Diffuse Layer Model Research Articles

Mechanistic study of the adsorption capabilities of heavy metals on the surface of ferrihydrite: batch sorption, modeling, and density functional theory.

Ferrihydrite (Fh), a widely distributed mineral in the environment, plays a crucial role in the geochemical cycling of elements. This study used experimental and computational approaches to investigate the adsorption behavior of seven heavy metal ions on Fh. The pH edge analysis revealed that the adsorption capacity followed the order: Pb2+ > Cu2+ > Zn2+ > Cd2+ > Ni2+ > Co2+ > Mn2+, with Pb2+ showed the highest adsorption. Competitive adsorption was observed in multi-metal systems, and adsorption isotherms confirmed that Pb2+ and Cu2+ exhibited significantly higher equilibrium adsorption capacities than the other ions. Diffuse Layer Model (DLM) analysis indicated that for most heavy metals (HMs), [triple bond, length as m-dash]FesOM and [triple bond, length as m-dash]FewOM were the predominant adsorption species, while for Pb2+, [triple bond, length as m-dash]FesOPb dominated. Density Functional Theory (DFT) calculations were employed further to investigate the molecular interactions between HMs and Fh. The DFT results revealed that the distribution of surface iron sites on Fh strongly influences the adsorption process. Larger metal ions, such as Pb2+, form stronger coordination bonds with hydroxyl groups on the Fh surface, leading to distinct adsorption mechanisms compared to smaller ions. These findings, combining experimental and computational data, emphasize the critical role of surface iron site distribution and ion size in governing the adsorption behavior of HMs on Fh.

Revisiting the natural convection effects at ultra-low redox concentration solutions: The influence of viscosity and diameter of wire electrode

Natural convection could arise even at ultra-low redox concentration solutions (1–10 mM). Models such as convection–diffusion layer model and spontaneous convection model have been established to describe this phenomenon. However, the driving forces as well as the parameters that influence this natural convection effects are still not clear. Herein we investigated the effects of viscosity on natural convection by introducing sodium alginate (SA), which enhanced viscosity without changing the diffusion coefficient of the redox couple. Resultantly, it allowed us to obtain the relationship between microscopic flow of solutions and the thickness of natural convection layer. Moreover, wire electrodes with various diameters were also tested to reveal the natural convection effects on mass transfer. An empirical equation was established to describing the influences of solution viscosity and diameter of wire electrode on the thickness of natural convection layer in ultra-low redox concentration solutions.

Significant effect of salinity on zinc adsorption on tropical coastal and floodplain soils

AbstractRising sea levels due to climate change are causing increased salinisation of low‐lying coastal and floodplain soils, and the impact of this process on the bioavailability of plant nutrients needs to be understood as mitigation strategies are adapted. Zinc (Zn) is an element of particular importance due to its function as a micronutrient for plants including rice and other staple foods. In the current study, our aim was to investigate the effects of salinisation on zinc adsorption onto soils representing at‐risk coastal and floodplain environments, addressing in particular our knowledge gap concerning the roles that solution chemistry and soil composition play. To this end, we conducted batch adsorption experiments in the laboratory and ran geochemical models in saline solutions up to 0.7 mol L−1 ion strength incorporating both (i) a multi surface model (MSM) for surface reactions containing three phases, that is iron hydroxides, organic matter and phyllosilicate clays, and (ii) aqueous‐phase complexation to dissolved organic and inorganic ligands. Surface reactions were modelled using the diffuse double layer model, the NICA–Donnan model and an ion exchange model using the Gaines–Thomas convention. We combined the experimentally determined mass composition of surface phases with generic modelling parameters taken from the literature. We first show that increasing salinity enhances the formation of aqueous Zn‐chloride complexes in the presence of dissolved organic matter and bicarbonate, thereby decreasing the availability of free Zn2+ and supressing the partitioning of zinc to the adsorbed phase. We demonstrate using batch adsorption experiments with a calcareous hydraquent and a tropaquept, that salinity decreases zinc adsorption strongly in the pH range between 3 and 6. Satisfactory agreement between experiments and model calculations was achieved with root‐mean‐square errors ranging for different salinities between 2.88% and 2.92% for the hydraquent and between 4.59% and 2.74% for the tropaquept soil. Model predictions of adsorption were slightly inferior at low salinity for the hydraquent soil and at high salinity for the tropaquept soil, pointing possibly to an incomplete geochemical model or to a need to parametrise surface adsorption models at higher ionic strengths. Present surface models have been largely parametrised at lower ionic strength. We lastly apply the MSM to examine zinc adsorption in five endoaquepts soils, representing soil series from Bangladesh. We show that increasing salinity decreases zinc adsorption to the soil organic matter and the clay fractions. We conclude from our findings that increased soil salinity due to rising sea levels and climate change will have a significant impact on zinc cycling and possibly other micronutrients in areas where coastal soils and floodplain soils overlap, such as deltas and estuaries. In particular, we predict a decrease in zinc adsorption in acidic to neutral soils. The availability of zinc for biouptake through the roots of crop plants including rice will be significantly disturbed following salinisation, most likely affecting crop production. Our study demonstrates the potential that geochemical modelling combined with experimental data has to improve our capability to assess the effects of salinity due to rising seawater levels in vulnerable regions of the world.

