Diffusion-limited Model Research Articles

Kinetics of thermal synthesis of cerium sulfides

One of the most promising applications for cerium sulfide is as a refractory for molten metal processing, particularly for reactive actinides. Separate processes were used to synthesize cerium monosulfide, cerium sesquisulfide (Ce 2S 3) and cerium hydride (CeH 2). High purity Ce 2S 3 was produced by reacting ceria (CeO 2) and hydrogen sulfide (H 2S) in an induction furnace using a carbon catalyst at temperatures above 2000 °C. CeH 2 was synthesized from cerium metal and hydrogen gas at 100 °C. Ce 2S 3 and CeH 2 were subsequently reacted together in an induction furnace at temperatures above 1700 °C to produce CeS. X-ray diffraction was used to analyze synthesized samples and the kinetics of the CeS synthesis reaction was modeled using a diffusion-limited reaction model. The activation energy for the process was estimated to be 190 kJ/mol.

Availability of phosphate for phytoplankton and bacteria and of glucose for bacteria at different <i>p</i>CO<sub>2</sub> levels in a mesocosm study

Abstract. Availability of phosphate for phytoplankton and bacteria and of glucose for bacteria at different pCO2 levels were studied in a mesocosm experiment (PeECE III). Using nutrient-depleted SW Norwegian fjord waters, three different levels of pCO2 (350 μatm: 1×CO2; 700 μatm: 2×CO2; 1050 μatm: 3×CO2) were set up, and nitrate and phosphate were added at the start of the experiment in order to induce a phytoplankton bloom. Despite similar responses of total particulate P concentration and phosphate turnover time at the three different pCO2 levels, the size distribution of particulate P and 33PO4 uptake suggested that phosphate transferred to the >10 μm fraction was greater in the 3×CO2 mesocosm during the first 6–10 days when phosphate concentration was high. During the period of phosphate depletion (after Day 12), specific phosphate affinity and specific alkaline phosphatase activity (APA) suggested a P-deficiency (i.e. suboptimal phosphate supply) rather than a P-limitation for the phytoplankton and bacterial community at the three different pCO2 levels. Specific phosphate affinity and specific APA tended to be higher in the 3×CO2 than in the 2×CO2 and 1×CO2 mesocosms during the phosphate depletion period, although no statistical differences were found. Glucose turnover time was correlated significantly and negatively with bacterial abundance and production but not with the bulk DOC concentration. This suggests that even though constituting a small fraction of the bulk DOC, glucose was an important component of labile DOC for bacteria. Specific glucose affinity of bacteria behaved similarly at the three different pCO2 levels with measured specific glucose affinities being consistently much lower than the theoretical maximum predicted from the diffusion-limited model. This suggests that bacterial growth was not severely limited by the glucose availability. Hence, it seems that the lower availability of inorganic nutrients after the phytoplankton bloom reduced the bacterial capacity to consume labile DOC in the upper mixed layer of the stratified mesocosms.

A Physiologically based Pharmacokinetic Model for Intravenous and Ingested Dimethylarsinic Acid in Mice

A physiologically based pharmacokinetic (PBPK) model for the organoarsenical dimethylarsinic acid (DMA(V)) was developed in mice. The model was calibrated using tissue time course data from multiple tissues in mice administered DMA(V) intravenously. The final model structure was based on diffusion limitation kinetics. In general, PBPK models use the assumption of blood flow-limited transport into tissues. This assumption has historically worked for small lipophilic organic solvents. However, the conditions under which flow-limited kinetics occurs and how to distinguish when flow-limited versus diffusion-limited transport is more appropriate, have been rarely evaluated. One important goal of this modeling effort was to systematically evaluate descriptions of flow-limited compared with diffusion-limited tissue distribution for DMA(V), using the relatively extensive pharmacokinetic data available in mice. The diffusion-limited model consistently provided an improved fit over flow-limited simulations when compared with tissue time course iv experimental data. After model calibration, an independent data set obtained by oral gavage of DMA(V), was used to further test model structure. Sensitivity analysis of the two PBPK model structures showed the importance of early time course data collection, and the impact of diffusion for kidney time course data description. In summary, this modeling effort suggests the importance of availability of organ specific time course data sets necessary for the discernment of PBPK modeling structure, motivated by knowledge of biology, and providing necessary feedback between experimental design and biological modelers.

