Prediction Of Particle Size Distribution Research Articles

An evaluation of size-resolved cloud microphysics scheme numerics for use with radar observations Part II: Condensation and evaporation

AbstractAccurate numerical modeling of clouds and precipitation is essential for weather forecasting and climate change research. While size-resolved (bin) cloud microphysics models predict particle size distributions without imposing shapes, results are subject to artificial size distribution broadening owing to numerical diffusion associated with various processes. Whereas Part 1 addressed collision-coalescence, here we investigate numerical diffusion that occurs in solving condensation and evaporation. In a parcel model framework, all of the numerical schemes examined converge to one solution of condensation and evaporation as the mass grid is refined, and the advection-based schemes are recommended over the reassigning schemes. Including Eulerian vertical advection in a column limits the convergence to some extent, but that limitation occurs at a sufficiently fine mass grid, and the number of iterations in solving vertical advection should be minimized to reduce numerical diffusion. Insubstantial numerical diffusion in solving condensation can be amplified if collision-coalescence is also active, which in turn can be substantially diminished if turbulence effects on collision are incorporated. Large-eddy simulations of a drizzling stratocumulus field reveal that changes in moments of Doppler spectra obtained using different mass grids are consistent with those obtained from the simplified framework, and that spectral moments obtained using a mass grid designed to effectively reduce numerical diffusion are generally closer to observations. Notable differences between the simulations and observations still exist, and our results suggest a need to consider whether factors other than numerical diffusion in the fundamental process schemes employed can cause such differences.

Population Balance and CFD Simulation of Particle Aggregation and Growth in a Continuous Confined Jet Mixer for Hydrothermal Synthesis of Nanocrystals

Population balance and computational fluid dynamics models are built and integrated to carry out a simulation study of the reactive crystallisation process in a confined jet mixer (CJM) for the continuous flow synthesis of TiO2 nanoparticles at a supercritical water condition. In the population balance model, the crystal growth in size is modelled as being due to combined nanocrystal aggregation as well as surface growth. A free molecular model is used to predict the particle aggregation. The performance of the combined aggregation and surface growth models is compared with models that only consider surface growth as the only mechanism for particle size enlargement. It was found that the combined model gives a more accurate prediction of particle size distribution.

Non-negative differential evolution for particle sizing from ultrasonic attenuation spectroscopy

Ultrasonic attenuation spectroscopy (UAS) is a potentially characterising technique for nano-meter size materials. It is the inversion of the ultrasonic attenuation spectrum to particle size distribution (PSD) by using an optimisation technique. Because the particle size is non-negative number, the inversion has to be optimised in the non-negative real number domain. However, many optimisation techniques have traditionally added the non-negative constrain into a cost function as a result the function becoming complex. In this article, the modification of the differential evolution (DE) technique has been proposed to narrow the searching solution domain bounded in the non-negative real number domain. An absolute function has been added to a mutant vector of the DE technique to guarantee the solution is non-negative real number. This technique is called DE-Nonneg technique. The technique has been demonstrated by characterising size of silica suspension. The optimisation results show that the PSD predictions are comparatively to simulated annealing (SA) technique. Moreover, the performance of DE-Nonneg could be improved via adjusting the parameters (expanding factor, cross over, number of parameters and mutation type) following the guideline addressed here. In addition, it is also possible to predict the PSD without using the structural PSD model. With this advantage, DE-Nonneg could possibly be applied for other non-negative optimisation problems.

Development of high-performance hybrid ANN-finite volume scheme (ANN-FVS) for simulation of pharmaceutical continuous granulation

A hybrid model was developed for simulation of continuous wet granulation of pharmaceutical formulations via twin-screw granulator. The model was based on population balance model (PBM) for prediction of particle size distribution, while artificial neural network (ANN) was used for estimation of mean residence time which is required for numerical solution of PBM. A new numerical scheme based on finite volume approach was developed for solution of one dimensional PBM to predict granule size distribution obtained in a twin-screw granulator. The model takes into account liquid and feed flow rates, and screw speed, while the granule size distribution is the model's main output. Aggregation and breakage were considered as the main mechanisms in the process, and the model was developed and solved for different zones of extruder, i.e. conveying and kneading ones. The model's predictions were validated through comparing with experimental data collected using a 12mm twin-screw extruder for granulation of microcrystalline cellulose. The results indicated that the model is facile, robust and valid, which can predict the performance of twin-screw granulator for pharmaceutical formulations.

