Particle Size Evolution Research Articles

Particle modelling in biomass combustion using orthogonal collocation

Development of an accurate and computational efficient biomass particle model to predict particle pyrolysis and combustion is the focus of this paper. Partial differential equations (PDEs) for heat and mass balance are transformed into a system of coupled ordinary differential equations (ODEs) with the use of orthogonal collocation as the particle discretization method. The orthogonal collocation method is incorporated with comprehensive physicochemical mechanisms to predict the behavior of biomass components during particle pyrolysis and combustion. Heat adsorption by evaporated gas and water movement by diffusion inside the biomass matrix are included in the present work, in parallel with the effect of Stefan flow on the heat and mass transfer rates at the particle surface. Abandoning the classical interface-based modelling approach, the present approach allows decoupling between biomass components and spatial resolution, and the prediction of continuous intra-particle profiles.The new particle model is proven to be accurate and stable through its high degree of agreement with simulation results for particle pyrolysis and combustion experiments using different particle moisture contents and geometrical shapes. The intra-particle temperature gradient, as well as particle mass and size evolution, can be predicted accurately, as validated against experimental data. It is shown that six collocation points provide satisfying resolution. The computational efficiency is confirmed by the short simulation time that was found to be approximately three orders of magnitude faster than mesh-based simulations. This implies that the current model can be used for computational fluid dynamic (CFD) analysis through implementation as sub-grid-scale models to design, for example, biomass furnaces.

Trends in Stability of Pt-Based Catalysts for PEM Fuel Cells

The design of catalysts for Polymer Electrolyte Membrane Fuel Cells is guided by two important principles, improving specific catalytic activity and increasing lifetime [1]. Over the past 3 decades, there was a tremendous effort to understand at the atomic and molecular levels the key parameters that control the catalytic activity of the interface for the oxygen reduction reaction (ORR), the limiting reaction for high performance devices. Understanding the functional links between structure-activity relationships from Pt single crystalline surfaces to PtNi alloy single crystals established the importance of controlling structure, composition in both bulk and particularly at the surface, leading to real catalytic reactivity enhancement of almost 2 orders of magnitude [2]. These studies paved the way to synthesis of advanced nanostructures with well-defined parameters such as particle size, distribution, and alloy composition, culminating with PtNi nanoframes, displaying one of the highest specific activities measured for the ORR [3]. While there are room for improvement with increasing precision in nanostructure synthesis, the corresponding understanding of durability of Pt-based is far less developed. One of the limitations is that measuring durability has always been linked to a particular experimental protocol, leading to the development of accelerated stress tests (AST). These protocols measure the changes in surface area, as well as catalytic activity as a function of cycle number, but provide very little information about the mechanism of degradation. Transmission Electron Microscopy helped shed light on particle size evolution as a function of cycle number, where small particles (ca. 3nm) often coalesce and grow to large sizes, ranging from 5 to 7nm [4]. Carbon corrosion can also contribute to Pt degradation especially under start-stop conditions. However, only recently after the development of an in situ that is sensitive enough to measure rates of Pt dissolution as a function of electrode potential we were able to begin establishing structure-stability relationships that goes beyond simple changes to surface area. In this talk, we will present how the stability trends observed from well-defined single crystal Pt surfaces can help understand durability of nanoparticle systems. First, we reveal how the mechanism of Pt-oxide induced dissolution is highly sensitive on surface structure, where dissolution from (110) surface is almost 10 times higher than on (111) surfaces [5]. The effect anions and other species present at the interface is also relevant for stability of Pt surface atoms. Beyond Pt dissolution, we discuss the effects of redeposition processes that can occur after fast changes in electrode potential, leading to a clear pathway to understand the kinetics of nanoparticle evolution. Further comparison between the rates of Pt dissolution measured from nanoparticles to extended surfaces (single crystal and thin films), helped elucidate the importance of controlling particle size, distribution and support loading. Overall, establishing the functional link between structure-stability can provide a deeper understanding on how to control the durability of fuel cell catalysts, together with advances in catalytic activity that can bring fuel cell technology one step closer to a cost–effective widespread commercialization. [1] Stamekovic, V.; Strmcnik, D.; Lopes, P. P.; Markovic, N. M., Nature Materials, 16, 57-69, 2017 [2] Stamenkovic, V. et al., Science 315, 493-497, 2007 [3] Chen, C. et al., Science 343, 1339-1343, 2014 [4] Borup, R. et al., Chemical Reviews, 107, 3904-3951, 2007 [5] Lopes, P. P. et al., ACS Catalysis, 6, 2536-2544, 2016

