving the time-dependent diffusion equation for time-varying external radon concentration was developed. Results show that concentrations measured using a diffusion chamber are the real concentrations at the measuring site. However, it was also found that the validity of results is not a universal property, as shown in the current paper. In some cases, results can be wrong. For some extreme conditions when diffusion coefficients are disrupted calibration using stationary conditions model will lead to incorrect results of real measurements in experiments where ambiental concentration is time-varying.

Electricity-driven dealkalization of bauxite residue based on thermodynamics, kinetics, and mineral transformation.

High alkalinity content of bauxite residue is a major factor that hinders resource reutilization and pollutes the environment. Although acid neutralization is a direct and effective method, the amount of acid and secondary waste of sodium salt are still difficult problems to solve. Herein, we innovatively integrated an electric field into the acid neutralization dealkalization of bauxite residue and analyzed the dealkalization behavior by thermodynamics, kinetics, and mineral transformation. The results show that the pH of the anode chamber was maintained at the acidic levels of 3-6 after 30min of galvanostatic electrolysis, and bauxite residue can realize dealkalization by acid neutralization. In the anode chamber, Na+ was released into the leachate via the reactions of Na3Al3Si3O12 and the removal of encapsulated soluble alkali. The stainless steel wire mesh anode exhibited its superiority and decreased the Na2O content in bauxite residue from 9.48 to 3.13% through convective mass transfer driven by the electric field and steady-state diffusion under stirring. This research provides a promising method for the electricity-driven dealkalization of bauxite residue, thus facilitating the development of multifield coupling theory and the application of electric fields in the alumina industry.

Mathematical Analysis of Nonlinear Differential Equations in Polymer Coated Microelectrodes

A theoretical analysis is conducted on the electrochemical behaviour of micro disk electrodes coated with thin coatings of electroactive polymers. The main focus of efforts to characterize the planar diffusion chemical reaction within polymer-modified ultra-microelectrodes is the creation of a theoretical model that explicitly takes into account the potential for the polymer film to cover the inlaid micro disc support surface. Approximate formulae for the steady-state amperometric response and formulation of the boundary value problem are given. The impact of substrate concentration, mediator concentration and current responsiveness in the solution besides the polymer film is also investigated. Akbari-Ganji method (AGM) and differential transformation method (DTM), two adequate and widely available analytical methods, were utilized to determine the steady-state non-linear diffusion equation. The approximate analytical solution for the substrate concentration and mediator concentration and the current for the small experimental kinetic values and diffusion coefficients are presented. We additionally determine the problem’s numerical solution using the MATLAB tool. A satisfactory agreement can be seen when the numerical outcomes verify with the analytical findings.

Evaluation of the influence of Mihrab shape on sound quality in Mosques

A mihrab, a niche in the mosque wall indicating the qibla or the direction of Mecca, plays a crucial role in determining the acoustics within the mosque space. This study explores the impact of mihrab shape on sound characteristics in a mosque. Various mihrab shapes, including a flat wall and seven distinct shapes, were tested. Steady State Diffusivity (Dss) values were calculated. Polar response, Echo Criterion (EC), and Sound Transmission Index (STI) measurements were conducted using a 1:10 scale model omni-directional sound source with Dirac measurement system. The outcomes of this study show that the Trapezium Mihrab, Triangular Mihrab, and Flat Wall configurations demonstration distribution across all proposed parameters. This research lights the significant impact of mihrab shape on the acoustic environment within mosques, offering valuable insights for architects and designers and seeking to optimize its sound quality. The Trapezium Mihrab, characterized by its unique shape, demonstrates notable efficiency in acoustic performance. Similarly, the Triangular Mihrab and Flat Wall configurations also prove to be conducive to effective sound distribution within the mosque main hall. These findings highlight the crucial role that mihrab design plays in shaping the overall acoustics of a mosque. By recognizing the influence of mihrab shape on acoustic elements, architects and designers can make good decisions to enhance the acoustical environment for worshippers. This could contribute to the creation of harmonious and acoustically optimized mosque spaces.