Numerical modeling of secondary breakup in molten metals gas-atomization using dimensionless analysis

Numerical modeling of secondary breakup in gas atomization of molten metals has been successfully performed by others to optimize the powder particle size distribution for various additive manufacturing techniques and metal alloys. The application of breakup analytical models has been tested and validated through experimental campaigns by several researchers. They have demonstrated the suitability of the models in predicting particle size distribution as a function of process parameters.The limit of these models is a lack of information about the particle shape. Assessing the particle morphology could be of great relevance for optimizing the gas atomization parameters of already produced or new alloys.To overcome this limitation, the method described in this paper resorts to the Volume Of Fluid (VOF) modeling approach. This method does not apply to gas atomization breakup because supersonic velocities bring to unaffordable computation times and lack of metal mass conservation. The new approach is conceived to scale down the high velocity flow towards much lower intensities. It makes use of a reference frame moving with the primary droplet and of the similarity theory. At present, the model has been validated through the comparison with DPM results. It demonstrated to be a reliable alternative model allowing to gain deeper insights. Heat transfer among gas and droplets is not simulated yet, thus the droplet deformation does not stop at the solidification time. Further developments are forecast to allow to freeze the particle shape at the time it is completely solidified.

Numerical simulation of ammonium perchlorate particles based on a population balance equation model in Taylor-Couette flow

Taylor-Couette flow, multiple vortex rings, is developed by rotating a co-axial rod in a cylindrical reactor. It is helpful in applying stable shear forces to suspended particles in the fluid domain. Recently, by using the Taylor-Couette flow, various experiments were performed to prepare micro-size particles at the laboratory level. However, unlike the simple concept of particle preparation by the Taylor-Couette flow, it is challenging to predict particle size distributions in the fluid domain, especially in the scale-up issue of a Taylor-Couette reactor. In this reason, computational methods are required to calculate particle growth in fluid flow. In this paper, ammonium perchlorate particles in the Taylor-Couette flow are simulated by using a population balance equation model, connected to a module of computational fluid dynamics. First of all, physical and empirical parameters for the population balance equation are determined by using experimental data in a Taylor-Couette flow reactor. Secondly, particle size distributions in a scale-up reactor are predicted by using the proposed method. Finally, validity and applicability of the suggested method are fully discussed on the basis of simulation results. As a major result, the simulation model for ammonium perchlorate particles was reliable in predicting their sizes along time. In addition, without changing the model parameters, the simulation results matched well with the experiments in the scale-up reactor. Based on the simulation results, it is expected that the suggested method can be utilized to estimate particle size distributions in various boundary and operating conditions.

Feasibility of handheld mid-infrared spectroscopy to predict particle size distribution: influence of soil field condition and utilisation of existing spectral libraries

Partial least-squares regression (PLSR), using spectra from a handheld mid-infrared instrument (the ExoScan), was tested for the prediction of particle size distribution. Soils were sampled from agricultural sites in the Eyre Peninsula under field conditions and with varying degrees of soil preparation. Issues relevant to field sampling were identified, such as sample heterogeneity, micro-aggregate size and moisture content. The PLSR models for particle size distribution were derived with the varying degrees of preparation. Cross-validation of clay content in the as-received in situ soils resulted in low accuracy: coefficient of determination (R2) = 0.55 and root mean square error (RMSE) = 7%. This was improved by manual mixing, drying, sieving to < 2 mm and fine grinding, resulting in R2 values of 0.64, 0.75 and 0.81, and RMSE of 6%, 5% and 4% respectively; less improvement resulted for sand, with corresponding R2 values of 0.82, 0.88, 0.91 and 0.89, and RMSE of 10%, 8%, 6% and 7%. Predictions for silt remained poor. Where only archival benchtop calibration models were available, predictions of clay contents for spectra scanned with the handheld ExoScan spectrometer resulted in high error because of spectral intensity mismatch between benchtop and handheld spectra (R2 = 0.72, RMSE = 24.2% and bias = 21%). Pre-processing the benchtop spectra by piecewise direct standardisation resulted in more successful predictions (R2 = 0.73, RMSE = 6.7% and bias = –1.5%), confirming the advantage of piecewise direct standardisation for prediction from archival spectral libraries.