Intercalation dynamics in rechargeable battery materials: General theory and phase-transformation waves in LiFePO 4

A general continuum theory is developed for ion intercalation dynamics in a single crystal of rechargeable-battery composite electrode material. It is based on an existing phase-field formulation of the bulk free energy and incorporates two crucial effects: (i) anisotropic ionic mobility in the crystal and (ii) surface reactions governing the flux of ions across the electrode/electrolyte interface, depending on the local free energy difference. Although the phase boundary can form a classical diffusive “shrinking core” when the dynamics is bulk-transport-limited, the theory also predicts a new regime of surface-reaction-limited (SRL) dynamics, where the phase boundary extends from surface to surface along planes of fast ionic diffusion, consistent with recent experiments on LiFePO 4. In the SRL regime, the theory produces a fundamentally new equation for phase transformation dynamics, which admits traveling-wave solutions. Rather than forming a shrinking core of untransformed material, the phase boundary advances by filling (or emptying) successive channels of fast diffusion in the crystal. By considering the random nucleation of SRL phase-transformation waves, the theory predicts a very different picture of charge/discharge dynamics from the classical diffusion-limited model, which could affect the interpretation of experimental data for LiFePO 4.

Junction Stability in Ion-Implanted Mercury Cadmium Telluride

Ion implantation into HgCdTe results in the production of Hg interstitials, which can be subsequently driven into the HgCdTe by an annealing process. This diffusive drive-in of the Hg interstitials fills vacancies and kicks out group I impurities and results in the formation of an n-p junction. In this work we report on the production of interstitials during baking subsequent to the ion implantation process. Various concentrations of metal vacancies were first introduced into mid-wavelength infrared (MWIR, 3 μm to 5 μm) HgCdTe by annealing under tellurium-saturated conditions at various temperatures. Baking subsequent to planar implantation of boron produced n-p junctions whose depths were measured by defect etching. The results were modeled using a simple diffusion limited model from a fixed surface concentration. The surface concentration was allowed to decrease exponentially to zero after a time, found to be of the order of ∼80 h to 150 h. Exhaustion of the interstitials sources produced by the implantation was nearly complete after ∼400 h. The total number of mercury interstitials produced was approximately 50% of the implant dosage.

Abrupt self-termination of vertically aligned carbon nanotube growth

Real-time height measurements demonstrate that growth of millimeter-high carbon nanotube (CNT) forests terminates abruptly after first exhibiting a steady decay in growth rate. Termination is accompanied by a distinct loss of alignment among the CNTs, which is quantified by small-angle x-ray scattering. Previously suggested diffusion-limited and decay-limited models of kinetics accurately fit the growth period, yet fail to capture the termination behavior and incorrectly predict that growth will continue for much longer durations than observed. It appears that structural disorder is a distinct chemical and/or mechanical signature of self-terminated CNT forest growth.

Hypoxic Cell Death is Reduced by pH Buffering in a Model of Engineered Heart Tissue

In this report, we tested the ability of HEPES-buffered culture medium to reduce acidotic cell death in hypoxic monolayer cell cultures and in a diffusion-limited model of engineered heart tissue (EHT). Neonatal rat cardiomyocytes were either plated (monolayers) or suspended in a hydrogel disc containing HEPES. Monolayers cultured in 0% oxygen exhibited a pH drop to 5.46 +/- 0.27 after 4 days with no HEPES, or 7.11 +/- 0.09 with 50 mM HEPES. The lowest observed pH in EHTs was estimated as 6.2 with no HEPES and 7.1 with 50 mM HEPES, which were endpoints of noticeably different pH gradients across the EHTs. Addition of HEPES to hypoxic monolayers corresponded with fewer propidium iodide-positive cells and TUNEL-positive cells; addition of HEPES to EHTs resulted in greater calcein staining and less LDH release. Effective pH buffering reduces cell death by attenuating the acidosis that accompanies anaerobic metabolism.