Optimal control of molecular weight and particle size distributions in a batch suspension polymerization reactor

Mechanistic modelling is an engineering approach to simulate reasonable physical and chemical processes to develop a model to describe the behaviour of a system. Mathematical models are commonly adopted to explore the physical limits of a process, and are applied to process development, optimization and control. In this work, the population balance model and the moment technique have been utilized to model a suspension polymerization reactor and predict the dynamic evolution of particle size and molecular weight distributions. These distributions are two important factors that affect the physical, rheological and mechanical properties of a polymer, and its final product quality. The cell average technique has been applied to solve the population balance equation, and demonstrate the model predictive capability by comparing its predictions with those obtained from experimental data published in the literature. In addition, the effects of initiator, chain transfer agent, stabilizer concentrations, temperature, and agitation rate on the final particle size and molecular weight distributions have been investigated. An optimal control strategy has been used to obtain the desired molecular weight distribution by manipulating the initiator concentration, concentration of the chain transfer agent and its addition time, and controlling the reactor temperature. Also, the impeller speed and initial value of the stabilizer have been utilized to achieve the desired final particle size distribution. The simulation results indicate that the control objectives have been achieved, and show that the proposed controllers are robust to a mismatched model.

The effect of fragmentation on the distribution of hillslope rock size and abundance: Insights from contrasting field and model data

The disintegration of rocks into soil plays an important role in geomorphological processes, such as the evolution of hillslopes and river valleys. Nevertheless, the factors and processes controlling the physical weathering of rock particles are poorly understood. In this study, the surface and subsurface distribution of rock fragments abundance and size is measured in ten soil profiles along three hillslopes transects. For the surface horizons, we observed a significant linear relation between the ninth decile of the diameter, d90, and hillslope gradient and for both surface and subsurface horizons, a significant logarithmic relation between d90 and rock fragment abundance. For the first time, the performance of various fragmentation models is compared against field data to evaluate if the surface rock distribution can be explained from fragmentation of the subsurface material only. In six profiles these fragmentation models adequately reproduced the observed particle size distribution. In the other four profiles, all located on eroding hillslopes, armouring dominates over fragmentation and the surface rock distribution is coarser compared to the subsurface. Generally, the profiles have a good fit to almost all models with the exception of two. However, we can differentiate two zones in terms of fragmentation mechanism according to the modelling results. The profiles in the transect located along a gently sloping hillslope, and the two other profiles, along a steep river valley.In the models, we consider physical weathering as the single factor of particle size evolution, except or two models where conceptual chemical weathering of the fine fraction is considered, although this chemical weathering was not specifically designed to explore soil water chemistry or mineralogy in detail. The observed discrepancies between field data and the results of this study, especially in the fine fraction, reveal the possible relevance of chemical or biological weathering, redistribution processes and the lower accuracy of the number of fine fraction classes established and measured than in the coarse fraction for the field data.

Influence of Mixing on the Precipitation of Organic Nanoparticles: A Lagrangian Perspective on Scale‐up Based on Self‐Similar Distributions

AbstractPrecipitation of nanoparticles is applied in various fields with a rising interest in the formulation of poorly soluble drugs. The impact of fluid mixing on the precipitation of organic nanoparticles is analyzed. Direct numerical simulations are applied to determine the spatiotemporal evolution of the liquid phase composition and to estimate the particle evolution along Langragian trajectories. The simulation results are compared with laboratory experiments of mixing and particle size evolution, which use a recently developed approach to rapidly stabilize the precipitated nanoparticles. The impact of mixing on precipitation is revealed, thereby enabling a parameter‐free estimation of the mean particle sizes and the particle size distributions. The distributions of residence time, supersaturation time, and particle size are self‐similar for Reynolds numbers in the turbulent regime and allow the derivation of scale‐up rules.

