Fick's Law Of Diffusion Research Articles

Heat and mass transfer during conductive drying of washing phosphate sludge

This study investigates the influence of drying temperature on the conductive drying behavior of washing phosphate sludge. A mathematical model, based on Fourier's Fick diffusion law and the heat transfer equation, was developed to simulate coupled heat and mass transfer during the drying process, incorporating the shrinkage effect. The sludge samples, obtained from the Khouribga phosphate plant in Morocco, were subjected to drying at temperatures of 70°C and 95°C. The experimental setup included continuous monitoring of temperature, humidity, and mass loss throughout the process. COMSOL Multiphysics software was used to solve the nonlinear equations governing heat and mass transfer. Results indicate that increasing the drying temperature significantly accelerates the drying rate. The model successfully predicts the moisture content and temperature distribution over time, aligning well with experimental data. Statistical validation, using the determination coefficient (R²) and root mean square error (RMSE), confirms that the model accurately describes the drying behavior, with R² values of 0.9957 and 0.9967 at 70°C and 95°C, respectively. The inclusion of the shrinkage effect enhances the model's precision in describing the drying kinetics under varying conditions.

Poly (lactic acid) electrospun nanofiber membranes: Advanced characterization for biomedical applications with drug loading performance studies

Traditional dressings have shortcomings such as poor moisture absorption and easy to adhere, making the development of new dressings crucial. In this work, a PLA/PVP crosslinked drug-loaded nanofiber membrane was prepared through electrospinning and ultraviolet crosslinking, with poly (lactic acid) (PLA), polyvinylpyrrolidone (PVP), and salicylic acid (SA) as starting materials. The results demonstrated that the inclusion of PVP notably boosted the viscosity and conductivity of the blend spinning solution. The roughness of the fabricated fiber was elevated, and the diameter of the fibers was more uniform. Additionally, the incorporation of PVP not only enhanced the porosity of the fiber membrane but also effectively decreased its contact angle. Notably, when the PVP content reached 40 %, the contact angle underwent a substantial reduction, decreasing significantly from 125.4° to 82.2°. The SA drug-loaded fiber membrane exhibited a notable bacteriostatic effect against Escherichia coli and Staphylococcus aureus, with its release behavior adhering to Fick's diffusion law. In the cell viability experiment, the cell proliferation rate increased from 94 % to 129 % after 3 days. This shows that the prepared membrane has good antibacterial effect and cell compatibility, which provides a theoretical basis for the construction of a new medical dressing.

Comparison of permeability of topical Cream drug through polymer synthetic membranes of different structures using Franz Cell diffusion test

In this study, in-vitro release experiments were performed using a Franz Diffusion Cell system for Terbinafine Hydrochloride, which is used in the treatment of various fungal infections in the skin caused by many susceptible dermatophytes. In order to evaluate TH transdermally, it was aimed to compare the permeability between polymeric membranes synthesized with polyvinyl alcohol and chitosan mixtures and commercial membranes. In the transdermal drug delivery system calculations, the Fick Diffusion Law was modified and the obtained data were compared. The study was evaluated according to the USP <1724> topical drug products in semisolid form - performance tests. A new high-performance liquid chromatography method was validated for the assay of TH released into the receptor medium in accordance with the ICH guideline. According to the results obtained during the validation process, the limit of detection value was calculated as 0.005 µg/mL and the limit of quantification value was 0.013 µg/mL. Since polymer-based synthetic membranes provide permeability according to molecular size, properties and the ideal environment for measuring and analyzing the diffusion rate of a compound, in experiments conducted using membranes of different structures, the permeability profiles of selected polymer synthetic membranes were statistically evaluated. It has been noted that the hydroxyl groups in PVA and the hydrophilic CS-g-PNDMAAm graft copolymer act at varying rates to enhance or reduce the permeability across the membrane by promoting its diffusion. NaY zeolite has been shown to function as an adsorbent against the medication, lessening the impact of hydrophilic PVA without supplying permeability.

