Diffusion-reaction Models Research Articles

The Thermal-Oxidation Behavior of Pristine and Doped Magnéli Phase Titanium Oxides

Magnéli phase titanium oxides (Ti n O 2n-1 , 4 < n < 10)1 are promising alternatives to carbon-based materials in aqueous electrochemical technologies,2 –5 but their passivation during operation remains an important challenge to address.6 –8 To elucidate the mechanism for their oxidation and to investigate the influence of doping on their oxidation stability, the thermal-oxidation behavior in air of Ti4O7 doped with V, Cr, Fe, and Ga was investigated by thermogravimetric analysis. Both thermal and electrochemical oxidation of Ti4O7 form the electrically-insulating TiO2 in sufficiently oxidizing conditions. V- and Fe-doping improved the thermal stability of Ti4O7 as evidenced by higher onset temperatures in their thermograms. Three-dimensional diffusion reaction models adequately describe the solid-state kinetics of thermal oxidation of Ti4O7 in air as demonstrated by linear model-fitting. Doping shows a mixed influence on these kinetics reducing both the Arrhenius pre-exponential factor and the activation energy. Cr-doping significantly shortens the lifetime of Ti4O7 in ambient conditions as determined by kinetic predictions. References S. Andersson, B. Collén, B., U. Kuylenstierna and A. Magnéli, A. Acta Chem. Scand., 11, 1641 (1957).J. R. Smith, F. C. Walsh and R. L. J. Clarke, J. Appl. Electrochem., 28, 1021 (1998).F. C. Walsh and R. G. A. Wills, Electrochim. Acta, 55, 6342 (2010).B. Xu, H. Y. Sohn, Y. Mohassab and Y. Lan, RSC Adv., 6, 79706 (2016).B. P. Chaplin, Acc. Chem. Res., 52, 596 (2019).W. Kao, P. Patel, P. and S. L. Haberichter, J. Electrochem. Soc., 144, 1907 (1997).G. Chen, C. C. Waraksa, H. Cho, D. D. Macdonald and T. E. Mallouka, J. Electrochem. Soc., 150, E423 (2003).D. Bejan, J. D. Malcolm, L. Morrison and N J. Bunce, Electrochim. Acta, 54, 5548 (2009). Figure 1

The Thermal-Oxidation Behavior of Pristine and Doped Magnéli Phase Titanium Oxides

Magnéli phase titanium oxides (Ti n O2n–1, 4 ≤ n ≤ 10) are promising alternatives to carbon-based materials in aqueous electrochemical technologies, but their passivation during operation remains an important challenge to address. To elucidate the mechanism for their oxidation and investigate the influence of doping on their oxidation stability, the thermal-oxidation behavior in air of Ti4O7 doped with V, Cr, Fe, and Ga was investigated by thermogravimetric analysis. V-doping and Fe-doping improved the thermal stability of Ti4O7 as evidenced by higher onset temperatures in their thermograms. Three-dimensional diffusion reaction models adequately describe the solid-state kinetics of thermal oxidation of Ti4O7 in air as demonstrated by linear model-fitting. Doping shows a mixed influence on the kinetics for thermal oxidation in air reducing both the Arrhenius pre-exponential factor and the activation energy. Cr-doping significantly shortens the lifetime of Ti4O7 in ambient conditions as determined by kinetic predictions.

Electrochemical Atomic Layer Etching (e-ALE) of Copper - Thermodynamic and Diffusion-Reaction Considerations of the Surface-Limited Sulfidization of Copper

Electrochemical atomic layer etching (e-ALE) presents a facile approach for etching metals with unprecedented atomic-scale precision. In e-ALE of copper (Cu) metal, the crucial first step is the surface-limited sulfidization of Cu to form a cuprous sulfide (Cu2S) monolayer. In this work, we investigate the thermodynamic, kinetic and transport properties of the sulfidization reaction. By comparing steady-state and non-steady-state experimental studies with equilibrium and non-equilibrium (diffusion-reaction) models, system parameters such as equilibrium constant, reaction rate constant and diffusion coefficient were precisely determined. Knowing these parameters enabled the quantification of rate-limiting factors in the sulfidization process thereby improving our understanding of the chronoamperometry features observed in sulfidization studies.

Numerical algorithm for morphogen synthesis region identification with indirect image-type measurement data.