Kinetics and mechanism of selective leaching of bismuth from molybdenite and bismuthinite mixed ore

In the conventional beneficiation process for handling mixed ore containing molybdenite and bismuthinite, the co-extraction issues involving molybdenum and bismuth, exemplified by mutual content of molybdenite and bismuthinite, may lead to the shutdown of the production line. Under acidic conditions, Bi3+ and Cl− can form stable coordination complex anions, whereas Mo4+, Mo6+, and Cl− do not exhibit this behavior. This insight offers a novel approach for the chemical separation of molybdenum and bismuth from mixed ore using hydrochloric acid. Through a kinetic study of the hydrochloric acid leaching process applied to bismuth extraction from mixed molybdenite and bismuthinite ore, we have investigated various factors that influence leaching efficiency, such as stirring speed, particle size, acid concentration, and reaction temperature. Experimental results and computational results have revealed that the apparent activation energy is 56 kJ mol−1. The kinetic analysis suggests that the leaching process is governed by the product layer diffusion model. Moreover, the use of hydrochloric acid in leaching the mixed ore is shown to alter the surface structure, thereby increasing the effective reaction area. This, in turn, leads to improved leaching efficiency and enhances the overall leaching process.

Arsenate and phosphate adsorption onto Mg-Fe layered double hydroxides: The charge-distribution multisite complexation (CD-MUSIC) modeling as a tool to predict competitive oxyanion behavior

The adsorption of arsenate and phosphate onto natural or synthetic layered double hydroxides (LDHs) has emerged as a promising solution to minimize the environmental effects of these compounds in soils and waters. In the present work, the adsorption of these oxyanions onto Mg-Fe LDHs in both single-ion and competitive systems was studied through wet chemistry experiments, solid-state analyses, and advanced surface complexation modeling (SCM). The Mg-Fe LDH showed a good efficiency to remove both As and P, being the pH of the system a major driver for the adsorption levels observed. Adsorption results for competitive systems showed a decrease for both oxyanions compared to the single-ion adsorption systems. The adsorption behavior is mechanistically described using two types of SCM, namely the diffusion layer model (DLM) and the charge-distribution multisite complexation model (CD-MUSIC). The later model captures better the influence of pH and ionic strength on the adsorption of arsenate and phosphate onto LDH in both single-ion and multicomponent systems. The best description of the experimental results was obtained when combining two types of surface complexes, namely monodentate inner-sphere complex at lower pH values and monodentate outer-sphere complex at higher pH values. This model approach provides more detailed information about the surface properties of LDHs, which may be beneficial for future studies dealing with LDHs as reactive phases influencing metal(loid) mobility in water or soil systems.