Modeling of the Time-Dependent H2 Emission and Equilibrium Time in H2-Enriched Polymers with Cylindrical, Spherical and Sheet Shapes and Comparisons with Experimental Investigations.

Time-dependent emitted H2 content modeling via a reliable diffusion analysis program was performed for H2-enriched polymers under high pressure. Here, the emitted hydrogen concentration versus elapsed time was obtained at different diffusivities and volume dimensions for cylinder-, sphere- and sheet-shaped specimens. The desorption equilibrium time, defined as the time when the H2 emission content is nearly saturated, was an essential factor for determining the periodic cyclic testing and high-pressure H2 exposure effect. The equilibrium time in the desorption process was modeled. The equilibrium time revealed an exponential growth behavior with respect to the squared thickness and the squared diameter of the cylinder--shaped specimen, while it was proportional to the squared diameter for the sphere-shaped specimen and to the squared thickness for the sheet-shaped specimen. Linear relationships between the reciprocal equilibrium time and diffusivity were found for all shaped polymers. The modeling results were confirmed by analysis of the solutions using Fick's second diffusion law and were consistent with the experimental investigations. Numerical modeling provides a useful tool for predicting the time-dependent emitted H2 behavior and desorption equilibrium time. With a known diffusivity, a complicated time-dependent emitted H2 behavior with a multi-exponential form of an infinite series could also be predicted for the three shaped samples using a diffusion analysis program.

Hygrothermal aging effect on static and fatigue behavior of three-dimensional five-directional hybrid braided composites under tension

This paper attempts to study the hygrothermal aging effect on static and fatigue behavior of carbon/glass fiber three-dimensional five-directional (3D5D) hybrid braided composites under tension. Firstly, moisture absorption tests and micro-CT scanning analysis were conducted on the composite specimens. The results show that the moisture absorption behavior follows the Fickian diffusion law well and the aging damage is dominated by matrix cracks/pores and interfacial debonding which is more severe in the braiding glass fiber yarn and surrounding regions than the axial carbon fiber yarn and surrounding regions. Then tensile tests and fatigue tests were performed on the unaged and aged composite specimens. It was found that hygrothermal aging has significant detrimental influence on the static tensile and tension-tension fatigue behavior of the composites. From experimental observations and failure analysis, it was also concluded that hygrothermal aging has impact on the failure mechanisms of the composites under both static tensile and fatigue loading owing to the extensively existed aging damage and deteriorated material properties in the aged composites.

Morphological, thermal and mechanical properties of wheat‐straw reinforced copper nanocomposite

AbstractThe work summarizes an innovative nanocomposite including synthesized copper nanoparticle (CuNP) impregnated wheat straw (WS) (the agronomic waste from an wheat plant) reinforced unsaturated polyester resin has been established. The addition of nanoparticles (NPs) increased the antifungal properties (~11%), durability (~9%), and strength (~39%) of the composites. Therefore, these nanoparticles have been synthesized from a copper chloride dihydrate precursor and they have been impregnated into wheat straw via cationization. This copper‐impregnated wheat straw (CuIWS) was formulated and employed to create a strong and long‐lasting nanocomposite with unsaturated polyester resin. Their morphological, mechanical, chemical, biodegradability (BD), and thermal properties were estimated and relationships were explicated systematically. Particularly, the tensile strength of polyester resin, crude and treated WS (cationized and copper‐impregnated) composites were 11.70, 14.20, 20.92, and 22.34 N/mm2 respectively. Therefore the reinforcement capability for crude, cationized and copper‐impregnated WS composites increased by ~22%, 75%, and 92% respectively. The residual ash was just about 16.23%, 12.04% and 6.56% for copper impregnated wheat straw composite (CuIWSC), Cationized wheat straw composite (CWSC) and untreated wheat straw composite (UTWSC) respectively point to the existence of ~4.1% Cu incorporated into the wheat straw which holds up the energy dispersive x‐ray (EDX) spectra of ~4.2% copper content. Thermogravimetric analysis (TGA) indicates that the nanocomposites are stable up to 325°C. These nanocomposites also show superlative crystallinity compared to other ones. Water uptake capacity followed typical Fickian diffusion law. The developed nanocomposites might be suitable for automobile and aircraft parts, furniture, and other indoor to outdoor applications.Highlights TS of the composites increased by increasing the WS filling up to 15%. The crystallinity increased after the addition of nanoparticles. The typical water uptake properties followed the Fickian diffusion rule. Incorporation of nanoparticles increased 11% antifungal properties. The developed nanocomposites are used for inside and outside applications.