Evolution of particle size and shape towards a steady state: Insights from FDEM simulations of crushable granular materials

We add the recent advances in particle shape representation, particle breakage modeling, and fragmental particle size and shape acquisition to the combined finite and discrete element method (FDEM). The granular material is modeled as an assembly of crushable and irregularly shaped polyhedral particles. The particle breakage is simulated by the breakable cohesive interface elements (CIEs) embedded between any pairs of tetrahedrons in the finite element discretization of individual particles. Without calibrating the model parameters to a particular kind of granular material, the FDEM simulation results are qualitatively in good agreement with laboratory tests and DEM simulations, which indicates that the FDEM approach has revealed the primary mechanisms of crushable granular materials. Particle breakage occurs mostly by the major splitting due to tensile crack propagation or by shearing off the local asperities. We analyze the evolutions of particle size distribution and particle shape in the particle breakage process. From the FDEM simulations and other experimental results, we believe that granular soils may reach a steady state when compressed to sufficiently high stress levels or sheared to very large strains. When arriving steady state, the particle breakage is almost ceased and the particle size and shape distributions stay almost unchanged.

A Numerical Simulation Study on the Kinetics of Asphaltene Particle Flocculation in a Two-dimensional Shear Flow

In the current study, the kinetics of asphaltene particle flocculation is investigated under a shear flow through numerical simulation. The discrete element method (DEM) is coupled with computational fluid dynamics (CFD) to model the agglomeration and fragmentation processes. In addition, a coalescence model is proposed to consider the attachment of colliding particles. The changes in mean asphaltene floc size, the particle size distribution (PSD) of asphaltene flocs over simulation time, and the average fractal dimension are presented. Moreover, the effect of fluid velocity on the kinetics of asphaltene flocculation is examined. The mean asphaltene floc size increases exponentially at first, and then the growth slows; finally, it ceases due to the establishment of a dynamic equilibrium between the agglomeration and fragmentation processes. As expected, asphaltene PSD’s move from fine to coarse sizes during the simulation. Log-normal distribution matches the PSDs best, which is in agreement with the nature of asphaltene. As fluid velocity increases, the dynamic equilibrium is attained more rapidly at a smaller mean floc size and higher average fractal dimension; furthermore, PSDs shift to smaller asphaltene floc sizes. The obtained average fractal dimensions of the asphaltene flocs are in the range of 1.65 to 1.74, which is compatible with the values reported in the literature. Eventually, a semi-analytical model is utilized to fit the simulation results. It is found out that the semi-theoretical model is capable of predicting the evolution of asphaltene particle size appropriately.

Mechanistic aspects in the formation of nano- and submicron particles in a batch and a continuous microfluidic reactor: Experiment, modeling and simulation

To investigate mechanistic contrasts in particle formation between a batch and a continuous microreactor, a coupled computational fluid dynamics (CFD)-population balance equation (PBE) based model is proposed; incorporating mixing, reaction, nucleation, diffusion-growth, Brownian-coagulation, shear-induced coagulation and Ostwald ripening (OR), occurring simultaneously. This enables prediction of nanoparticle size over a wide range of temperatures, flow-fields and solvents. This has been possible for the first time, since we included: (i) effect of evaporative-loss of solvent at a high synthesis temperature in our batch reactor experiments, along with (ii) turbulent-shear coagulation of nanoparticles in this reactor, due to the imposed strong forced convection; while accounting for, in contrast, (iii) laminar-shear coagulation in the microreactor [Gutierrez et al. (Chem. Eng. J., 2011, 674–683)], due to prevailing low Reynolds number flow-synthesis in their experiments. We find that, evaporation significantly reduces particle size by reducing critical radius for OR. Consequently, without it, a strikingly high over-prediction error (about 40% with respect to our experimental particle size) is seen for synthesis of SiO2 particles in ethanol itself, with a more pronounced effect in methanol, a more volatile solvent. Furthermore, in contrasting flow fields of the two reactors, inclusion of the correct function, either turbulent-shear or laminar-shear based coagulation, for batch or microreactor, respectively, enables us to predict temporal particle size evolution accurately. For batch reactor, prediction is completely a priori, while for microreactor, coagulation efficiency as a single adjustable parameter achieves that; without these, existing models suffer about 20% and 15% under-prediction in particles size, respectively, compared to experimental data.

