Evolution Of Particle Size Distribution Research Articles

An LES-PBE-PDF approach for predicting the soot particle size distribution in turbulent flames

In this article, we combine the large eddy simulation (LES) concept with the population balance equation (PBE) for predicting, in a Eulerian fashion, the evolution of the soot particle size distribution in a turbulent non-premixed hydrocarbon flame. In order to resolve the interaction between turbulence and chemical reactions/soot formation, the transport equations for the gas phase scalars and the PBE are combined into a joint evolution equation for the filtered pdf associated with a single realization of the gas phase composition and the soot number density distribution. With view towards an efficient numerical solution procedure, we formulate Eulerian stochastic field equations that are statistically equivalent to the joint scalar-number density pdf. By discretizing the stochastic field equation for the particle number density using an explicit adaptive grid technique, we are able to accurately resolve sharp features of evolving particle size distributions, while keeping the number of grid points in particle size space small. Compared to existing models, the main advantage of our approach is that the LES-filtered particle size distribution is predicted at each location in the flow domain and every instant in time and that arbitrary chemical reaction mechanisms and soot formation kinetics can be accommodated without approximation. The combined LES-PBE-PDF model is applied to investigate soot formation in the turbulent non-premixed Delft III flame. Here, the soot kinetics encompass acetylene-based rate expressions for nucleation and growth that were previously employed in the context of laminar diffusion flames. In addition, both species consumption by soot formation and radiation based on the assumption of optical thinness are accounted for. While the agreement of our model predictions with experimental measurements is not perfect, we indicate the benefits of the LES-PBE-PDF model and demonstrate its computational viability.

Simulation of fine polydisperse particle condensational growth under an octadecane–nitrogen atmosphere

The evolution of particle size distribution (PSD) of fine polydisperse particles at high number concentrations (>105cm−3) was simulated through a combined model employing direct quadrature method of moments (DQMOM) with heat and mass transfer equations. The PSD was assumed to retain log-normal distribution during the heterogeneous condensation process. The model was first verified by exact solution and experimental data prior to investigating the influence of initial conditions on final PSD under an octadecane–nitrogen atmosphere. Low particle number concentrations and high vapor concentrations were beneficial to shift the PSD to larger particles having a narrower distribution. Additionally, vapor depletion has more influence on the final PSD than the heat release parameter for a number concentration of 106cm−3. This study may assist the design process of a gas–solid separating cyclone, to eliminate dust from high-temperature volatiles by pyrolysis of solid fuels.

A pseudo-coupled DEM–non-linear PBM approach for simulating the evolution of particle size during dry milling

A multi-scale modeling approach is formulated which combines the use of the discrete element method (DEM) and population balance model (PBM) to simulate the evolution of particle size distribution (PSD) in dry milling. As a major novelty, a pseudo-coupled DEM–non-linear PBM approach is proposed, in which the parameters of a non-linear PBM were calibrated using the DEM simulations of the microdynamic environment in a mill by using the DEM intermittently. To demonstrate the application of this approach, breakage dynamics of silica particles in a vibrating cylindrical vessel containing an alumina grinding ball was simulated numerically. DEM simulations were performed to obtain the collision frequency and impact energy spectra, calculate the first-order breakage rate parameters from short milling of mono-sized feeds, and calibrate the parameters of the effectiveness factor of the non-linear PBM. As another novelty, the form of the effectiveness factor chosen accounted for both acceleration effects and deceleration effects simultaneously, which have been observed in various experimental milling studies. By incorporating DEM input, the non-linear PBM with the effectiveness factor was used to simulate the evolution of the PSD. This study demonstrates that a non-linear PBM, whose parameters were calibrated using DEM at early milling times, could predict the PSD evolution during prolonged milling and potentially obviate the need for using computationally expensive DEM simulations for the whole milling duration.

Identification, size classification and evolution of Laves phase precipitates in high chromium, fully ferritic steels

To fulfil the new challenges of the German “Energiewende” more efficient, sustainable, flexible and cost-effective energy technologies are strongly needed. For a reduction of consumed primary resources higher efficiency steam cycles with increased operating parameters, pressure and temperature, are mandatory. Therefore advanced materials are needed. The present study focuses on a new concept of high chromium, fully ferritic steels. These steels, originally designed for solid oxide fuel cell applications, provide favourable steam oxidation resistance, creep and thermomechanical fatigue behaviour in comparison to conventional ferritic-martensitic steels. The strength of this type of steel is achieved by a combination of solid-solution hardening and precipitation strengthening by intermetallic Laves phase particles. The effect of alloy composition on particle composition was measured by energy dispersive X-ray spectroscopy and partly verified by thermodynamic modelling results. Generally the Laves phase particles demonstrated high thermodynamic stability during long-term annealing up to 40,000h at 600°C. Variations in chemical alloy composition influence Laves phase particle formation and consequently lead to significant changes in creep behaviour. For this reason particle size distribution evolution was analysed in detail and associated with the creep performance of several trial alloys.