Diffusion-reaction models are used to describe development processes in the framework of morphogen theory. The images of the concentration fields for the subset of the interacting morphogens are available. In order to interpret this data in terms of the model parameters, the inverse source problem is stated. The sensitivity operator, composed of the independent adjoint problem solutions ensemble, allows transforming the inverse problem to the family of nonlinear ill-posed operator equations. The equations are solved with the Newton-Kantorovich-type algorithm. The approach is applied to the morphogen synthesis region identification problem for the model of regulation of the renewing zone size in biological tissue.

Advanced Hepatitis C Virus Replication PDE Models within a Realistic Intracellular Geometric Environment.

The hepatitis C virus (HCV) RNA replication cycle is a dynamic intracellular process occurring in three-dimensional space (3D), which is difficult both to capture experimentally and to visualize conceptually. HCV-generated replication factories are housed within virus-induced intracellular structures termed membranous webs (MW), which are derived from the Endoplasmatic Reticulum (ER). Recently, we published 3D spatiotemporal resolved diffusion–reaction models of the HCV RNA replication cycle by means of surface partial differential equation (sPDE) descriptions. We distinguished between the basic components of the HCV RNA replication cycle, namely HCV RNA, non-structural viral proteins (NSPs), and a host factor. In particular, we evaluated the sPDE models upon realistic reconstructed intracellular compartments (ER/MW). In this paper, we propose a significant extension of the model based upon two additional parameters: different aggregate states of HCV RNA and NSPs, and population dynamics inspired diffusion and reaction coefficients instead of multilinear ones. The combination of both aspects enables realistic modeling of viral replication at all scales. Specifically, we describe a replication complex state consisting of HCV RNA together with a defined amount of NSPs. As a result of the combination of spatial resolution and different aggregate states, the new model mimics a cis requirement for HCV RNA replication. We used heuristic parameters for our simulations, which were run only on a subsection of the ER. Nevertheless, this was sufficient to allow the fitting of core aspects of virus reproduction, at least qualitatively. Our findings should help stimulate new model approaches and experimental directions for virology.

Time-Space Characterization of Wellbore-Cement Alteration by CO2-Rich Brine

The risk of CO2 leakage from damaged wellbore is identified as a critical issue for the feasibility and environmental acceptance of CO2 underground storage. For instance, Portland cement can be altered if flow of CO2-rich water occurs in hydraulic discontinuities such as cement-tubing or cement-caprock interfaces. In this case, the raw cement matrix is altered by diffusion of the solutes. This fact leads to the formation of distinctive alteration fronts indicating the dissolution of portlandite, the formation of a carbonate-rich layer and the decalcification of the calcium silicate hydrate, controlled by the interplay between the reaction kinetics, the diffusion-controlled renewing of the reactants and products, and the changes in the diffusion properties caused by the changes in porosity induced by the dissolution and precipitation mechanisms. In principle, these mass transfers can be easily simulated using diffusion-reaction numerical models. However, the large uncertainties of the parameters characterizing the reaction rates (mainly the kinetic and thermodynamic coefficients and the evolving reactive surface area) and of the porosity-dependent diffusion properties prevent making reliable predictions required for risk assessment. In this paper, we present the results of a set of experiments consisting in the alteration of a holed disk of class-G cement in contact with a CO2-rich brine at reservoir conditions (P = 12 MPa and T = 60 °C) for various durations. This new experimental protocol allows producing time-resolved data for both the spatially distributed mass transfers inside the cement body and the total mass transfers inferred from the boundary conditions mass balance. The experimental results are used to study the effect of the fluid salinity and the pCO2 on the overall reaction efficiency. Experiments at high salinity triggers more portlandite dissolution, thinner carbonate layers, and larger alteration areas than those at low salinity. These features are accompanied with different spatial distribution of the alteration layers resulting from a complex interplay between salinity-controlled dissolution and precipitation mechanisms. Conversely, the effect of the pCO2 is more intuitive: Increasing pCO2 results in increasing the overall alteration rate without modifying the relative distribution of the reaction fronts.

Adsorption of trace Iron from nickel sulfate solutions using Monophos resin

This paper deals with the removal of trace iron from nickel sulfate solution using Monophos resin. Kinetics, thermodynamics and adsorption mechanism of iron adsorption were studied. Kinetic and thermodynamic parameters as well as equilibrium constants were calculated based on various equilibrium models. Liquid film diffusion, particle diffusion and chemical reaction models were used to fit the experimental data. It was shown that the adsorption mechanism was well represented by particle diffusion model. And pseudo-second-order and intra-particle diffusion model were more consistent with the adsorption process and clearly predicted the intra-particle distribution of iron concentration. Langmuir isotherm well described the adsorption data. Thermodynamic parameters indicated that the adsorption process was spontaneous and endothermic. An iron adsorption rate of 89% was reached with iron concentration being reduced from 1.92 mg/L to 0.21 mg/L.