Modelling of particle size distributions produced by a Diesel engine fueled with different fossil and renewable fuels under like urban and extra-urban operating conditions

The use of particle filters, both in diesel and gasoline engines, is increasingly widespread, it being the most used way to reduce the emission of this pollutant into the atmosphere. Predictive knowledge of particle size distributions, both under different operating modes or with fuels of different origin, is increasingly important and necessary. The predictive knowledge of particle distribution is a key factor when it comes to understanding the efficiency of filters and the reactivity of retained particulate matter and thereby helping the design of the regeneration processes of these filters during the lifetime of the vehicle, with the lowest fuel consumption. This work presents a phenomenological model of prediction of particle size distributions under different operating modes, typical of the urban driving conditions with four different fuels, two of fossil origin: diesel without biodiesel and gas-to-liquid derived from natural gas and two of renewable origin: biodiesel (mixture of palm and soy biodiesel) and farnesane (obtained by means of biotechnological processes of sugarcane sub-products). The results show a very good ability of the model to reproduce the particle size distributions at the engine cylinder outlet, independently of the engine mode tested and/or the fuel used.

A novel hyperspectral microscope imaging technology for rapid evaluation of particle size distribution in matcha

Hyperspectral microscope imaging (HMI) technology as a novel approach was proposed to evaluate physical characteristics of matcha. Particle size distribution as one of the significant physical characteristics was investigated. Data fusion which integrated of textural features from images at 524 nm and key spectral features selected by competitive adaptive reweighed sampling (CARS) were as the raw data for modeling. Models were optimized by cross-validation. Results showed that the performance of models was improved with data fusion. The best ANN models with data fusion were achieved with Rp (correlation coefficient in prediction set) of 0.8020 for D10, 0.8414 for D20, 0.8238 for D30, 0.8124 for D40, 0.8058 for D50, 0.8157 for D60, 0.7643 for D70, 0.7360 for D80, and 0.6313 for D90, respectively. This work demonstrated that HMI technology as a rapid, accurate and high effective protocol has great potential in predicting particle size distribution in matcha powder.

Modelling energy and size distribution in cone crushers

The modelling of breakage in compression breakage has traditionally been done using population balance modelling, and the research has been developed over the last decades into advanced dynamic models. This paper presents a model for predicting particle size distribution and energy consumption. The particle size distribution model is derived using a first-order differential equation for how the coefficient of variance depends on the compression length. The coefficient of variance model is combined with a bimodal Weibull distribution to predict the cumulative size distribution. The power consumption is modelled in a similar way using Weibull analysis to determine the relationship between power consumption and the coefficient of variance.

Performance evaluation of hybrid FFA-ANFIS and GA-ANFIS models to predict particle size distribution of a muck-pile after blasting

Accurately predicting the particle size distribution of a muck-pile after blasting is always an important subject for mining industry. Adaptive neuro-fuzzy inference system (ANFIS) has emerged as a synergic intelligent system. The main contribution of this paper is to optimize the premise and consequent parameters of ANFIS by firefly algorithm (FFA) and genetic algorithm (GA). To the best of our knowledge, no research has been published that assesses FFA and GA with ANFIS for fragmentation prediction and no research has tested the efficiency of these models to predict the fragmentation in different time scales as of yet. To show the effectiveness of the proposed ANFIS-FFA and ANFIS-GA models, their modelling accuracy has been compared with ANFIS, support vector regression (SVR) and artificial neural network (ANN). Intelligence predictions of fragmentation by ANFIS-FFA, ANFIS-GA, ANFIS, SVR and ANN are compared with observed values of fragmentation available in 88 blasting event of two quarry mines, Iran. According to the results, both ANFIS-FFA and ANFIS-GA prediction models performed satisfactorily; however, the lowest root mean square error (RMSE) and the highest correlation of determination (R2) values were obtained from ANFIS-GA model. The values of R2 and RMSE obtained from ANFIS-GA, ANFIS-FFA, ANFIS, SVR and ANN models were equal to (0.989, 0.974), (0.981, 1.249), (0.956, 1.591), (0.924, 2.016) and (0.948, 2.554), respectively. Consequently, the proposed ANFIS-GA model has the potential to be used for predicting aims on other fields.