Recovery of lead from the leaching residue derived from zinc production plant: process optimization and kinetic modeling

ABSTRACT This study aimed to extract lead from a zinc production plant residue containing 3.67% PbO, 2.79% ZnO, 8.75% SiO2, 24.8% SO2, 2.38% Fe2O3, and 4.46% Al2O3. In this regard, response surface modeling based on the central composite design was utilized to scrutinize and optimize the operating parameters such as NaCl concentration, HCl concentration, pulp mixing rate, solid percentage, and leaching time on the leaching efficiency of lead. Our findings demonstrated that NaCl concentration and solid percentage were the most effective parameters on the leaching of lead, in which higher concentrations of chloride and lower solid contents led to an enhancement in lead recovery. To attain the maximum recovery of lead (75.72%) at room temperature, the optimum conditions were found to be 2 mol/L HCl, 350 g/L NaCl, solid percent 10%, stirring rate 300 rpm, and leaching time 90 min. The leaching kinetics was also examined based on the shrinking core models to realize the process mechanism and develop a new kinetic model. The results exhibited that the kinetics control mechanism was the product layer diffusion model with an activation energy of 16.69 kJ/mol. Finally, a kinetic model is developed based on the diffusion model and effective parameters.

Thermodynamic and kinetic modeling of electrocatalytic reactions using a first-principles approach.

The computational modeling of electrochemical interfaces and their applications in electrocatalysis has attracted great attention in recent years. While tremendous progress has been made in this area, however, the accurate atomistic descriptions at the electrode/electrolyte interfaces remain a great challenge. The Computational Hydrogen Electrode (CHE) method and continuum modeling of the solvent and electrolyte interactions form the basis for most of these methodological developments. Several posterior corrections have been added to the CHE method to improve its accuracy and widen its applications. The most recently developed grand canonical potential approaches with the embedded diffuse layer models have shown considerable improvement in defining interfacial interactions at electrode/electrolyte interfaces over the state-of-the-art computational models for electrocatalysis. In this Review, we present an overview of these different computational models developed over the years to quantitatively probe the thermodynamics and kinetics of electrochemical reactions in the presence of an electrified catalyst surface under various electrochemical environments. We begin our discussion by giving a brief picture of the different continuum solvation approaches, implemented within the abinitio method to effectively model the solvent and electrolyte interactions. Next, we present the thermodynamic and kinetic modeling approaches to determine the activity and stability of the electrocatalysts. A few applications to these approaches are also discussed. We conclude by giving an outlook on the different machine learning models that have been integrated with the thermodynamic approaches to improve their efficiency and widen their applicability.

Plasticiser leaching from polyvinyl chloride microplastics and the implications for environmental risk assessment

Microplastics in aquatic environments is a growing concern, particularly due to the leaching of chemical additives such as plasticisers. To develop comprehensive environmental risk assessments (ERAs) of high-concern polymers and plasticisers, an understanding of their leachability is required. This work investigated diethylhexyl phthalate (DEHP) and bisphenol A (BPA) leaching from polyvinyl chloride (PVC) microplastics (average diameter = 191 μm) under simulated marine conditions. Leaching behaviours were quantified using gel permeation chromatography (GPC) and thermal gravimetric analysis (TGA), and the polymer's physiochemical properties analysed using differential scanning calorimetry (DSC), Fourier Transform-Infrared Spectroscopy (FT-IR) and optical microscopy. Experimental data were fitted to a diffusion and boundary layer model, which found that BPA leaching was temperature-dependent (diffusion-limited), whereas DEHP leaching was controlled by surface rinsing. Model predictions also highlighted the importance of microplastic size on leaching dynamics. These data contribute towards greater accuracy in ERAs of microplastics, with implications for water quality and waste management, including decommissioning of plastic infrastructure.

Dose decision of HSK7653 oral immediate release tablets in specific populations clinical trials based on mechanistic physiologically-based pharmacokinetic model