Detailed modeling of CO2 addition effects on the evolution of soot particle size distribution functions in premixed laminar ethylene flames

This study investigates computationally the influence of CO2 addition on the sooting behavior in premixed laminar ethylene/ oxygen/ argon burner stabilized stagnation (BSS) flames at the atmospheric pressure. The discrete sectional aerosol dynamics method combined with a reversible nucleation model and a novel model of reversible polycyclic aromatic hydrocarbon (PAH) condensation were employed to predict the size evolution of the particle size distribution (PSD) function. The predicted temperature profiles and PSD functions are in reasonably good agreement with the experimental data for nascent soot measured in the BSS configuration. The evolution of the PSD functions shows that CO2 addition reduces the soot nucleation and mass growth rates, consequently lowering the soot yield. The addition of CO2 reduces the concentrations of H, C2H2, C6H6, and large PAHs (e.g., pyrene) which all suppress the soot formation process through a chemical effect; the thermal effect of CO2 is not as strong as the chemical effect.

DEM modeling of shear bands in crushable and irregularly shaped granular materials

A method of modeling convex or concave polygonal particles is proposed. DEM simulations of shear banding in crushable and irregularly shaped granular materials are presented in this work. Numerical biaxial tests are conducted on an identical particle assembly with varied particle crushability. The particle crushing is synchronized with the development of macroscopic stress, and the evolution of particle size distribution can be characterized by fractal dimension. The shear banding pattern is sensitive to particle crushability, where one shear band is clearly visible in the uncrushable assembly and X-shaped shear bands are evident in the crushable assembly. There are fewer branches of strong force chains and weak confinement inside the shear bands, which cause the particles inside the shear bands to become vulnerable to breakage. The small fragments with larger rotation magnitudes inside the shear bands form ball-bearing to promote the formation of shear bands. While there are extensive particle breakages occurring, the ball-bearing mechanism will lubricate whole assembly. With the increase of particle crushability the shear band formation is suppressed and the shear resistance of the assembly is reduced. The porosity inside the shear bands are related to the particle crushability.

Biological synthesis of Pt nanoparticles in a microfluidic chip and modeling of the formation process withPBMandCFD

AbstractBACKGROUNDBiological synthesis of platinum nanoparticles (PtNPs) withCacumen platycladi(C. platycladi) in a microfluidic chip and numerical simulation of formation processes were studied. The effect of volumetric flow rate onPtNPs' size distribution was investigated in detail not only by experimental methods but also by means of numerical simulation. Computational fluid dynamics (CFD) and a population balance model (PBM) combined with reactive kinetics were employed to simulatePtNPs' formation and to calculate the particle size distributions (PSD).RESULTSThe experimental results confirmed the validity of the model and its practicality in predicting the formation ofPtNPsandPSDevolution in the microfluidic chip. In addition, the numerical simulation results also tested and verified the accuracy of the results and conclusions acquired from the experiment.CONCLUSIONIt is concluded thatPSDwas influenced not only by mixing efficiency but also by residence time in the microfluidic chip, and that the two factors were determined by volumetric flow rate. There is a specific volumetric flow rate to achieve equilibrium (optimal mixing and residence time) that results in the average particle size reaching its maximum value. This work provides useful insight into the microfluidic biological synthesis ofPtNPsand the influence of volumetric flow rate on size distribution in a microfluidic chip. © 2017 Society of Chemical Industry

Enhanced Crystallization of Lysozyme Mediated by the Aggregation of Inorganic Seed Particles

We show that aggregation plays a major role in seeded growth of protein crystals. The seeded batch approach provides the opportunity to set the starting conditions for protein crystallization by adding a defined amount of well-characterized seed particles. The experimental observations for tetragonal hen egg-white lysozyme (LSZ) confirm the concept of the oriented aggregation of larger building blocks to form a protein crystal. It was shown that the aggregation of the seed particles/bioconjugates is advantageous for the product quality in terms of larger and more defined LSZ crystals and in terms of accelerated reaction kinetics. We present a population balance (PB) model for the seeded batch crystallization of LSZ considering the aggregation of growth units to form protein crystals. For the modeling of crystal growth, evolving particle size distributions (PSDs) of agglomerating LSZ molecules were measured by dynamic light scattering (DLS). Moreover, the aggregation of seed particles in LSZ solutions unde...