High-resolution digital soil mapping of multiple soil properties: an alternative to the traditional field survey?

Spatial information on soil particle size distribution and soil organic carbon (SOC) are important for land-use management, environmental models and policy-making. Digital soil mapping (DSM) techniques can quantitatively predict these soil properties using minimal resources. However, DSM has not been adequately evaluated at the farm-scale. The aim of this study was to optimise the DSM framework to produce farm-scale soil maps for 366 ha in the Sandspruit catchment, Western Cape, South Africa. Four feature selection techniques and eight predictive models were evaluated on their ability to predict particle size distribution and SOC. A boosted linear feature selection produced the highest accuracy for all but one soil property. The top-performing predictive models were robust linear models for gravel (ridge regression, RMSE 9.01%, R 2 0.75), sand (support vector machine, RMSE 4.69%, R 2 0.67), clay (quantile regression, RMSE 2.38%, R 2 0.52) and SOC (ridge regression, RMSE 0.19%, R 2 0.41). Random forest was the best predictive model for silt content (RMSE 4.12%, R 2 0.53). This approach appears to be robust for farm-scale soil mapping where the number of observations is often small but high-resolution soil data are required.

A Computationally Efficient Surrogate-Based Reduction of a Multiscale Comill Process Model

Particle breakage in milling operations is often modeled using population balance models (PBMs). A discrete element method (DEM) model can be coupled with a PBM in order to explicitly identify the effect of material properties on breakage rate. However, the DEM-PBM framework is computationally expensive to evaluate due to high-fidelity DEM simulations. This limits its application in continuous process modeling for dynamic simulation, optimization, or control purposes. The current work proposes the use of surrogate modeling (SM) techniques to map mechanistic data obtained from DEM simulations as a function of processing conditions. To demonstrate the benefit of the SM-PBM approach in developing integrated process models for continuous pharmaceutical manufacturing, a comill-tablet press model integration utilizing the proposed framework is presented. The SM-PBM approach is in excellent agreement with the DEM-PBM approach to predict particle size distributions (PSDs) and dynamic holdup, with a maximum sum of square errors of 0.0012 for PSD in volume fraction and 0.93 for holdup in grams. In addition, the time taken to run a DEM simulation is in the order of days whereas the proposed hybrid model takes few seconds. The SM-PBM approach also enables comill-tablet press model integration to predict tablet properties such as weight and hardness. The proposed hybrid framework compares well with a DEM-PBM framework and addresses limitations on computational expense, thus enabling its use in continuous process modeling.

Active Learning Strategy for Online Prediction of Particle Size Distribution in Cobalt Oxalate Synthesis Process

Cobalt oxalate synthesis process is a nonlinear batch process. However, the lack of online sensors for the quality variable (e.g., average particle size) has become the main obstacle of controlling the process accurately and optimally. An active learning strategy for selecting the informative training data is proposed to improve the soft sensor prediction performance. First, an initial data set which is collected from the process is used to establish an LSSVR soft sensor model. Second, the LSSVR model prediction error is obtained and the joint probability distribution for the prediction error and input variables can be described through a Gaussian mixture model (GMM). Then, the conditional error variance, which can be calculated from the error GMM, is used to select the representative data which can be added to the initial data set and can improve the current LSSVR model for better performance. In addition, an evaluation index is presented to implement the active learning procedure. Finally, the proposed method applicability to an industrial cobalt oxalate synthesis process is demonstrated.