HSK7653, an oral dipeptidyl peptidase-4 inhibitor administered every 2 weeks, is a candidate for the treatment of type 2 diabetes mellitus. The major elimination pathway of HSK7653 in vivo is renal excretion, and hepatic metabolism and fecal excretion of unchanged compound contribute less to the systemic clearance of HSK7653. Considering the disposition characteristics and the potential indication population of HSK7653, evaluating the HSK7653 exposure in patients with renal impairment and geriatric populations is a prerequisite for bringing more benefits to the patients. Here, a PBPK model was developed based on in vitro experimental results, such as dissolution, permeability, and metabolism, and the in vivo renal clearance, to evaluate the effects of physiological factors and food on HSK7653 exposure in specific populations, including adult and elder individuals with renal impairment and geriatric populations. Simulation results showed that the AUC of HSK7653 increased by 46%, 82%, and 129% in adult patients with mild, moderate, and severe renal impairment, and by 56%, 78%, and 101% in patients aged 65–75, 75–85 and 85–95 years, respectively. The AUC increased in the range of 62%–83%, 98%–133%, and 153%–195% in elderly patients (65–95 years) with mild, moderate, and severe renal impairment, respectively. Moreover, two different absorption model development methods (dissolution profile method and the diffusion layer model method) predicted that food had no effect on the exposure of the same simulated population. Since the predicted AUC of HSK7653 at the 10 mg dose in various specific populations was still within the relatively flat results of the exposure-response analysis, the 10 mg dose of HSK7653 was first used to explore the exposure in the renal impairment population (CTR20221952).

Research on gold leaching of carbonaceous pressure-oxidized gold ore via a highly effective, green and low toxic agent trichloroisocyanuric acid

In this work, trichloroisocynauric acid (TCCA) are used for gold leaching with the advantages of fast reaction rate, high leaching efficiency, low toxicity and environmentally friendly. In addition, an important feature is the continuous hydrolysis of TCCA in an aqueous solution to produce oxidants (HClO) while maintaining the effective chlorination concentration at a high level. The various factors affecting TCCA leaching carbonaceous pressure-oxidized gold ore were investigated and the leaching kinetics were established. According to the results of orthogonal experiments, the optimal conditions of TCCA concentration 0.25 mol L−1, NaCl concentration 50 g L−1, pH 5.5, leaching temperature 45 °C and solid-liquid ratio 1:6 could be obtained, and the gold leaching efficiency reached (88.64 ± 0.37) % within 3 h. After the three stages of TCCA leaching, a gold leaching efficiency was increased to 94.39%. Furthermore, TCCA leaching process could be divided into three steps, the findings of kinetic models revealed that in the early leaching step (0–2 h), TCCA leaching was controlled by solid products layer diffusion model, and yet shifted to be controlled by interfacial chemical reaction model in the final step. Importantly, TCCA leaching solution might be converted into a disinfectant with an effective chlorination concentration of 16.075% treated with resin adsorption and alum removal, enabling the secondary utilization of wastewater resources.

Interfacial interactions controlling adsorption of metal cations on montmorillonite

Abstract Montmorillonite (Mt) is a ubiquitous swelling clay mineral and major component of soft rocks, sediments, and soils with an inherent capability to sorb metal cations. This unique feature renders Mt important for the enrichment and mobilization of environmentally important metal cations, retardation of heavy metals and radionuclide ions, the evolution of clay mineral itself, soils and sediments, and other geological processes. Understanding the interfacial interactions of Mt with metal cations at the molecular level is of fundamental importance in all these processes, but still remains elusive, due to the chemical and structural complexity of Mt surfaces and the diverse chemistries of metal cations. In this Review, we aim to provide the reader with a comprehensive overview of the adsorption modes of metal cations on basal and edge surfaces of Mt, local chemical environments of the cation binding sites, the driving forces for metal sorption, and factors influencing the dynamics of cation uptake onto Mt surfaces. Various surface complexation models [i.e., nonelectrostatic model (NEM), constant capacitance model (CCM), diffuse layer model (DLM), and triple-layer model (TLM)], advanced spectroscopic techniques (i.e., NEM, CCM, DLM, and TLM), and atomistic simulation methods (i.e., MD, DFT, and FPMD) have been used in conjunction with macroscopic adsorption experiments to gain detailed insights into the interfacial interactions of metal cations on Mt. Mt adsorbs metal cations via three independent pathways: (1) cation exchange; (2) surface complexation; and (3) nucleation and surface precipitation. The principal driving force for cation exchange is electrostatic interaction, while chemical bonding governs the two other mechanisms that depend on the basal and edge surface properties of Mt. The siloxane cavities on the tetrahedral basal plane exhibit the strongest adsorption sites for cation exchange and are greatly affected by the the degree of Al3+/Si4+ tetrahedral substitutions. At the amphoteric edge surfaces bearing hydroxyl groups, metal cations could form mono/multiden-tate surface complexes on Mt [010] and [110] edges. Ionic strength, pH, the presence of competing cations, temperature, and layer charge have been shown to affect the adsorption mechanisms and quantity of adsorbed cations. The updated information on the interfacial interactions of metal cations with Mt basal and edge surfaces presented in this review provides an improved understanding of the enrichment of metals, formation of metal ores, and natural biogeochemical cycles, as well as may promote technological and engineering applications of this important clay mineral in environmental remediation, geological repository, petroleum exploration and extraction, and extraterrestrial research.