The process of sucrose crystallization in the supersaturated solution

Crystallization processes of the solid phase in supersaturated solutions of products of plant origin are used in processing technologies. The theory of diffusion (molecular) mass transfer of the target substance has become widespread when solving problems of technology improvement. The driving force of this process is the difference in the concentration of the solid phase in the solution towards the crystallization center, where the concentration of the solid phase is reduced. During the analytical and quantitative study of the process of solid phase deposition in the crystallization center, Fick's diffusion laws have been used. The influence of solution temperature, concentration of the solid phase, its geometry and dispersed composition on the course of this process have been considered. Based on a diffusion model of the process of crystal formation of sucrose in a vacuum apparatus, a numerical analysis of factors in sugar production technology not covered in the literature has been presented. The problem of quantitative analysis of the process of sucrose crystallization in the working volume of a vacuum apparatus for the production of sugar and other products of plant origin of high commercial standards requires further in-depth study.

Ultrasound-assisted extraction of emodin from Rheum officinale Baill and its antibacterial mechanism against Streptococcus suis based on CcpA

Emodin was extracted from Rheum officinale Baill by ultrasound-assisted extraction (UAE), and ethanol was chosen as the suitable solvent through SEM and molecular dynamic simulation. Under the optimum conditions (power 541 W, time 23 min, liquid to material ratio 13:1 mL/g, ethanol concentration 83 %) predicted by RSM, the yield of emodin was 2.18 ± 0.11 mg/g. Moreover, ultrasound power and time displayed the significant effects on the extraction process. Extracting dynamics analysis indicated that the extraction process of emodin by UAE conformed to Fick's second diffusion law. The results of antibacterial experiments suggested that emodin can damage cell membrane and inhibit the expression of cps2A, sao, mrp, epf, neu and the hemolytic activity of S. suis. Biolayer interferometry and FT-IR multi-peak fitting assays demonstrated that emodin induced a secondary conformational shift in CcpA. Molecular docking and molecular dynamics confirmed that emodin bound to CcpA through hydrogen bonding (ALA248, GLU249, GLY129 and ASN196) and π-π T-shaped interaction (TYR225 and TYR130), and the mutation of amino acid residues affected the affinity of CcpA to emodin. Therefore, emodin inhibited the sugar utilization of S. suis through binding to CcpA, and CcpA may be a potential target to inhibit the growth of S. suis.

A Grey-box Model with Neural Ordinary Differential Equations for the Slow Voltage Dynamics of Lithium-ion Batteries: Model Development and Training

Lithium-ion batteries exhibit slow voltage dynamics on the minute time scale that are usually associated with transport processes. We present a novel modelling approach toward these dynamics by combining physical and data-driven models into a Grey-box model. We use neural networks, in particular neural ordinary differential equations. The physical structure of the Grey-box model is borrowed from the Fickian diffusion law, where the transport domain is discretized using finite volumes. Within this physical structure, unknown parameters (diffusion coefficient, diffusion length, discretization) and dependencies (state of charge, lithium concentration) are replaced by neural networks and learnable parameters. We perform model-to-model comparisons, using as training data (a) a Fickian diffusion process, (b) a Warburg element, and (c) a resistor-capacitor circuit. Voltage dynamics during constant-current operation and pulse tests as well as electrochemical impedance spectra are simulated. The slow dynamics of all three physical models in the order of ten to 30 min are well captured by the Grey-box model, demonstrating the flexibility of the present approach.