Effects of the diffusion path on the effective diffusion coefficient of hydrogen isotope in tungsten with helium bubbles

In irradiated tungsten (W), the formation of numerous helium (He) bubbles has a significant impact on the diffusion behaviors of hydrogen (H) isotopes. To investigate the influence of the microstructure of He bubbles on the diffusion behaviors of deuterium (D), we utilize the reconstructed experimental data, the phase-field method, and the steady-state diffusion equation to calculate the effective diffusion coefficients of D based on four possible diffusion paths, i.e., D atoms diffuse in the bulk W, inside the He bubbles, and along the outer and inner surface of He bubbles. Simulation results based on the reconstructed depth-dependent distribution of He bubbles reveal that the diffusion paths remarkably affect the effective diffusion coefficient of D. By varying the radius and number density of He bubbles, the effective diffusion coefficient of D undergoes significant changes. Subsequently, we fit an empirical formula of the effective diffusion coefficient of D as a function of the radius and number density of He bubbles for different diffusion paths of D based on simulation data. Besides, the growth behaviors of He bubbles are simulated by the phase-field model, and the effective diffusion coefficient of D as a function of the evolutionary time for different diffusion paths is also discussed. At last, we investigate the influence of the D concentration and temperature on the effective diffusion coefficient of D along different diffusion paths. These results indicate that the effective diffusion coefficient of D increases with decreasing the D concentration and increasing the temperature for four diffusion paths. The current study provides a reference for investigating the diffusion behaviors of D in W in the presence of He bubbles, and may benefit the efforts of developing low D retention W-based materials.

Convection-diffusion-electromigration coupled numerical simulation of water and chloride in cement-based materials

The transport of chloride in cement-based materials is influenced by various factors, and the chloride diffusion coefficient in numerical models should be the steady-state value under specific conditions, which is difficult to obtain through traditional experiments. In this article, based on an improved non-contact resistivity instrument, the steady-state chloride diffusion coefficient and porosity of cement-based materials are characterized. Considering the acceleration effect of moisture convection and electric field on chloride transport, a numerical model for moisture and chloride transport coupling diffusion, convection, and electromigration is established. Based on the measured steady-state chloride diffusion coefficient and porosity values, the influence of interface transition zone (ITZ), electric field type, chloride binding effect, initial conditions, and boundary conditions on moisture and chloride transport is numerically analyzed. It is found that the increase of ITZ thickness, electric field strength, boundary concentration, and initial concentration can accelerate chloride transport. The chloride concentration distribution curve exhibits a “shoulder peak” caused by chloride binding effect, and its peak height and width are positively correlated with the chloride binding coefficient. In conclusion, this study aims to better understand the ion transport behavior inside cement-based materials under coupling of convection, diffusion, and electromigration, and identify the key factors influencing this behavior, which provide a feasible scheme for durable design of concrete construction in environments rich in erosive media.

Resistivity and chloride diffusion coefficient of cement-based materials characterized by non-contact electrical resistivity method and resistivity model

The present study involves the application of the non-contact electrical resistivity measurement (NC-ERM) as a non-destructive method to continuously and in-situ measure the resistivity changes of cement-based materials. The NC-ERM was enhanced and utilized to evaluate the resistivity of the materials, and the steady-state chloride diffusion coefficients of various types of cement-based materials were experimentally determined. The results revealed that the highest resistivity was observed in mortar with a sand-to-cement ratio of 1.0 and concrete with an aggregate-to-cement ratio of 0.6, and the steady-state chloride diffusion coefficient increased with the concentration of the pore solution. Furthermore, a novel multi-level series-parallel model was developed to predict the resistivity and steady-state chloride diffusion coefficient of cement-based materials, with calculated values differing by 5% or less. The calculated chloride diffusion coefficient closely matched the value obtained from NC-ERM, indicating the satisfactory accuracy of the non-destructive experiment and theoretical calculation model.