Modeling Agglomeration Behavior in High Temperature Gas–Solid Fluidized Beds via Monte Carlo Method

Particles and bubbles are important discrete elements in gas–solid fluidized beds. The interactions between them affect the evolution of agglomerates. Based on the analyses of microscopic physical processes, mathematical models of particle coalescence and agglomerate breakage caused by bubble expansion were developed. Coupling with the constant-number Monte Carlo method, the evolution of particle size distribution was simulated. Modeling results matched well with cold-mode experiment results, which demonstrated that the approach is a promising way to predict agglomeration behavior in the fluidized beds. Also, the coalescence efficiency β0 and breakage efficiency βb extracted from Monte Carlo results can provide rate constants for the kernels in population balance modeling. Further investigations of the effects of process parameters show that decreasing bed temperature or increasing superficial gas velocity reduces the coalescence efficiency and increases the breakage efficiency, which are beneficial to pr...

Model based prediction of nanostructured thin film morphology in an aerosol chemical vapor deposition process

The aerosol chemical vapor deposition (ACVD) process has been demonstrated as a promising approach to the single step synthesis of nanostructured metal oxide thin films. Multiple process parameters control the nanostructure morphology and the growth of thin films. This work focuses on utilizing a simulation based approach to understand the role of these parameters in governing the morphology of the thin film. A finite element based computational fluid dynamics model, coupled with a discrete-sectional aerosol model, and a boundary layer diffusion and sintering model has been formulated to predict the evolution of particle size distribution and the morphology of the synthesized nanostructured film. The morphology predicted by the model was validated by experimental observations. The model enables scale up and wider application of the ACVD process and can be extended to other gas phase deposition systems.

A Facile pH Controlled Citrate-Based Reduction Method for Gold Nanoparticle Synthesis at Room Temperature.

The synthesis of gold nanoparticles using citrate reduction process has been revisited. A simplified room temperature approach to standard Turkevich synthesis is employed to obtain fairly monodisperse gold nanoparticles. The role of initial pH alongside the concentration ratio of reactants is explored for the size control of Au nanoparticles. The particle size distribution has been investigated using UV-vis spectroscopy and transmission electron microscope (TEM). At optimal pH of 5, gold nanoparticles obtained are highly monodisperse and spherical in shape and have narrower size distribution (sharp surface plasmon at 520 nm). For other pH conditions, particles are non-uniform and polydisperse, showing a red-shift in plasmon peak due to aggregation and large particle size distribution. The room temperature approach results in highly stable “colloidal” suspension of gold nanoparticles. The stability test through absorption spectroscopy indicates no sign of aggregation for a month. The rate of reduction of auric ionic species by citrate ions is determined via UV absorbance studies. The size of nanoparticles under various conditions is thus predicted using a theoretical model that incorporates nucleation, growth, and aggregation processes. The faster rate of reduction yields better size distribution for optimized pH and reactant concentrations. The model involves solving population balance equation for continuously evolving particle size distribution by discretization techniques. The particle sizes estimated from the simulations (13 to 25 nm) are close to the experimental ones (10 to 32 nm) and corroborate the similarity of reaction processes at 300 and 373 K (classical Turkevich reaction). Thus, substitution of experimentally measured rate of disappearance of auric ionic species into theoretical model enables us to capture the unusual experimental observations.Electronic supplementary materialThe online version of this article (doi:10.1186/s11671-016-1576-5) contains supplementary material, which is available to authorized users.