A coupled hygro-elastic 3D model for steady-state analysis of functionally graded plates and shells

Abstract This 3D coupled hygro-elastic model proposes the three-dimensional (3D) equilibrium equations associated with the 3D Fick diffusion equation for spherical shells. The primary unknowns of the problem are the displacements and the moisture content. This coupled 3D exact shell model allows to understand the effects of the moisture field in relation with the elastic field on stresses and deformations in different plates and shells. This model is specifically developed for configurations including functionally graded material (FGM) layers. Four different geometries are analyzed using an orthogonal mixed curvilinear reference system. The main advantage of this reference system for spherical shells is the degeneration of the equations to those for simpler geometries. The solving method is the exponential matrix method in the thickness direction. The closed-form solution is possible because of simply supported sides and harmonic forms for displacements and moisture content. The moisture content amplitudes are directly applied at the top and bottom outer faces through steady-state hypotheses. The final system is based on a set of coupled homogeneous second-order differential equations. The moisture field effects are evaluated for the static analysis in terms of displacement, strain, and stress components. After preliminary validations, used to better understand how to properly define the calculation of the curvature-related terms and FGM properties, four new benchmarks are proposed for several thickness ratios, geometrical data, FGM configurations, and moisture values imposed at the external surfaces. From the results, it is clear the accordance between the uncoupled hygro-elastic model and this new coupled hygro-elastic model when the 3D Fick diffusion law is employed. Both effects connected with the thickness layer and the embedded material are included in the 3D hygro-elastic analyses proposed. The 3D coupled hygro-elastic model is simpler than the uncoupled one because the 3D Fick diffusion law does not have to be separately solved.

Fractal derivative model with time dependent diffusion coefficient for chloride diffusion in concrete

More research and experiments have indicated that, under different water cement ratios, the binding effect of concrete on chloride ions and the blocking effect of hydration on chloride ions are clearly dominant. During this time period, the diffusion rate of chloride ions will increase or decrease with time, resulting in the classical Fickian diffusion law no longer being applicable. This study establishes an improved fractal model with a time-dependent diffusion coefficient for chloride diffusion in concrete. An explicit solution is derived in terms of the complementary error function. The proposed model is verified by fitting the chloride ion concentration data from different concrete immersion tests. The results show that the fractal model can fit the data in different spatial scales, and the corresponding prediction accuracy is rather high when compared to the three integer order models with constant, variable diffusion coefficient, and curing age. Therefore, the fractal derivative model is feasible in describing the anomalous diffusion of chloride ions in concrete.

Hygro-Elastic Coupling in a 3D Exact Shell Model for Bending Analysis of Layered Composite Structures

In this work, a 3D fully coupled hygro-elastic model is proposed. The moisture content profile is a primary variable of the model’s displacements. This generic fully coupled 3D exact shell model allows the investigations into the consequences arising from moisture content and elastic fields in terms of stresses and deformations on different plate and shell configurations embedded in composite and laminated layers. Cylinders, plates, cylindrical and spherical shells are analyzed in the orthogonal mixed curvilinear reference system. The 3D equilibrium equations and the 3D Fick diffusion equation for spherical shells are fully coupled in a dedicated system. The main advantage of the orthogonal mixed curvilinear coordinates is related to the degeneration of the equations for spherical shells to simpler geometries thanks to basic considerations of the radii of curvature. The exponential matrix method is used to solve this fully coupled model based on partial differential equations in the thickness direction. The closed-form solution is related to simply supported sides and harmonic forms for displacements and the moisture content. The moisture content amplitudes are directly applied at the top and bottom outer faces through steady-state hypotheses. The final system is based on a set of coupled homogeneous second-order differential equations. A first-order differential equation system is obtained by redoubling the number of variables. The moisture field implications are evaluated for the static analysis of the plates and shells in terms of displacement and stress components. After preliminary validations, new benchmarks are proposed for several thickness ratios, geometrical and material data, lamination sequences and moisture values imposed at the external surfaces. In the proposed results, there is clearly accordance between the uncoupled hygro-elastic model (where the 3D Fick diffusion law is separately solved) and this new fully coupled hygro-elastic model: the differences between the investigated variables (displacements, moisture contents, stresses and strains) are always less than 0.3%. The main advantages of the 3D coupled hygro-elastic model are a more compact mathematical formulation and lower computational costs. Both effects connected with the thickness layer and the embedded materials are included in the conducted hygro-elastic analyses.