Particle size evolution of V–4Cr–4Ti powders in high energy vibrating and planetary ball milling

In a current research, V–4Cr–4Ti alloy powders were prepared by high energy vibrating balling and planetary ball milling, respectively. X-ray diffraction (XRD) and Rietveld refinement were employed to estimate dislocations density and grain size of ball milled powder. Scanning electron microscopy (SEM) was used to characterize the morphologies of alloy powder. The results show that dislocation density of planetary ball milled powder was much lower than vibrating ball milling at similar input energy. Based on the researches of particle size, dislocation density and grain size, ball milling process of V alloy powder could be described as two basic stages, initial stage and final stage. At initial stage, input energy was absorbed by the increase of dislocation density and fine grains; accordingly, in final stage, input energy was absorbed by powder cracking. The initial stage in planetary ball milling lasts much longer. The development of particle size was highly affected by ball size because of the difference of critical energy for plastic deformation. Another result based on this critical energy was that high energy ball milling could not be replaced by accumulation of long-time ball milling at relatively low energy. Besides, the evolution of microstructure was highly correlated with ball to powder rate (BPR).

Multiscale Computational Model for Particle Size Evolution during Coprecipitation of Li-Ion Battery Cathode Precursors.

Next generation lithium ion batteries require higher energy and power density, which can be achieved by tailoring the cathode particle morphology, such as particle size, size distribution, and internal porosity. All these morphological features are determined during the cathode synthesis process, which consists of two steps, (i) coprecipitation and (ii) calcination. Transition metal hydroxide precursors are synthesized during the coprecipitation process, whereas their oxidation and lithiation occur during calcination. The size and size distribution of crystalline primary and aggregated secondary particles and their internal porosity are determined during coprecipitation. Operating conditions of the chemical reactor, such as solution pH, ammonia concentration, and stirring speed control the final morphological features. Here, a multiscale computational model has been developed to capture the nucleation and growth of crystalline primary particles and their aggregation into secondary transition metal hydroxide precursor particles. The simulations indicate that increasing solution pH and decreasing ammonia concentration lead to smaller sizes of the secondary particles. A phase map has been developed that can help identify the synthesis conditions needed for a specified particle size and size distribution.

Fluorescence Enhancement of Tb3+ in the Tb3+‐Trimesic Acid‐Gd3+ Complex: Role of Polynuclear Structures

AbstractThe mechanism of fluorescence enhancement of Tb3+ in Tb3+‐trimesic acid‐Gd3+ systems has been explored using dynamic light scattering. In earlier work, the mechanism of fluorescence enhancement of Tb3+ in these systems was proposed to be due to the formation of a polynuclear complex involving Tb3+, trimesic acid and Gd3+. However, no direct experimental evidence was presented for the mechanism in that work. In this work, we have used dynamic light scattering (DLS), to measure changes in the mean hydrodynamic diameter (Zavg) of the Tb3+‐trimesic acid‐Gd3+ complex, as a function of time. The Zavg was found to increase monotonically as a function of time, indicating a continuous growth in the particle size. The Eu3+‐β‐diketones‐Gd3+ system also shows enhancement of Eu3+ fluorescence; though a different mechanism was believed to be operating in this case; namely intermolecular energy transfer. If the two systems followed different mechanisms for fluorescence enhancement, the Eu3+‐β‐diketones‐Gd3+ system, is expected to show a different time evolution of particle size. The DLS study showed that the Zavg increased rapidly to a maximum value and then remained nearly constant throughout our measurements; that is, no gradual increase in Zavg was seen as in the Tb3+‐trimesic acid‐Gd3+ system. These DLS studies of the Tb3+‐trimesic acid‐Gd3+ and Eu3+‐β‐diketones‐Gd3+ systems, therefore confirms that different mechanisms of fluorescence enhancement are operative in the two systems.