A Method for Evaluating Coalbed Methane Reservoir Productivity Considering Drilling Fluid Damage

In the process of coalbed methane development, drilling fluid and fracturing fluid cannot achieve absolute compatibility with formation. The incompatibility between the working fluid and reservoir will lead to the intrusion of working fluid into the reservoir and cause reservoir pollution. This is a very common phenomenon. There is a large amount of pulverized coal in the coal seam, and the intrusion of working liquid will be combined with the pulverized coal to form cement to block the seepage space in the reservoir. Since pressure relief and fracturing fluid backflow will be performed at the first time after fracturing, the intrusion range of the working fluid is small, generally reaching 10 m to 50 m. Compared with a conventional gas reservoir or shale gas reservoir, the working fluid loss during CBM development will seriously affect the subsequent production project and even make the gas well lose production capacity. On the other hand, in order to avoid this phenomenon, measures such as acidification or volumetric fracturing are sometimes used to improve the seepage environment near the well and near the fracture. The purpose of this study is to quantitatively evaluate the impacts of working fluid filtration and reservoir reconstruction on production. In this study, a single well productivity evaluation model and sensitivity analysis method considering drilling fluid filtration loss, fracturing fluid filtration loss, reservoir reconstruction and other processes is proposed. The formation mechanism of fluid loss during drilling and fracturing is described, and the productivity evaluation model considering fluid loss is combined with the Langmuir isothermal adsorption equation, steady-state diffusion law, Darcy’s seepage law and Duhamel convolution formation. Combined with the distribution of actual gas reservoir flow characteristics, the sensitivity of single well productivity to gas reservoir porosity, gas reservoir permeability, coal seam adsorption coefficient, working fluid filtration loss and reservoir reconstruction measures are analyzed. Through the analysis and fitting of the actual production data on site, the relationship curve can better fit the field production data, and the evaluation results are in line with the drilling and fracturing conditions at that time and the subsequent production conditions, with small errors. The obtained method is suitable for predicting the productivity of fractured vertical wells in different working conditions and provides a basis for the development and productivity prediction of CBM reservoirs in China and in international cooperation.

An Efficient and Robust ILU(k) Preconditioner for Steady-State Neutron Diffusion Problem Based on MOOSE

Jacobian-free Newton Krylov (JFNK) is an attractive method to solve nonlinear equations in the nuclear engineering community, and has been successfully applied to steady-state neutron diffusion k-eigenvalue problems and multi-physics coupling problems. Preconditioning technique plays an important role in the JFNK algorithm, significantly affecting its computational efficiency. The key point is how to automatically construct a high-quality preconditioning matrix that can improve the convergence rate and perform the preconditioning matrix factorization efficiently and robustly. A reordering-based ILU(k) preconditioner is proposed to achieve the above objectives. In detail, the finite difference technique combined with the coloring algorithm is utilized to automatically construct a preconditioning matrix with low computational cost. Furthermore, the reordering algorithm is employed for the ILU(k) to reduce the additional non-zero elements and pursue robust computational performance. A 2D LRA neutron steady-state benchmark problem is used to evaluate the performance of the proposed preconditioning technique, and a steady-state neutron diffusion k-eigenvalue problem with thermal-hydraulic feedback is also utilized as a supplement. The results show that coloring algorithms can automatically and efficiently construct the preconditioning matrix. The computational efficiency of the FDP with coloring could be about 60 times higher than that of the preconditioner without the coloring algorithm. The reordering-based ILU(k) preconditioner shows excellent robustness, avoiding the effect of the fill-in level k choice in incomplete LU factorization. Moreover, its performances under different fill-in levels are comparable to the optimal computational cost with natural ordering.