Use of carminic acid immobilized in agarose gel as a binding phase for DGT: A new approach for determinations of rare earth elements

Recently, rare-earth elements (REEs) have attracted great interest due to their importance in several fields, such as the high-technology and medicine industries. Due to the recent intensification of the use of REEs in the world and the resulting potential impact on the environment, new analytical approaches for their determination, fractionation and speciation are needed. Diffusive gradients in thin films are a passive technique already used for sampling labile REEs, providing in situ analyte concentration, fractionation and, consequently, remarkable information on REE geochemistry. However, data based on DGT measurements until now have been based exclusively on the use of a single binding phase (Chelex-100, immobilized in APA gel). The present work proposes a new method for the determination of rare earth elements using an inductively coupled plasma‒mass spectrometry technique and a diffusive gradients in thin films (DGT) technique for application in aquatic environments. New binding gels were tested for DGT using carminic acid as the binding agent. It was concluded that acid dispersion directly in agarose gel presented the best performance, offering a simpler, faster, and greener method for measuring labile REEs compared to the existing DGT binding phase. Deployment curves obtained by immersion tests in the laboratory show that 13 REEs had linearity in their retention by the developed binding agent (retention x time), confirming the main premise of the DGT technique obeying the first Fick's diffusion law. For the first time, the diffusion coefficients were obtained in agarose gels (diffusion medium) and carminic acid immobilized in agarose as the binding phase for La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm, Yb and Lu, which were 3.94 × 10−6, 3.87 × 10−6, 3.90 × 10−6, 3.79 × 10−6, 3.71 × 10−6, 4.13 × 10−6, 3.75 × 10−6, 3.94 × 10−6, 3.45 × 10−6, 3.97 × 10−6, 3.25 × 10−6, 4.06 × 10−6, and 3.50 × 10−6 cm2 s−1, respectively. Furthermore, the proposed DGT devices were tested in solutions with different pH values (3.5, 5.0, 6.5 and 8) and ionic strengths (I = 0.005 mol L−1, 0.01 mol L−1, 0.05 mol L−1 and 0.1 mol L−1 – NaNO3). The results of these studies showed an average variation in the analyte retention for all elements at a maximum of approximately 20% in the pH tests. This variation is considerably lower than those previously reported when using Chelex resin as a binding agent, particularly for lower pH values. For the ionic strength, the maximum average variation was approximately 20% for all elements (except for I = 0.005 mol L−1). These results indicate the possibility of a wide range of the proposed approach to be used for in situ deployment without the use of correction based on apparent diffusion coefficients (as required for using the conventional approach). In laboratory deployments using acid mine drainage water samples (treated and untreated), it was shown that the proposed approach presents excellent accuracy compared with data obtained from Chelex resin as a binding agent.