Probe sampling to map and characterize nanoparticles along the axis of a laminar methane jet diffusion flame

Nanoparticles generated by a laminar methane jet diffusion flame were characterized by direct sampling through the pinhole of a probe and sized with a nano-scanning mobility particle sizer. Particular attention was paid to verify the validity of the probe-sampling technique. Results showed that the particle size distributions (PSD) were strongly affected by sample dilution immediately after extraction. Within the flame, the soot PSD did not become independent of dilution ratio until the sample was diluted several thousand times (depending on initial concentration) within a few milliseconds of extraction. A method for on-line measurement of dilution ratio was also introduced by measuring CO2 concentration continuously during the tests.High spatially resolved experimental results at different heights (typically 1mm apart) along the central axis of the flame showed the evolution of PSD for particles larger than 2nm covering early nucleation and growth to oxidation regions. Moving upward from the fuel-side, prior to the visible flame, the PSD in the particle nucleation region was bimodal (with one of the modes being smaller than 2nm) and gradually turned into a unimodal PSD with a median of 10nm due to particle growth. Nearer to the visible flame, the PSD became bimodal again with the larger-diameter mode growing in magnitude and being made up of ever-larger particles, while the smaller-diameter mode gradually shrunk in size until it vanished. Eventually, as the flow was leaving the visible flame, all the particles gradually oxidized until at the tip of the flame they reached a median diameter of 9nm and in very low concentrations.

Temperature and oxygen effects on oxidation-induced fragmentation of soot particles

In this work soot oxidation induced-fragmentation is modeled by using a Multi-Sectional approach. The model has been developed previously and applied successfully, confirming the role of oxidation-induced fragmentation in soot burnout under different combustion conditions. The Multi-Sectional model was used without further modification to understand the mechanism governing the oxidation-induced fragmentation of soot aggregates and particles by modeling particle size distributions (PSDs) previously measured in a two-stage burner under a wide range of temperature and in both fuel-lean and fuel-rich overall conditions. The model was able to reproduce the experimental data in all the investigated conditions both in terms of PSDs and total mass of oxidized particles.An analysis of model results suggested that when temperature decreased, small particles produced by oxidation-induced fragmentation could not be completely oxidized and, thus, could be emitted; on the other hand, when temperature increased, the global oxidation process was more effective and small particles were oxidized and reduced in number concentration.When studying fuel rich conditions, the model predicted that the local presence of a relevant oxygen concentration caused the oxidation-induced fragmentation mechanism, producing small particles, which could eventually be emitted.Finally, a sensitivity analysis was conducted on oxidation-induced fragmentation indicating that aggregate fragmentation controlled soot burnout whereas particle fragmentation was responsible for small particle formation. However, the sensitivity analysis also suggested that both mechanisms were needed for the correct prediction of the evolution of PSDs.

Application of a multi-component mean field model to the coarsening behaviour of a nickel-based superalloy

A multi-component mean field model has been applied to predict the particle evolution of the γ′ particles in the nickel based superalloy IN738LC, capturing the transition from an initial multimodal particle distribution towards a unimodal distribution. Experiments have been performed to measure the coarsening behaviour during isothermal heat treatments using quantitative analysis of micrographs. The three dimensional size of the γ′ particles has been approximated for use in simulation. A coupled thermodynamic/mean field modelling framework is presented and applied to describe the particle size evolution. A robust numerical implementation of the model is detailed that makes use of surrogate models to capture the thermodynamics. Different descriptions of the particle growth rate of non-dilute particle systems have been explored. A numerical investigation of the influence of scatter in chemical composition upon the particle size distribution evolution has been carried out. It is shown how the tolerance in chemical composition of a given alloy can impact particle coarsening behaviour. Such predictive capability is of interest in understanding variation in component performance and the refinement of chemical composition tolerances. It has been found that the inclusion of misfit strain within the current model formulation does not have a significant affect upon predicted long term particle coarsening behaviour. Model predictions show good agreement with experimental data. In particular, the model predicts a reduced growth rate of the mean particle size during the transition from bimodal to unimodal distributions.

Evaluation of the relationship between energy input and particle size distribution in comminution with the use of piecewise regression analysis

ABSTRACTIt is known that the single linear Gates–Gaudin–Schuhmann (GGS) model is in some cases unable to fully describe the particle size distribution of comminution products. In order to overcome this shortcoming, piecewise regression analysis was used to predict the size distributions derived, after grinding for various periods four mono-sized fractions of quartz and marble in a laboratory ball mill. The single line was divided into two straight lines, which indicate the presence of two domains of particle sizes and therefore the involvement of two distinct breakage mechanisms. The obtained GGS model parameters were used to determine the evolution of particle size distribution as a function of the energy input.In addition, the existing relationships between energy input and particle size distribution were improved, by taking into account the effects of the feed size and material type. The new relationships obtained can be used for a more accurate estimation of the required energy for breakage.