Aggregation of ferrihydrite nanoparticles: Effects of pH, electrolytes,and organics

To better understand the fate and transport of ferrihydrite nanoparticles (FNPs), which carry many contaminants in natural and engineered aquatic environments, the aggregation of FNPs was systematically investigated in this study. The pH isoelectric point (pHIEP), surface zeta potential, and particle size evolutions of FNPs were measured under varied aqueous conditions using dynamic light scattering (DLS). The influence of pH (5.0 ± 0.1 and 7.0 ± 0.1), ionic strength (IS), electrolytes (NaCl, CaCl2 and Na2SO4), and organics (humic acid, fulvic acid and CH3COONa) on the aggregation behaviors of FNPs were explored. Meanwhile, Derjaguin-Landau-Verwey-Overbeek (DLVO) theory was employed to better understand the controlling mechanisms of FNP aggregation. In the presence of sulfate, the surface charge of FNPs was neutralized under varied pH and ionic strength due to ion adsorption and FNPs phase transformation to schwertmannite based on FT-IR results. This phase transformation resulted in rapid aggregation in all water chemistries tested, whereas other salt species affected the aggregation primarily by ion adsorption and charge screening. Presence of increasing concentrations of the organic acids significantly shifted the pHIEP of FNPs (7.0 ± 0.2) to lower pH (< 4.0) due to adsorption of organics on FNPs surfaces making them negatively charged. The adsorption of HA/FA inhibited FNP aggregation significantly while CH3COONa did not, due to different effects on steric and/or electrosteric interactions among FNPs by organics with varied pKa values and molecular weights. After accounting for the important effects of pH, electrolytes, and organics in modifying FNPs’ surface charge, DLVO calculations agreed well with measured critical coagulation concentrations (CCC) values of FNPs at both pH 5.0 ± 0.1 and 7.0 ± 0.1 in the presence of NaCl. This study will hence be useful to better predict and control the fate and transport of FNPs in the presence of electrolytes and organics with different molecular weights, as well as the fate of the associated contaminants in natural and engineered systems.

Effect of Heat Treatment Combined with an Alternating Magnetic Field on Microstructure and Mechanical Properties of a Ni-Based Superalloy

The effect of a two-step heat treatment including solution and aging heat treatments in an alternating magnetic field (AMF) on microstructure and mechanical properties of the Ni-based superalloy DZ483 was investigated. In the solution heat treatment, the AMF significantly reduced the chemical segregation. In the aging heat treatment, the application of the AMF was found to not only modify the partition ratios of some elements like Al and Ti between the γ′ precipitate and the γ matrix, but also to distinctly accelerate coarsening of γ′ precipitates and to result in a larger mean particle size. Additionally, the morphology of γ′ precipitates gradually evolved from a quasi cube without an AMF to a regular cubic shape in the AMF. Mechanical performance tests showed that hardness and tensile strength of the samples heat treated in the AMF were increased in comparison with those without an AMF. It is shown that the enhanced diffusivity in the AMF is mainly responsible for the change in microsegregation, particle size, and morphology evolution. Furthermore, the AMF promotes the solid solution strengthening and the order strengthening, both of which contribute to the improvement of mechanical properties.