Fluorescence dynamics and energy migration in Er 3+-doped SRSO structure

Decay time properties of erbium ions in silicon rich silicon oxide multilayers are reported. A non-exponential time behaviour for the 4I 13/2 decay profile is observed and is interpreted in a diffusion-limited model. Furthermore, an appreciable increase of the lifetime of the 4I 13/2 is observed when the sample temperature is lower than 50 K. The lifetime dependence of the 4I 13/2 as a function of temperature was successfully fitted with a model taking into account the temperature dependence of the energy migration between Er 3+ ions in the presence of quenching impurities.

Analysis of oxygen transport in a diffusion‐limited model of engineered heart tissue

Cardiac tissue engineering has made notable progress in recent years with the advent of an experimental model based on neonatal cardiomyocytes entrapped in collage gels and purified basement membrane extract, known as "engineered heart tissues" (EHTs). EHTs are a formidable display of tissue-level contractile function and cellular-level differentiation, although they suffer greatly from mass transport limitations due to the high density of metabolically active cells and the diffusion-limited nature of the hydrogel. In this report, a mathematical model was developed to predict oxygen levels inside a one-dimensional, diffusion-limited model of EHT. These predictions were then compared to values measured in corresponding experiments with a hypoxia-sensitive stain (pimonidazole). EHTs were cast between two plastic discs, which allowed for mass transfer with the culture medium to occur in only the radial direction. EHTs were cultured for up to 36 h in the presence of pimonidazole, after which time they were snap-frozen, histologically sectioned, and stained for bound pimonidazole. Quantitative image analysis was performed to measure the distance from the culture medium at which hypoxia first occurs under various conditions. As tested by variation of simple design parameters, the trends in oxygen profiles predicted by the model are in reasonable agreement with those obtained experimentally, although a number of ambiguities related to the specific model parameters led to a general overprediction of oxygen concentrations. Based on the sensitivity analysis in the present study, it is concluded that diffusion-reaction models may offer relatively precise predictions of oxygen concentrations in diffusion-limited tissue constructs.

In situ Surface-Enhanced Infrared Absorption Spectroscopy for the Analysis of the Adsorption and Desorption Process of Au Nanoparticles on the SiO2/Si Surface

The adsorption and desorption of Au nanoparticles (AuNP) in colloidal D2O suspension on the (3-aminopropyl)triethoxysilane treated SiO2/Si surface was investigated by in situ attenuated total reflection surface enhanced infrared absorption (ATR-SEIRA) spectroscopy with a liquid flow cell. With increasing surface density of AuNP, the absorption of the vibrational modes of D2O and of the citrate molecules covering the AuNP increases due to SEIRA. Repulsive electrostatic Coulomb forces between the AuNP lead to the saturation of the AuNP surface density at submonolayer coverage. We show that the adsorption kinetics can be investigated by monitoring in situ the molecular vibrational modes of D2O and the citrate molecules. Furthermore, we clarify that the adsorption process can be described very well by a diffusion-limited first-order Langmuir kinetics model. When exposing a saturated AuNP submonolayer to 2-aminoethanethiol (AET)/D2O solution, the AuNP are removed from the surface and the IR absorption of the D2O vibrational modes become weaker again. Taking into account the time dependencies of the OD and the CH peaks, we propose a microscopic model where the AET molecules quickly adsorb on the AuNP by replacing most of the precovering citrate molecules exposed to the AET solution. As this takes place, the AuNP agglomerate-as we could detect with scanning electron microscopy-and are finally removed from the surface.

Initial Condition and Calculation Method for the Numerical Simulation of LPE

A diffusion-limited model has been used to describe supersaturation in liquid phase epitaxy (LPE). LPE is not often treated in chemical engineering, but the equations in a diffusion-limited model are similar to those used in thermal engineering. Therefore, we can deal with these equations analytically and solve them numerically. This paper solves the problem that the numerical solutions of the diffusion-limited model depend on the mesh sizes and comprises two parts. The first part provides an update of the traditional equation to describe the initial condition in the diffusion-limited model. The second part is a proposal of methods to calculate the compositional variation using the diffusion-limited model. The mesh sizes for the numerical simulations are determined systematically to calculate the solid phase composition within a desired tolerance limit.