Decoupling of water and oxygen diffusion phenomena in order to prove the occurrence of thermo-oxidation during hygrothermal aging of thermosetting resins for RTM composite applications

A novel experimental/numerical method is set up in order to decouple water and oxygen diffusion phenomena and to prove the occurrence of thermo-oxidation during hygrothermal aging of thermosetting resins for RTM composite applications. The method consists of creating artificial environmental conditions under pure water, pure oxygen and a water/oxygen mixture and in following the mass uptake of polymer samples during aging. Global and local (ultra-microindentation) mechanical properties of samples are then measured during and after aging, for each environmental conditioning. By analyzing the gravimetric curves with the aid of diffusion–reaction models and the results of mechanical tests, it is shown that water and oxygen diffusion phenomena are coupled in a complex way and that diffusion/reaction phenomena between water and oxygen take place during hygrothermal aging.

Many-Body Theory of Proton-Generated Point Defects for Losses of Electron Energy and Photons in Quantum Wells

The effects of point defects on the loss of either energies of ballistic electron beams or incident photons are studied by using a many-body theory in a multi-quantum-well system. This includes the defect-induced vertex correction to a bare polarization function of electrons within the ladder approximation as well as the intralayer and interlayer screening of defect-electron interactions are also taken into account in the random-phase approximation. The numerical results of defect effects on both energy-loss and optical-absorption spectra are presented and analyzed for various defect densities, number of quantum wells, and wave vectors. The diffusion-reaction equation is employed for calculating distributions of point defects in a layered structure. For completeness, the production rate for Frenkel-pair defects and their initial concentration are obtained based on atomic-level molecular-dynamics simulations. By combining defect-effect, diffusion-reaction and molecular-dynamics models proposed in this paper with a space-weather forecast model for the first time, it will be possible to enable specific designing for electronic and optoelectronic quantum devices that will be operated in space with radiation-hardening protection, and therefore, will effectively extend the lifetime of these satellite onboard electronic and optoelectronic devices.

Propulsion of catalytic Janus spheres in viscosified Newtonian solutions

In many applications of synthetic motors objects are moved through environments with component mixtures. Here active colloid propulsion is experimentally probed versus solution viscosity in hydrogen peroxide solutions, and interpreted with existing diffusion reaction models of self-diffusiophoresis.

Model adaptivity for goal-oriented inference using adjoints

An inverse problem seeks to infer unknown model parameters using observed data. We consider a goal-oriented inverse problem, where the goal of inferring parameters is to use them in predicting a quantity of interest (QoI). Recognizing that multiple models of varying fidelity and computational cost may be available to describe the physical system, we formulate a goal-oriented model adaptivity approach that leverages multiple models while controlling the error in the QoI prediction. In particular, we adaptively form a mixed-fidelity model by using models of different levels of fidelity in different subregions of the domain. Taking the solution of the inverse problem with the highest-fidelity model as our reference QoI prediction, we derive an adjoint-based third-order estimate for the QoI error from using a lower-fidelity model. Localization of this error then guides the formation of mixed-fidelity models. We demonstrate the method for example problems described by convection–diffusion–reaction models. For these examples, our mixed-fidelity models use the high-fidelity model over only a small portion of the domain, but result in QoI estimates with small relative errors. We also demonstrate that the mixed-fidelity inverse problems can be cheaper to solve and less sensitive to the initial guess than the high-fidelity inverse problems.

Trichloramine Removal with Activated Carbon Is Governed by Two Reductive Reactions: A Theoretical Approach with Diffusion-Reaction Models.

Mechanisms underlying trichloramine removal with activated carbon treatment were proven by batch experiments and theoretical analysis with diffusion-reaction models. The observed values of trichloramine and free chlorine were explained only by the model in which (1) both trichloramine and free chlorine were involved as reactants, (2) the removals of reactants were affected both by the intraparticle diffusion and by the reaction with activated carbon, and (3) trichloramine decomposition was governed by two distinct reductive reactions. One reductive reaction was expressed as a first-order reaction: the reductive reaction of trichloramine with the basal plane of PAC, which consists of graphene sheets. The other reaction was expressed as a second-order reaction: the reductive reaction of trichloramine with active functional groups located on the edge of the basal plane. Free chlorine competitively reacted with both the basal plane and the active functional groups. The fact that the model prediction succeeded even in experiments with different activated carbon doses, with different initial trichloramine concentrations, and with different sizes of activated carbon particles clearly proved that the mechanisms described in the model were reasonable for explaining trichloramine removal with activated carbon treatment.