CFD-PBE simulation to predict particle growth in a fluidized bed melt granulation batch process

The fluidized bed spray granulation process unites the steps of solid formation and product formulation in one apparatus and is used to produce granulate products out of a liquid. According to different applications of granules, a specific product particle size distribution is required. Thus, the ability to predict the development of the particle size distribution is crucial for process design, optimization and scale-up. For this reason, population balance equations can be solved where the knowledge of particle size-dependent growth rates are the important quantities, which are difficult to obtain by experiments.Using a computational fluid dynamics multiphase model with one nozzle at its center, an advanced two-fluid model with five fluid phases is solved for short process times (~s) considering a high local and temporal resolution of the granulation process (including fluid dynamics, drop deposition and energy equations) to evaluate size-dependent growth rates, as a function of the current state of the process. By transferring particle growth rates to population balance equations, the development of particle size distribution can be finally predicted for long process times (~min).The present work applies the predictive model to an industrial melt spray granulation process in batch mode. Experimental data show that this model could be implemented successfully.

Effects of CO2 addition on the evolution of particle size distribution functions in premixed ethylene flame

The effect of CO2 addition on sooting behavior in premixed ethylene/oxygen/argon flat flames at atmospheric pressure was investigated both experimentally and computationally. The evolution of soot particle size distribution functions (PSDFs) was examined using Burner-Stabilized Stagnation (BSS) probe/Scanning Mobility Particle Sizer (SMPS) technique. To explain the experimental observations, numerical simulations of the flames were carried out to analyze the thermal and chemical effects of CO2 addition on the precursor chemistry. The evolution of PSDFs of nascent soot showed that the CO2 addition gave rise to a decline in soot nucleation rate and a slower mass growth rate, hence significantly lowering soot yield. The inhibition of soot formation by CO2 addition is found to be mainly through chemical effect, while the thermal effect only plays a minor role.

Results of measurements of particulate matter concentrations inside a pig fattening facility

Description of the subject. This research note discusses the results of measurements of particulate matter concentrations inside a pig fattening facility. Objectives. The objectives of the present study were to investigate the correlations between the different size fractions of indoor particulate matter (PM) inside a pig fattening facility and to investigate the evolution of particle size distribution (PSD) through a fattening period and between two housing systems and two cleaning protocols. Method. Data from two consecutive fattening periods in a commercial pig barn were used. Results. Very high correlations were found between PM10 and PM2.5 indoor concentrations. Depending on the measuring instrument, high or low correlations were found between PM1 and PM10 or PM2.5 indoor concentrations. No differences in PSD could be found between the two housing systems or the two cleaning protocols. Conclusions. The results from the present study showed high correlations between the indoor concentrations of PM10 and PM2.5. In the present study, no differences in PSD were found.

In Situ Study on the Evolution of Multimodal Particle Size Distributions of ZnO Quantum Dots: Some General Rules for the Occurrence of Multimodalities.

Properties of small semiconductor nanoparticles (NPs) are strongly governed by their size. Precise characterization is a key requirement for tailored dispersities and thus for high-quality devices. Results of a careful analysis of particle size distributions (PSDs) of ZnO are presented combining advantages of UV/vis absorption spectroscopy, analytical ultracentrifugation, and small-angle X-ray scattering (SAXS). Our study reveals that careful cross-validation of these different methods is mandatory to end up with reliable resolution. PSDs of ZnO NPs are multimodal on a size range of 2-8 nm, a finding that is not yet sufficiently addressed. In the second part of our work the evolution of PSDs was studied using in situ SAXS. General principles for the appearance of multimodalities covering a temperature range between 15 and 45 °C were found which are solely determined by the aging state indicated by the size of the medium-sized fraction. Whenever this fraction exceeds a critical diameter, a new multimodality is identified, independent of the particular time-temperature combination. A fraction of larger particles aggregates first before a fraction of smaller particles is detected. Fixed multimodalities have not yet been addressed adequately and could only be evidenced due to careful size analysis.

Method of particle characterisation; morphology by image analysis

The aim of our work is to establish a morphological characterization of particles. The particle size analysis determines the size distribution of a population of particles using a laser granulometer device. The evolution of particle size distributions is complemented by a study on the particle shape. Thus, morphological analysis consists to acquire images of the particles by using a scanning electron microscopy which will be then processed using an algorithm. The treatment is a set of operations that are thresholding, erosion, expansion and reconstruction of the image. Data processing is performed based on a set of dimensional parameters.