PHYSICAL AND MATHEMATICAL MODELS OF BIO-OIL COMBUSTION

This article discusses classical analytical models with respect to their ability to model bio-oil droplet combustion and, especially, the heating period before the droplet microexplosion. Following an analysis of the droplet combustion histories published in several literature sources, a diffusion limit model with a radiative heating term and Stefan boundary condition was identified as the most adequate for the droplets' preheating period. Considering the multiphase nature of the bio-oil, a bubble-shell model was developed. The basic assumption of this model is that the bio-oil volatile matter forms a core with an expanding radius and growing pressure, while the solids and the low-volatile matter form a membrane (shell). Special attention was paid to the assumption that droplet microexplosions are due to the superheating of droplet kernel liquid. In this regard, several approaches to calculate the limiting temperature, and consequently the droplet preexplosion time, were discussed. These approaches are mainly based on the assumption that impurities in the kernel play roles of nuclei in microbubble growth. An idea for how to define the bio-oil superheat limits via intersection of asymptotes of bio-oil surface temperature evolution with temperature was conceived and a method defining the bio-oil superheat limit based on surface tension variation with temperature was developed. An alternative shrinking-core model of bio-oil droplet explosive disruption was also discussed. A scale analysis defined the parameters that must be determined in preliminary tests of bio-oils, enabling an estimation of the significance of the preexplosion controlling parameters and testing of the results with the published data.

Simulation of Compositional Variation in Liquid Phase Epitaxy InGaP Using a Two Dimensional Model

Compositional variation in initial growth was observed in Liquid Phase Epitaxy (LPE) experiments. It is thought that the cause is the flow of the melt which is induced by the slide of the entire melt from the place where there isn't substrate to the substrate before growth. The phenomenon was simulated with a one dimensional model in InGaP growth with a convection term added to a diffusion-limited model. The velocity of flow in the melt was approximated to Stokes's first problem. It was shown that composition of In in grown solid with the flow is larger than that without the flow. In this paper, InGaP LPE growth is considered and a two dimensional model of the flow is used. For the solute transport, a two dimensional model is also adopted except at the growth interface. A result similar to the one dimensional model was obtained. In the two dimensional model, In composition is greater than that in the case without flow for the greater part of the growth time, but decreases when the flow transports dilute solution. This decrease doesn't appear in the one dimensional model. This phenomenon can be explained by considering the influence of the flow on the mole fraction near the boundary layer.

Diffusion-limited model for a lithium/air battery with an organic electrolyte

A diffusion-limited transient mathematical model for a lithium/air cell, with the air cathode pores flooded with an organic electrolyte, has been developed. During cell discharge, the cathode pore radius profile is reflective of the distribution of the lithium peroxide product in the cathode. The cathode pore radius profile has been predicted as a function of time, current density, oxygen gas pressure, and cathode thickness for an assumed initial porosity and average cathode pore size. Transient concentration profiles of the dissolved oxygen in the electrolyte were also determined. Capacities of the lithium/air cell were predicted and compared favorably with literature experimental results.

Factors Influencing Arsenite Removal by Zero-Valent Iron

The effects of pH, alkalinity, and mass transfer efficiency on the removal of arsenite [As(III)] by zero-valent iron (ZVI) were evaluated in this study. The optimum pH range for removal of As(III) was found to be between 7 and 8. As(III) removal varied with salinity, pH, alkalinity conditions, and As(III) concentration. Degradation of As(III) removal performance was observed only under conditions of high alkalinity and arsenic concentrations [alkalinity >10 g CaCO3/L and 2.9 mg∕L As(III)]. A strong correlation between As(III) removal and increasing Reynolds number in batch testing suggests that mass transfer efficiency plays an important role in the removal of As(III) by ZVI. A diffusion-limited adsorption model was used to describe the removal of As(III) as the result of adsorption to precipitated iron oxides generated from ZVI corrosion. After an initial period of As(III) rapid adsorption to surface rusts formed during manufacturing and exposure to air, As(III) removal rate is most likely controlled by ...