Kinetics of ozone decomposition in porous In2O3 monoliths.

The performance of many chemical gas-phase reactions is strongly influenced by the interaction of reactants with interfaces. Nanoporous materials, which exhibit pore diameters up to 100 nm and high specific surface areas, can be utilized to reduce the amount of cost-intensive materials (e.g. noble metals). However, due to limitations in material transport and reaction kinetics detailed knowledge of the diffusion and the kinetics of a chemical reaction is necessary to improve the performance of chemical processes in industry and research. To experimentally study the diffusion and reaction kinetics of gaseous species inside such pores, the chemoresistive behavior of certain metal oxides such as In2O3 can be utilized. In this work, we present a model system based on hierarchically porous monolithic indium oxide (In2O3) which allows the determination of kinetic effects by utilizing its gas transducing properties. The experimental data obtained by electrical measurements are compared to two diffusion and diffusion-reaction models. Using these methods, the rate constant of ozone decomposition in porous In2O3 is estimated. The results are the basis for a suitable material design for semiconducting gas sensors, on the nano-, meso- and macroscale, which helps in understanding the underlying mechanisms of diffusion and reaction.

The effect of bioturbation in pelagic sediments: Lessons from radioactive tracers and planktonic foraminifera in the Gulf of Aqaba, Red Sea

Studies of recent environmental perturbations often rely on data derived from marine sedimentary records. These records are known to imperfectly inscribe the true sequence of events, yet there is large uncertainty regarding the corrections that should be employed to accurately describe the sedimentary history. Here we show in recent records from the Gulf of Aqaba, Red Sea, how events of the abrupt disappearance of the planktonic foraminifer Globigerinoides sacculifer, and episodic deposition of the artificial radionuclide 137Cs, are significantly altered in the sedimentary record compared to their known past timing. Instead of the abrupt disappearance of the foraminifera, we observe a prolonged decline beginning at core depth equivalent to ∼30y prior to its actual disappearance and continuing for decades past the event. We further observe asymmetric smoothing of the radionuclide peak. Utilization of advection–diffusion–reaction models to reconstruct the original fluxes based on the known absolute timing of the events reveal that it is imperative to use a continuous function to describe bioturbation. Discretization of bioturbation into mixed and unmixed layers significantly shifts the location of the modeled event. When bioturbation is described as a continuously decreasing function of depth, the peak of a very short term event smears asymmetrically but remains in the right depth. When sudden events repeat while the first spike is still mixed with the upper sediment layer, bioturbation unifies adjacent peaks. The united peak appears at an intermediate depth that does not necessarily correlate with the timing of the individual events. In a third case, a long lasting sedimentary event affected by bioturbation, the resulting peak is rather weak compared to the actual event and appears deeper in the sediment column than expected based on the termination of the event. The model clearly shows that abrupt changes can only endure in the record if a thick sediment layer settled on the sediment–water interface at once or if bioturbation rates decreased to very low values for a prolonged period of time. In any other case smearing by bioturbation makes an abrupt event appear to have started shortly before the real timing and end long after its true termination.

Acetophenone hydrogenation on Rh/Al2O3 catalyst: Intrinsic reaction kinetics and effects of internal diffusion

Acetophenone hydrogenation on 1% Rh/Al2O3 catalyst was conducted using various support sizes to study intrinsic kinetics and internal diffusion effects. In the first part of this work, results from different noble metals and supports were compared, and the 1% Rh/Al2O3 was selected. From experiments at 60–100°C, 1.1–4.1MPa PH2 and 0.04–0.4M CAP.o using powder catalysts, intrinsic reaction kinetic modeling with the Langmuir–Hinshelwood mechanism was conducted. The selected kinetic model included dissociative and non-competitive hydrogen adsorption, along with saturated active sites for organic species, and surface reaction as the rate determining step. With the obtained intrinsic reaction kinetics, internal diffusion effects were investigated using two catalyst particle sizes and diffusion–reaction models. The properties of the egg-shell type catalyst particles, including metal dispersion, were characterized and utilized in the models. The concentration–time profiles calculated from models developed in this work correspond well with the experimental results, explaining the effects of internal diffusion inside catalyst particles on reaction rates and selectivity, and are suitable for future use in trickle-bed reactor modeling studies.

Influence of Wind Pressure on the Carbonation of Concrete.