Shape optimization of the energy efficiency of building retrofitted facade

The current state of research indicates a necessity of further examination in both numerical and experimental studies related to optimizing shapes of building enclosures for the enhancement of their energy efficiency. The demand for research primarily arises due to the numerical complexities associated with optimizing shapes for this specific purpose. Consequently, the primary objective of this article is to address and bridge these gaps in the field. To achieve this, a two-dimensional steady-state heat diffusion model is assumed to represent the physical processes occurring within building facades of varying shapes. A third type boundary condition is applied to the exterior boundary, encompassing convective and incident short-wave solar radiation effects. The calculation of short-wave radiation accounts for factors such as sunlight exposure and shading, influenced by the surrounding urban environment. The internal boundary interfaces with the indoor ambient air, and thus, a Robin boundary condition is adopted. To tackle the computational demands while ensuring accuracy, the boundary element method (BEM) is employed by discretizing the domain boundary into discrete elements. Then, two heat transfer design objectives are define according to the period of investigations: ones related to enhancing heat transfer and ones focused on thermal insulation problem. Last, a real-world case study is conducted, considering a house wall under varying climate conditions throughout the year. Optimal shapes for the external wall boundary are determined with the constraint that the optimized facade utilizes the same amount of material as the reference flat one. The results demonstrate a substantial increase in energy efficiency compared to the reference flat wall case.

Influence of Terrestrial Parameters on the Ecophysiological Composition of Young Plants Kahya Senegalensis in Saline Environment

This study aims at analyzing the behavior of young African mahogany plants in a saline environment, focusing on perceptions related to transpiration, photosynthetically active radiation and water potential. The experiment was conducted in drainage lysimeters, using different salinity levels of irrigation water. Environmental data, such as photosynthetically active radiation, water potential and electrical conductivity, were collected to investigate their influence on the transpiration of African mahogany plants. The research was carried out in an experimental field in the northeast region of Brazil, over a period of four months, with young African mahogany plants (Khaya senegalensis), using water with an electrical conductivity of 0.5 dS.m -1 (control treatment); 1.25 dS.m -1; 2 dS.m -1; 2.75 dS.m -1; 3.5 dS.m -1; 4.25 dS.m -1 and 5 dS.m -1 in a total of seven treatments, with three replications and 21 experimental units (plants). Plant transpiration was measured using a steady-state diffusion porometer. The electrical conductivity of the irrigation water was monitored using a portable conductivity meter. The results presented in the analyzes indicate a complex and interdependent relationship between leaf transpiration, photosynthetically active radiation and plant water potential. Leaf transpiration is influenced by variations in solar radiation, which plays a crucial role in regulating this process. It was observed that leaf transpiration is lower in the morning, from 7 to 9 am and in the late afternoon, from 5 to 6 pm, when incident solar radiation is at lower values.

Fe2B layer growth kinetics on ASTM A307 steel evaluated by two diffusion models

Abstract In this study, we implemented two simple models to simulate the growth of the Fe2B layer on ASTM A307 steel through boriding. The first model considered steady-state boron diffusion, while the second model incorporated transient regime effects. In the steady-state model, the boron concentration profile within the Fe2B layer exhibited linearity. By correlating the boron chemical potential with the inward mass flux at the (Fe2B/substrate) interface, we confirmed the parabolic nature of layer growth. Both models were employed to determine the boron activation energies, yielding the same value of approximately 164 kJ mol−1. Experimental validation of the two models was conducted under two additional boriding conditions (1323 K for 1.5 and 2 h). Finally, the simulated layer thicknesses matched with the experimental values.

Multigrid for two-sided fractional differential equations discretized by finite volume elements on graded meshes

It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As a consequence of this, and due to the conservative nature of the problem, we adopt a finite volume elements discretization approach over a generic non-uniform mesh. We focus on grids mapped by a smooth function which consists in a combination of a graded mesh near the singularity and a uniform mesh where the solution is smooth. Such a choice gives rise to Toeplitz-like discretization matrices and thus allows a low computational cost of the matrix–vector product and detailed spectral analysis. The obtained spectral information is used to develop an ad-hoc parameter-free multigrid preconditioner for GMRES, which is numerically shown to yield good convergence results in presence of graded meshes mapped by power functions that accumulate points near the singularity. The approximation order of the considered graded meshes is numerically compared with the one of a certain composite mesh given in literature that still leads to Toeplitz-like linear systems and is then still well-suited for our multigrid method. Several numerical tests confirm that power-graded meshes result in lower approximation errors than composite ones and that our solver has a wide range of applicability.

Cationic-motif-modified exosomes for mRNA delivery to retinal photoreceptors.