Theoretical and Experimental Analysis of Arrayed Imaging Reflectometry as a Sensitive Proteomics Technique

Arrayed imaging reflectometry (AIR) is a newly developed label-free optical biosensing technique based on the creation and perturbation of a condition of zero reflectance on a silicon substrate. The antireflective coating is formed by covalently immobilizing arrayed probes on a silicon dioxide film. Probe-target complex formation causes a localized increase in optical thickness and a measurable reflectance change. To evaluate the performance of AIR, we have employed two proteins, intimin and tir, from enteropathogenic E. coli that are critical to the bacterium's mechanism of host infection. Using substrates functionalized with the intimin-binding domain of tir, we demonstrate detection of the extracellular domain of intimin at concentrations as low as 10 pM. Through the use of a diffusion-limited model for the intimin-tir binding interaction at this concentration, we estimate the detected intimin surface concentration to be 0.33 pg/mm2.

Modeling and simulation of the injection of urea-water-solution for automotive SCR DeNOx-systems

The evaporation of water from a single droplet of urea water solution is investigated theoretically by a Rapid Mixing model and a Diffusion Limit model, which also considers droplet motion and variable properties of the solution. The Rapid Mixing model is then implemented into the commercial CFD code Fire 8.3 from AVL Corp. Therein, the urea water droplets are treated with Lagrangian particle tracking. The evaporation model is extended for droplet boiling and thermal decomposition of urea. CFD simulations of a SCR DeNOx-system are compared to experimental data to determine the kinetic parameters of the urea decomposition. The numerical model allows to simulate SCR exhaust system configurations to predict conversion and local distribution of the reducing agent.

Analysis of Internal Gettering of Iron Based on the Nucleation Model of Iron Precipitation

We propose a new simulation model to describe the behavior of the internal gettering of Fe by oxygen precipitates. The internal gettering of Fe has typically been described by the diffusion-limited model proposed by Gilles et al. While the diffusion-limited model is effective in describing the gettering behavior at low temperature (< 400oC), it fails to do so at practical gettering temperature of 600oC and above. The model proposed here accurately describes the internal gettering behavior of Fe at both low and practical temperatures by considering the nucleation of iron silicide on the oxygen precipitates. Our model also explains how the gettering behavior is influenced by the product of NRo at low temperature and by the product of NRo3 at high temperature, where N and Ro are the density and radius of the oxygen precipitates, respectively.

Exploring a Mathematical Model for the Kinetics of β-Amyloid Molecular Imaging Probes through a Critical Analysis of Plaque Pathology

Amyloid plaques are highly heterogeneous in content, size, density, and macromolecular crowding, as they are composed of masses of fibrils and other cellular material. Given this target architecture, the aggregated microenvironment offers a unique imaging target for ligands and positron emission tomography (PET) molecular imaging probes (MIPs). In this work, we address how the heterogeneous microenvironment of a plaque and its evolution may affect the kinetic rate constant of PET MIPs. We argue that macromolecular crowding will result in anomalous diffusion within plaque regions. To account for anomalous diffusion within plaques, we propose a diffusion-limited ligand-receptor compartmental model. Given the current state of knowledge about the pathological progression of Alzheimer's disease (AD), the model's parameters may be a function of the pathological progression of AD, which could result in biased estimates of the true amyloid load. The bias may be partially overcome through evaluation in conjunction with other measures of AD progression including cerebral glucose metabolism rate, neuronal cell loss, and activated inflammatory presence.

Reversible adsorption of Au nanoparticles on SiO 2/Si: An in situ ATR-IR study

Adsorption and desorption of Au nanoparticles (AuNP) on the (aminopropyl)triethoxysilane (APTES) treated SiO 2/Si surface was monitored by in situ attenuated total reflection (ATR) infrared spectroscopy in combination with a liquid flow cell. With increasing the AuNP coverage at the surface, the absorption by water vibration was increased due to surface enhanced infrared absorption (SEIRA). Repulsive electrostatic forces between the incoming AuNP and the already adsorbed AuNP layer lead to saturation at submonolayer coverage of the surface. We clarified that the adsorption process can be described very well by a diffusion limited first-order Langmuir-kinetics model. Furthermore, we show that the AuNPs desorb from the surface when they are exposed to the solution of aminoethanethiol (AET).