Carbonation is one of the major deteriorations that accelerate steel corrosion in reinforced concrete structures. Many mathematical/numerical models of the carbonation process, primarily diffusion-reaction models, have been established to predict the carbonation depth. However, the mass transfer of carbon dioxide in porous concrete includes molecular diffusion and convection mass transfer. In particular, the convection mass transfer induced by pressure difference is called penetration mass transfer. This paper presents the influence of penetration mass transfer on the carbonation. A penetration-reaction carbonation model was constructed and validated by accelerated test results under high pressure. Then the characteristics of wind pressure on the carbonation were investigated through finite element analysis considering steady and fluctuating wind flows. The results indicate that the wind pressure on the surface of concrete buildings results in deeper carbonation depth than that just considering the diffusion of carbon dioxide. In addition, the influence of wind pressure on carbonation tends to increase significantly with carbonation depth.

A Fully Consistent, Minimal Model for Non-Linear Market Impact

We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order, that consistently generalizes previously proposed propagator models. We account for the universally observed square-root impact law, and predict non-trivial trajectories when trading is interrupted or reversed. We prove that our framework is free of price manipulation, and that prices can be made diffusive (albeit with a generic short-term mean-reverting contribution). Our model suggests that prices can be decomposed into a transient “mechanical” impact component and a permanent “informational” component.

Role of activated carbon properties in atrazine and paracetamol adsorption equilibrium and kinetics

Adsorption of two widespread emerging water contaminants (atrazine and paracetamol) onto three different activated carbons was investigated. The carbons were characterized and the influence of their physicochemical properties on the adsorption performance of atrazine and paracetamol was evaluated. The adsorption equilibrium data were fitted to different adsorption isotherm models (Langmuir, Freundlich, and Dubinin–Radushkevich) while the adsorption rates were described using three different kinetic models (pseudo second order, intraparticle diffusion and a new approach based on diffusion-reaction models). The results indicated that hydrophobic character of the compounds does not affect the sorption capacity of the tested carbons but does influence the uptake rate. The model proposed, based on mass balances, lead to interpret and compare the kinetic of different adsorbents in contrast to classical empirical models. The model is a simple and powerful tool able to satisfactorily estimate the sorption capacities and kinetics of the carbons under different operation conditions by means of only two parameters with physical meaning. All the carbons studied adsorbed paracetamol more effectively than atrazine, possibly due to the fact that sorption takes place by H-bonding interactions.

Diffusion–reaction models of genipin incorporation into fibrin networks

Genipin is a naturally derived small molecule that crosslinks compounds containing primary amines including many natural biopolymers. A diffusion-reaction model to predict the rates of delivery and incorporation of genipin into fibrin networks is presented. Genipin crosslink formation within fibrin hydrogels is a multi-step process that requires genipin diffusion and reaction with primary amines in hydrated networks. The reaction rate of genipin into fibrin gels was measured via spectroscopy while the rate of marginal crosslink formation was measured by rheology. Covalent coupling between genipin and primary amines in fibrin gels obeys second-order kinetics in genipin concentration with an effective activation energy of -71.9 ± 3.2 kJ-mol-1. Genipin diffusion-reaction within fibrin gels exhibits Thiele moduli between 0.02-0.28, which suggests that the systems studied herein are reaction-limited. Genipin-crosslinked fibrin clots are resistant to fibrinolytic degradation as measured by rheology. Finally, active genipin can be delivered from poly(D,L-lactide-co-glycolide) matrices to gels at rates that are comparable to the characteristic rate of incorporation in fibrin networks. Taken together, this work establishes a quantitative framework to engineer controlled release systems for genipin delivery into protein-based hydrogel networks.

Thermal characterization and pyrolysis kinetics of tropical biomass feedstocks for energy recovery

This paper aims to analyse energy related properties, thermal degradation behaviour and devolatilization kinetics of five Cameroonian biomasses namely, Palm Kernel Shells (PKS), Mesocarp Fibres (PMF), Coffee Husk (CH), Corn Cob (CC) and Peanut Shell (PNS). The thermal degradation was performed using thermogravimetric analysis (TG). Different behaviours related to the presence of chemical constituents such as cellulose, hemicellulose and lignin were obtained. Comparison of the thermal characterization shows that PMF is the most interesting feedstock with the highest heating values and reactivity due to higher volatile content. Decomposition of TG data was analysed by applying diffusion and chemical reaction kinetic models. Obtained results show that biomass pyrolysis is represented by two successive steps. The devolatilization stage characterized by high weight loss rate is well described by diffusion reaction models. In contrast, the char formation stage characterized by low weight loss rate is well described by third order chemical reaction models.