Quantitative study on release kinetics of thymol in food packaging films

A potato starch slow-release antibacterial film was prepared with mesoporous nano-silica (MCM-41) as a carrier to load thymol (Thy) by ultrasonic method. In order to evaluate the effect of temperature on the quantitative release of thymol from the film, release kinetics of thymol under different temperatures (5 °C, 10 °C, 20 °C, and 40 °C) were analyzed based on high-performance liquid chromatography (HPLC). Thy-MCM-41/potato starch film has good mechanical properties. Its tensile strength (TS), elastic modulus (EM) and elongation at break (EB) were 6.74 MPa, 34.94 MPa and 78.21%, respectively. Additionally, this film had a small WVP value (5.32 g m −1 ·h −1 ·Pa −1 ), indicating that the film had a good water barrier performance. For short-term diffusion, the estimated n-values were between 0.3978 and 0.4064, following Fick's diffusion law. The diffusion coefficient (D P ) was increased with increasing temperature. For long-term diffusion, the D P values were decreased by 10 2 times compared with short-term diffusion, and the partition coefficient (K P, F ) decreased as the temperature increased. The values of D P and K P, F reached 42.584 × 10 −12 cm 2 s −1 , 0.893, respectively, when the temperature was 40 °C. This work offers a new method for the preparation of potato starch sustained-release antibacterial film, and provides a theoretical basis and technical support for the development of active packaging. • Thy-MCM-41 improved the mechanical and physical properties of potato starch film. • The release kinetics into 50% ethanol followed Fick's diffusion law. • Thymol release was initially explosive, and then continuous. • Low temperature can prolong the release time of thymol.

Surface plasmon resonance chemical sensor modified with α-naphthylmethacrylate nano thin film for chloroform detection

The research on the rapid and sensitive detection of pollution caused by the products and technologies used has recently attracted attention in the literature. In the detection of volatile organic compounds (VOCs), polymers/monomers are used in the production of sensitive, fast-responding, reversible thin-film gas sensor elements. In this work, the monomer α-Naphthylmethacrylate was selected as thin film sensor element. The α-Naphthylmethacrylate-based nano thin films were prepared with technique of LB. Monomer LB thin films fabricated onto gold-coated glass substrate to investigate their vapour sensing properties by using Surface Plasmon Resonance (SPR) optical technique. This prepared monomer-based thin film sensor exposed to five different concentrations of chloroform vapors varying between 13.98x103-69.9x103 ppm and the sensor response values were recorded. Swelling dynamics’ of this monomer thin film sensor was also illuminated by using Fick's early-time diffusion law. Diffusion coefficients of α-Naphthylmethacrylate LB thin film sensor materials exposed to the five different concentrations of chloroform vapor were calculated with the help of reflected light intensity graph data and Fick's Law as a function of time. It was determined that the diffusion coefficient values of the first and second slope regions as varying between 5.72x10-17-21.97x10-17 cm2s-1 and 3.06x10-17-6.25x10-17 cm2s-1, respectively. SPR kinetic measurement results showed that α-Naphthylmethacrylate material is promising for the detection of chloroform vapor.

Numerical analysis of reinforced concrete beam subject to pitting corrosion

Abstract This paper presents a numerical study about the effects of chloride-induced corrosion on the service life of structures. A two-dimensional geometrically nonlinear mechanical model based on Finite Element Method (FEM) was developed for reinforced concrete structures. The corrosion initiation stage was evaluated by Fick's diffusion laws. The corrosion propagation was carried out by deterministic models based on Faraday's law. Pitting corrosion was simulated in the reinforcements by pit elements, distributed longitudinally on the steel rebars, which degrade the physical properties over time. The service life was determined by the crack width.Two parametric analyses were performed. In the first analysis, five models were created with a variablecover thickness and water/cement ratio (w/c). In the second analysis, the reduction in yield stress due to corrosion was considered.The results showed that the concrete cover thicknessand the w/c ratio significantly influence the service life. The reduction of the cover thickness from 30 mm to 25 mm resulted in 21.26% reduction in service life, whilethe increase in the w/c ratio from 0.50 to 0.55 caused 32.98% reduction in service life of the structural element analyzed.