Application of community data to surface complexation modeling framework development: Iron oxide protolysis

This study presents a comprehensive community data-driven surface complexation modeling framework for simulating potentiometric titration of mineral surfaces. Compiled community data for ferrihydrite, goethite, hematite, and magnetite are fit to produce representative protolysis constants that can reproduce potentiometric titration data collected from multiple literature sources. Using this framework, the impact of surface complexation model type and surface site density (SSD) on the fit quality and protolysis constants can be readily evaluated. For example, the non-electrostatic model yielded a poor data fit compared to diffuse double layer model and constant capacitance models due to the absence of known surface charge effects. Regardless of the choice of iron oxide mineral, pKa1 decreased with increasing SSD while the opposite tendency was observed for pKa2. This newly developed framework demonstrates a method to reconcile community data-wide potentiometric titration data using Findable, Accessible, Interoperable, Reusable data principles to produce mineral protolysis constants that improve robustness of surface complexation models for applications in metal sorption and reactive transport modeling. The framework is readily expandable (as community data increase) and extensible (as the number of minerals increase). The framework provides a path forward for developing self-consistent, comprehensive, and updateable surface complexation databases for surface complexation and reactive transport modeling.

Multi-objective optimization of gas diffusion layer structure parameters for proton exchange membrane fuel cell

ABSTRACT As an important component of a proton exchange membrane fuel cell, the structure of gas diffusion layer affects the transmission of materials, thus affecting the heat and current density. However, the current researches on gas diffusion layer are mostly about homogeneous structure, and additionally it is unknown to the performance influenced by the structure parameters. Firstly, a gas diffusion layer (GDL) model reflecting complex structure is constructed based on a random parameter method, and a micro-element model of fuel cell is established. Secondly, a Latin hypercube sampling is used to obtain sample points and an extreme learning machine (ELM) model is formulated to fit simulation data. The ELM model is verified by comparing with the actual results. Finally, the micro-element model performance affected by the structure variables is analyzed, and the optimal structural variables are obtained. The results show that the ELM model can accurately predict the fuel cell micro-element model performance and its prediction accuracy is better than that of the back propagation (BP) neural network model. The multi-objective optimal algorithm model can obtain the optimal GDL structure parameters corresponding to the minimum temperature, maximum current density, and good oxygen concentration uniformity.

Prediction of electrostatic properties of reservoir rock in low salinity water injection into carbonate reservoirs

Geochemical modeling along with chemical reactions is one of the challenges in modeling of low salinity water injection. The most important issue in the geochemical model is to determine the correct electrical charge distribution model and its tuning parameters. The composition of the rock as well as the candidate water used is effective in determining the type of model and its parameters, so that the tuning parameters are determined based on the history of zeta potential experiments. In this study, in order to determine the correct model of electrical charge distribution and its tuning parameters in carbonate rock samples, first, equilibrium samples of Candidate water with crushed rock are subjected to static zeta potential tests. Then, the diffuse electrical double layer model is used to determine the electrical charge of the rock/water and water/oil surfaces and to predict the zeta potential. In the following, by adjusting the tuning parameters of the model to match the prediction results of the model with the history of the laboratory data, the density of the carbonate rock surface, the equilibrium constants and the kinetics of the governing reactions are determined. The obtained results show that the range of error in zeta potential prediction by the model compared to the laboratory data is from 2 to 20%, which is within the acceptable range of the performance of electrical charge distribution models. Moreover, it could be observed that the error of prediction using DLM model is significantly less than the conventional models (CD-MUSIC and BSM) for different candidate water. Finally, the effect of calculated zeta potential changes is used to calculate the contact angle changes of low salinity water injection based on the coupling of DLVO theory and geochemical model. The results of the study prove that the prediction error is less than 5% compared to the results of the static wettability tests. Based on this, according to the good match between the model and the laboratory results, it is possible to determine the properties of surface sites in surface complexation models of carbonate samples using the proposed approach and the subsequent tuning data of the geochemical model.