The simulated in vitro infant gastrointestinal digestion of droplets covered with milk fat globule membrane polar lipids concentrate

Milk fat globule membrane polar lipids (MPL) are increasingly used as the surface-active components for emulsions in many infant food products. However, the precise effect of the emulsifier MPL on the digestion of lipids during gastrointestinal digestion has not been elucidated. This study investigated the lipid digestion of droplets covered with MPL with different sizes in a simulated in vitro infant gastrointestinal digestion assay. The well-used surface-active component casein was used as a control. Four types of emulsions were formulated: small and large droplets covered with MPL concentrate (MPL-S and MPL-L, with volumetric means of 0.35 ± 0.01 and 4.04 ± 0.01 μm, respectively), and small and large droplets covered with casein (CN-S and CN-L, with volumetric means of 0.44 ± 0.01 and 4.09 ± 0.03 μm, respectively). The emulsions were subjected to in vitro gastrointestinal digestion using a semidynamic model mimicking infant digestion. Through the determination of particle size evolution, zeta-potential, and microstructure of emulsions, the lipid droplets covered with MPL were found to be more stable than that of the CN-S and CN-L during gastrointestinal digestion. Moreover, although CN-S and CN-L showed a higher initial lipolysis rate at the beginning of gastric digestion, droplets covered by MPL exhibited a significantly higher amount of free fatty acid release during later digestion. The amount of free fatty acid release of the emulsions in both gastric and intestinal digestion could be generally classified as MPL-S ≥ MPL-L > CN-S > CN-L. Our study highlights the crucial role of MPL in the efficient digestion of emulsions and brings new insight for the design of infant food products.

Precise control of water content on the growth kinetics of ZnO quantum dots

The growth kinetics of quantum dots (QDs) is of great importance to control and understand their particle size evolution. Water content is an important parameter for the growth of ZnO QDs during the sol-gel process, which has not been precisely studied until now. Herein, a modified sol-gel method was proposed to prepare uniform and mono-dispersed ZnO QDs. In this method, water content was precisely controlled, which facilitated the thorough investigation concerning the effects of water content on growth kinetics of ZnO QDs. When the water content was low (≤90 mM), the precursor solution was stable and the generation of ZnO QDs could not be triggered. When the water content was too high (3 M), Zn-HDS was generated instead of ZnO. When the water content was in an appropriate range (360 mM-900 mM), the growth of ZnO QDs followed two stages: the oriented attachment (OA) and the Ostwald ripening (OR) stage. Based on our particle size calculation results by Sarma Model, which showed more distinct differentiation and better pertinence than EMA Model, it has been proved that the increase in the water content could not only promote the growth rate of OA stage, but also the OR stage. This results changed our previous thinking that water content has no influence to the OR stage.

Nanowire morphology and particle phase control by tuning the In concentration of the foreign metal nanoparticle

Controllable particle assisted growth (PAG) of III–V nanowires is today almost exclusively done with Au, Ga or In nanoparticles, whereas other metals often yield nanowires with uncontrolled growth directions. To improve the control of the initial growth direction in PAG, independent of choice of metal, we propose to initiate nanowire growth from a group-III-rich foreign metal particle. For III–V nanowire growth, the group III concentration of the particle can be made to increase or decrease with the relative supply of group III and group V material, which can be used to promote the liquid phase that is necessary for vapor–liquid–solid growth. In this paper, 30 nm Pd nanoparticles are used to develop growth conditions for In-rich PAG of InAs nanowires. The particle size evolution for different growth times and V/III ratios is correlated with changes in nanowire density and morphology. In addition, we demonstrate In-rich Co, Pd, Pt and Rh nanoparticles and optimized In-rich PAG from Au and Pd seeds. The Au and Pd seeded nanowires are remarkably similar and by tuning the particle composition we trigger a morphological change. The vertical nanowire morphology is associated with In-rich nanoparticles that contain a liquid phase. The curly nanowire morphology, with random growth directions have an In concentration less than or equal to that of the most In rich compound of the seed metal–In system.