The effect of water and sodium hydrogen carbonate content on flexible polyurethane's microstructure, water, and mechanical properties

AbstractIt is well known that blowing agents (BAs) and polyol are essential components in polyurethane (PU) composition. Utilizing renewable sources in the material's formulation might reduce its environmental hazards while extending its possible engineering applications. In this study, the samples have been synthesized by using palm kernel oil‐based polyol (PKOP). Water and sodium hydrogen carbonate (SHB) have been used as BAs. Scanning electron microscopy (SEM) has shown that adding the mix of BAs is causing the cells' average size to increase up to 227% and have reduced the lamellae width by up to 2% in comparison with the reference sample. The water tests have illustrated that combining two parts per hundred polyol by weight (php) water and 25 php SHB to the sample has increased its water capacity up to 617%. However, the samples are only able to retain 6% of the absorbed water at the 7th day. It has been also found that porosity has affected the water uptake and all the samples are following Fick's diffusion law, and diffusion is correlated to the square root of time. Multivariable power least squares method (MPLSM) and moving least squares method (MLSM) have been applied to find the relation between tear resistance value and BAs ratio. It is found that both methods have a dominant variable compared to the other variables, but MLSM provided optimizable equation with better R2.

Preparation and dynamic behavior of W-Mo-Y co infiltrated layer on the surface of 45 steel parts

In this paper, W-Mo-Y co infiltration were carried out on the surface of 45 steel wedge components by plasma solid-state surface metallurgy technology. The phase, hardness, friction and wear properties before and after W-Mo co infiltration and W-Mo-Y co infiltration were systematically studied. The diffusion kinetics such as diffusion coefficient and diffusion activation energy were calculated by Fick's second diffusion law, and the effect of Y on the diffusion of W and Mo atoms in the infiltrated layer was obtained. It is found that the addition of rare earth Y element increases the diffusion coefficient of W and Mo atoms and reduces the diffusion activation energy, which has a certain catalytic effect. And the W-Mo-Y co infiltration significantly improves the surface hardness and wears resistance of the parts and prolongs the service life of the parts.

Effects of stress-assisted migration on potentiostatic intermittent titration technique (PITT) in spherical particles

Determining the chemical diffusion in active materials is crucial to the modeling and simulation of the chemo-mechanical interaction during electrochemical cycling of lithium-ion batteries, in which the diffusion coefficient of lithium plays an important role in describing the migration of lithium. Among the existing electrochemical measurement techniques, potentiostatic intermittent titration technique (PITT) is relatively reliable in determining diffusion coefficient in an electrochemical system since this technique relies only on the electrode dimension, i.e. the electrode thickness or the particle radius. In this work, a two-way coupling chemo-mechanical model is established to investigate the electrode transient current under PITT operation by incorporating the contribution of mechanical energy (hydrostatic stress) in chemical potential. The electrode transient current with the contribution of hydrostatic stress is compared to the counterpart with classical Fick diffusion law. Two key factors controlling the stress-diffusion coupling in the analysis of the electrode transient current under PITT operation are investigated, i.e. partial molar volume and elastic modulus of spherical particle. A ratio of the “intrinsic” diffusion coefficient to the nominal diffusion coefficient is defined to quantitively analyze the effects of the stress-diffusion coupling on the diffusion coefficient determined from PITT operation. The numerical results reveal that a large partial molar volume and/or a large elastic modulus will result in significant deviation of the diffusion coefficient by using PITT technique without considering the stress-diffusion coupling effects.

Quantitatively relating the structural performance of polyamide layer with skin layer modified via in-situ precipitation

How the structure of skin layer determines the structure of incipient film and final membrane formed during interfacial polymerization is decisive for polyamide composite membranes but difficult to monitor. This work introduced a methodology to predict an estimated initial molar ratio between monomers (η) via introducing pore diameter (dp), porosity (εSkin), tortuosity (τSkin), and thickness (lSkin) of skin layer to Fick's diffusion law to correct flux of monomers. The structure of skin layer was regulated via in-situ preparation of sacrificial precipitation. With characterized parameters of dp = 25.91 nm, εSkin = 8.32%, τSkin = 7.41, and lSkin = 260 nm, η was 4.25. The resultant forward osmosis membrane exhibited flux of 58.83 ± 3.58 L/(m2·h) and reverse salt flux of 10.68 ± 2.38 g/(m2·h) under AL-DS mode with 1.0 mol/L NaCl and DI as draw and feed solution, respectively, which had broken historical upper boundary. The proposed methodology can make quantitative prediction for the structural performance of polyamide composite membranes.