Modeling and spectroscopic investigation of U(VI) removal on porous amidoxime-functionalized metal organic framework derived from macromolecular carbohydrate

The investigation of interaction mechanism of U(VI) selective removal on amidoxime-functionalized metal organic framework (i.e., UiO-66(Zr)-AO) derived from macromolecular carbohydrate is conducive to apply metal organic frameworks in actual environmental remediation. The batch experiments showed that UiO-66(Zr)-AO displayed the fast removal rate (equilibrium time of 0.5 h), high adsorption capacity (384.6 mg/g), excellent regeneration performance (<10 % decrease after three cycles) towards U(VI) removal due to the unprecedented chemical stability, large surface area and simple fabrication. U(VI) removal at different pH can be satisfactorily fitted by diffuse layer modeling with cation exchange at low pH and an inner-sphere surface complexation at high pH. The inner-sphere surface complexation was further demonstrated by X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) analysis. These findings revealed that UiO-66(Zr)-AO can be an effective adsorbent to remove the radionuclides from aqueous solution, which is crucial for recycling of uranium resource and decreasing the uranium harm to the environment.

Excitation of structures by partially correlated pressures: A review of diffuse acoustic field and turbulent boundary layer models

Structures are sometimes excited by pressure distributions which exhibit complex spatial correlation. This differs from common acoustic excitations since the pressure at one location is only partially correlated with the pressure at another location due to inherent spatial randomness within the forcing function. Two forcing functions which exhibit partially-correlated pressures are the diffuse acoustic field (DAF) and turbulent boundary layer (TBL) flow. A basic model for representing the spatial correlation for these two forcing functions will be reviewed in both the spatial and wavenumber domains. Recent approaches for computing the vibration of structures excited by DAF or TBL flow will then be summarized. Interesting physical effects, such as intermodal coupling, will be highlighted to illustrate the importance of properly modeling partial correlations when they exist.

Understanding plasticiser leaching from polystyrene microplastics.

Plastic pollution in our oceans is of growing concern particularly due to the presence of toxic additives, such as plasticisers. Therefore, this work aims to develop a comprehensive understanding of the leaching properties of plasticisers from microplastics. This work investigates the leaching of phthalate acid ester (dioctyl terephthalate (DEHT) and diethylhexyl phthalate (DEHP)) and diphenol (bisphenol A (BPA) and bisphenol S (BPS)) plasticisers from polystyrene (PS) microplastics (mean diameter = 136 μm to 1.4 mm) under controlled aqueous conditions (temperature, agitation, pH and salinity). The leaching behaviours of plasticised polymers were quantified using gel permeation chromatography, high performance liquid chromatography and thermal gravimetric analysis, and the particle's plasticisation characterised using differential scanning calorimetry. Leaching rates of phthalate acid ester and diphenol plasticisers were modelled using a diffusion and boundary layer model, whereby these behaviours varied depending on their plasticisation efficiency of PS, the size of the microplastic particle and the surrounding abiotic conditions. Leaching behaviours of DEHT and DEHP were strongly influenced by the microplastic-surface water boundary layer properties, thus wave action (i.e., water agitation) increased the leaching rate of these plasticiser up to 66 % over 21-days, whereas BPA and BPS plasticisers displayed temperature- and size-dependent leaching and were limited by molecular diffusion throughout the bulk polymer (i.e., the microplastic). This information will improve predictions of plasticiser concentration (both that remain in the plastic and released into the surrounding water) at specific time points during the lifetime of a plastic, ultimately ensuring greater accuracy in the assessment of toxicity responses and environmental water quality.