Topical treatment of vitreoretinal diseases remains a challenge due to slow corneal uptake and systemic clearance. Exosomes are emerging nanocarriers for drug delivery due to biocompatibility and cellular targeting properties. To apply them for retinal targeting via the topical route, exosomes must traverse various ocular barriers including the cornea, lens, vitreous humor (VH), and the retina itself. Here we engineered high-purity milk-derived exosomes by anchoring arginine-rich cationic motifs via PEG2000 lipid insertion on their surface. Modification enabled exosomes to use weak-reversible electrostatic interactions with anionic glycosaminoglycan (GAG) and water content of the tissue to enhance their transport rate and retention. Addition of cationic motifs neutralized the anionic surface charge of exosomes (-24 to -2 mV) without impacting size or morphology. Cationic-motif-modified exosomes exhibited two-fold faster steady state diffusivity through bovine corneas compared to unmodified exosomes. Fluorescence recovery after photobleaching confirmed that cationic-motif-modified exosomes can diffuse through VH without steric hindrance. In healthy VH, cationic-motif-modified exosomes demonstrated stronger binding resulting in three-fold lower average diffusivity that enhanced by six-fold in 50% GAG-depleted VH recapitulating advanced liquefaction. Cationic-motif-modified exosomes penetrated through the full-thickness of porcine retinal explants resulting in ten-fold higher uptake in photoreceptors and three-fold greater transfection with encapsulated eGFP mRNA compared to unmodified exosomes. Cationic-motif-modified exosomes are safe to use as they did not adversely affect the mechanical swelling properties of the cornea or lens nor impact retinal cell viability. Cationic-motif-modified exosomes, therefore, offer themselves as a cell-free nanocarrier platform for gene delivery to retinal photoreceptors potentially via the topical route.

Modeling large-scale bioreactors with diffusion equations. Part II: Characterizing substrate, oxygen, temperature, carbon dioxide, and pH profiles.

Large-scale fermentation processes involve complex dynamic interactions between mixing, reaction, mass transfer, and the suspended biomass. Empirical correlations or case-specific computational simulations are usually used to predict and estimate the performance of large-scale bioreactors based on data acquired at bench scale. In this two-part-study, one-dimensional axial diffusion equations were studied as a general and predictive model of large-scale bioreactors. This second part focused on typical fed-batch operations where substrate gradients are known to occur, and characterized the profiles of substrate, pH, oxygen, carbon dioxide, and temperature. The physically grounded steady-state axial diffusion equations with first- and zeroth-order kinetics yielded analytical solutions to the relevant variables. The results were compared with large-scale Escherichia coli and Saccharomyces cerevisiae experiments and simulations from the literature, and good agreement was found in substrate profiles. The analytical profiles obtained for dissolved oxygen, temperature, pH, and were also consistent with the available data. Distribution functions for the substrate were defined, and efficiency factors for biomass growth and oxygen uptake rate were derived. In conclusion, this study demonstrated that axial diffusion equations can be used to model the effects of mixing and reaction on the relevant variables of typical large-scale fed-batch fermentations.

Minimizing Interfacial Recombination in 1.8eVTriple-Halide Perovskites for 27.5% Efficient All-Perovskite Tandems.

All-perovskite tandem solar cells show great potential to enable the highest performance at reasonable costs for a viable market entry in the near future. In particular, wide-bandgap (WBG) perovskites with higher open-circuit voltage (VOC ) are essential to further improve the tandem solar cells' performance. Here, a new 1.8eV bandgap triple-halide perovskite composition in conjunction with a piperazinium iodide (PI) surface treatment is developed. With structural analysis, it is found that the PI modifies the surface through a reduction of excess lead iodide in the perovskite and additionally penetrates the bulk. Constant light-induced magneto-transport measurements are applied to separately resolve charge carrier properties of electrons and holes. These measurements reveal a reduced deep trap state density, and improved steady-state carrier lifetime (factor 2.6) and diffusion lengths (factor 1.6). As a result, WBG PSCs achieve 1.36V VOC , reaching 90% of the radiative limit. Combined with a 1.26eV narrow bandgap (NBG) perovskite with a rubidium iodide additive, this enables a tandem cell with a certified scan efficiency of 27.5%.