Measurement and Evaluation of the Crystallization Kinetics of l-Asparagine Monohydrate in the Ternary l-/d-Asparagine/Water System

Growth kinetics of l-asparagine monohydrate in racemic aqueous solutions as well as nucleation, growth, and dissolution kinetics of the same enantiomer crystallized from pure l-asparagine solutions are measured, and the kinetic parameters are estimated applying a recently developed shortcut method. The corresponding experimental procedure is based on a small number of preferential (seeded) cooling crystallizations where the crystal size distribution is monitored with an online microscope. Afterward, image analysis yields the transient particle size evolution of initially provided crystals, from which the response of the solid phase to the liquid-phase driving force can be extracted. Subsequently, parameter estimation is carried out applying these data together with the information on concentration and composition of the liquid phase to discriminate between different model approaches. The kinetics are validated finally with independent experiments to evaluate their quality. It is proven that growth kinetic...

Incremental damage and particle size reduction in a pilot SAG mill: DEM breakage method extension and validation

Applying DEM to prediction of tumbling mill performance is challenging because several different modes of breakage are active in the process. Here we use measured data from a well characterised ore in a well instrumented, 1.2 m diameter pilot scale mill to validate direct DEM prediction of particle size reduction. The key comminution mechanisms involved for a SAG mill are: (1) incremental breakage where parent particles break into progeny based on the cumulative energy absorption above the elastic damage threshold, (2) abrasion, and (3) chipping/rounding due to preferential contact and breakage of corners and edges of non-round particles. In this paper, a method for including incremental damage breakage in DEM is presented. The inclusion of all the size reduction mechanisms in the same DEM framework allows direct prediction of the evolution of the resident rock particle size and shape distributions and the product throughput rate. The surface mass loss mechanisms are shown to be critical for reducing the particle size to the point where the accumulation of incremental damage becomes significant leading to body breakage of these damaged particles. The energy split between ball and rock is also important for exceeding the elastic threshold and creating damage. Comparison of the predicted particle sizes at the completion of ten minutes of grinding operation with the measured experimental values from the pilot mill provides quantitative validation of the breakage predictions of this DEM breakage model.

Cementite coarsening during the tempering of Fe-C-Mn martensite

Cementite precipitation during martensite tempering has become an important processing step in some advanced high strength steels (AHSS). This tempering can lead to the formation of Mn-partitioned cementite which has a strong influence on subsequent austenite reversion during intercritical annealing. In this contribution, both the cementite Mn content and particle size evolution have been quantitatively monitored during the tempering of Fe-C-Mn martensite at temperatures between 400 °C and 600 °C. Mn progressively partitions to cementite during the coarsening reaction from the earliest tempering times. This coarsening of the cementite occurs in a matrix that contains strong Mn concentration gradients that drive partitioning of the Mn to the cementite. A model is developed to simultaneously describe the time, temperature and bulk alloy dependence of the mean cementite size and Mn composition evolution. In the model, both the Mn flux, driven by the composition gradient, and C flux, driven by capillarity, have been taken into account to determine the operative tie-lines at the cementite and martensite/ferrite interface. The effect of the cementite Mn content on the dissolution of smaller cementite particles that supply C to the larger particle growth is considered by coupling the growth and dissolution of cementite under conditions of multi-component diffusion.

Kinetic Model for Hydrolytic Nucleation and Growth of TiO2 Nanoparticles

A simple kinetic model is derived to describe the formation of TiO2 particles up to the size of a few hundred nanometers in an aqueous suspension. The model system for the kinetic experiments is the hydrolysis and condensation of titanium(IV)-bis(ammonium-lactato)dihydroxide under basic conditions. The formation of nanoparticles was followed by dynamic light scattering (DLS) and UV–vis spectrometric methods. The turbidity (i.e., the apparent absorbance at 500 nm) of a stable TiO2 suspension is shown to be proportional to the TiO2 concentration at a constant particle size and proportional to the size at a constant Ti concentration. The compilation of the DLS and UV–vis data yields characteristic sigmoid-shaped kinetic curves for the evolution of particle size. A kinetic model with three reaction steps is postulated which provides an excellent fit to the experimental data. First, the rapid hydrolysis of the precursor takes place to give primary particles for the subsequent steps. The dimerization of two pri...