Narrowband aperiodic multilayers with flat spectral response for plasma diagnostics

Aperiodic W/Si multilayer mirrors with the narrow bandwidth and the flat spectral response are presented as X-ray reflectors operated at 8.05 keV for plasma diagnostics. In this manuscript, aperiodic W/Si samples with different periods and thickness ranges were prepared on ultra-smooth silicon (100) substrates by direct-current magnetron sputtering. Grazing incidence X-ray reflection measurements were conducted to characterize the thickness distribution and the interfacial width of multilayer samples. Depth profiles of major elements in a periodic multilayer were investigated using time-of-flight secondary ion mass spectrometry to qualitatively estimate the effect of impurities from the residual gas. Cross-sectional transmission electron microscope images of the aperiodic multilayer indicate the asymmetric interfaces with the increasing interfacial width. The cumulative roughness model and the diffusion layer model were employed to fit the thickness sequence, interfacial roughness and diffusion zone width from GIXRR curves for further optimization with the given interfacial effect. The reflection spectrum of the optimal W/Si sample was measured at the beamline BL09B of Shanghai Synchrotron Radiation Facility. The measured results of the aperiodic W/Si multilayer exhibit the (56.2 ± 1.3)% reflectivity, 936eV bandwidth and 581eV flat-band region.

Improvement of diffusion layer model for steam condensation in the presence of non-condensable gas under turbulent free convection

Steam condensation plays a crucial role in predicting the pressure behavior and hydrogen distribution in nuclear power plant containment during a postulated loss-of-coolant accident or a severe accident. The stagnant film model and diffusion layer model are two commonly used heat and transfer analogy models for predicting film-wise condensation in the presence of non-condensable gas on a vertical wall in the nuclear engineering field. This study proposed a general formula for the equivalent condensation thermal conductivity, which can be used to convert between the traditional diffusion layer model and the stagnant film model. An improved diffusion layer model is established, which can be used to analyze steam condensation in the presence of non-condensable gas on a vertical flat surface or outer surface of condenser tubes under turbulent free convection. The density difference of water vapor at the bulk and at the gas–liquid interface is the driving force for steam condensation in the improved model, the traditional diffusion layer model’s assumption, e.g., diffusion layer thickness, constant gas mixture density, and the application of modified Clausius-Clapeyron equation, are no longer used. The newly established model also divides the condensation process into liquid film heat transfer, latent heat transfer, and sensible heat transfer. The three parts of heat transfer processes are linked together by the equivalent heat flux on both sides of the gas–liquid interface. The effects of gas compressibility, suction, fog formation, and liquid film waviness have been considered in this study. The influences of gas compressibility, the thermal resistance of condensate film, and sensible heat transfer on modeling steam condensation were discussed. Compared with various sources of experimental data (619 data points), more than 97% of the model predicted results are within the ±25.0% error band, and the mean absolute relative error is 10.2%, which indicates that the newly proposed model has high accuracy and widely applicable ranges.

Physiologically Based Pharmacokinetics Modeling in Biopharmaceutics: Case Studies for Establishing the Bioequivalence Safe Space for Innovator and Generic Drugs.

For successful oral drug development, defining a bioequivalence (BE) safe space is critical for the identification of newer bioequivalent formulations or for setting of clinically relevant in vitro specifications to ensure drug product quality. By definition, the safe space delineates the dissolution profile boundaries or other drug product quality attributes, within which the drug product variants are anticipated to be bioequivalent. Defining a BE safe space with physiologically based biopharmaceutics model (PBBM) allows the establishment of mechanistic in vitro and in vivo relationships (IVIVR) to better understand absorption mechanism and critical bioavailability attributes (CBA). Detailed case studies on how to use PBBM to establish a BE safe space for both innovator and generic drugs are described. New case studies and literature examples demonstrate BE safe space applications such as how to set in vitro dissolution/particle size distribution (PSD) specifications, widen dissolution specification to supersede f2 tests, or application toward a scale-up and post-approval changes (SUPAC) biowaiver. A workflow for detailed PBBM set-up and common clinical study data requirements to establish the safe space and knowledge space are discussed. Approaches to model in vitro dissolution profiles i.e. the diffusion layer model (DLM), Takano and Johnson models or the fitted PSD and Weibull function are described with a decision tree. The conduct of parameter sensitivity analyses on kinetic dissolution parameters for safe space and virtual bioequivalence (VBE) modeling for innovator and generic drugs are shared. The necessity for biopredictive dissolution method development and challenges with PBBM development and acceptance criteria are described.