The impact of channel fill level on internal forces during continuous twin screw wet granulation

The forces experienced by the particles inside a twin screw granulator (TSG) are one of the most difficult parameters to measure quantitatively. However, it is possible to perform accurately this measurement through the use of dye containing calibrated microencapsulated sensors (CAMES) whose rupture is directly dependant on their experienced shear stress. The current study measures the extent of local stresses in the transformation from powder to granules at different channel fills during TSG processing. Channel fill has shown good potential as a design tool, however, its validity for predicting particle size distributions has yet to be demonstrated in an 11-mm TSG. The results of this study showed that the particles within the twin screw granulator experienced stresses in the range of 350–1000 kPa and this value was not linear with the specific mechanical energy applied by the granulator. It was observed that the majority of these stresses were produced by material transport processes rather than the granulation in itself. In addition it was determined that the torque required by the TSG increases exponentially after a certain channel fill a feature that requires to be considered in order to design safer, predictable and reliable granulation workspaces.

Statistical methodology for scale-up of an anti-solvent crystallization process in the pharmaceutical industry

The scale-up of crystallization processes is a challenging step in production of active pharmaceutical ingredients (APIs). When moving from lab to industrial scale, the mixing conditions tend to modify due to the different geometry and agitation performance, which is particularly important in anti-solvent crystallizations where the size of the crystals depends on the mixing and incorporation of the anti-solvent in the solution. In this work, the results obtained in anti-solvent lab-scale crystallization experiments were used to develop multivariate statistical models predicting Particle Size Distribution (PSD) parameters (Dv10, Dv50 and Dv90) in function of predictors such as percentage of volume, power per volume and tip speed. Firstly, the collinearity among the predictors was assessed by Variance Inflation Factor (VIF) diagnosis. Subsequently, least squares method was employed to find correlations among the predictors and output variables. The optimization of the models was executed by testing quadratic, logarithmic and square root terms of the predictors and removing the least statistically significant regression coefficient. The quality of the fitting was evaluated in terms of adjusted R2 (R2adj). The modelled Dv10, Dv50 and Dv90 values presented a good fitting to the experimental data, with R2adj higher than 0.79, either when using power per volume or tip speed along the percentage of volume as predictors. Afterwards, the particle size distribution parameters of industrial scale production were predicted using the previously developed models. The deviations between predicted and experimental values were lower than 17%. This demonstrates that multivariate statistical models developed in lab-scale conditions can be successfully used to predict particle size distribution in industrial-size vessels.

Model development and prediction of particle size distribution, density and friability of a comilling operation in a continuous pharmaceutical manufacturing process

The comilling process plays an important role in solid oral dosage manufacturing. In this process, the granulated products are comminuted to the required size distribution through collisions created from a rotating impeller. In addition to predicting particle size distribution, there is a need to predict other critical quality attributes (CQAs) such as bulk density and tapped density, as these impact tablet compaction behavior. A comprehensive modeling approach to predict the CQAs is needed to aid continuous process modeling in order to simulate interaction with the tablet press operation. In the current work, a full factorial experiment design is implemented to understand the influence of granule strength, impeller speed and residual moisture content on the CQAs. A population balance modeling approach is applied to predict milled particle size distribution and a partial least squares modeling approach is used to predict bulk and tapped density of the milled granule product. Good agreement between predicted and experimental CQAs is achieved. An R2 value of 0.9787 and 0.7633 is obtained when fitting the mean particle diameters of the milled product and the time required to mill the granulated material respectively.

Kinetic modeling of soot formation in premixed burner-stabilized stagnation ethylene flames at heavily sooting condition

A detailed kinetic mechanism of soot formation and oxidation is revised and extended to include temperature-dependent collision efficiencies. The collision efficiency for various particle size is studied and compared with experimental data and molecular dynamics simulations for the PAH dimerization where the experimental data are not available. This revised kinetic model is validated in comparison with the premixed burner-stabilized stagnation ethylene flames at heavily sooting conditions. The results showed that quasi-one-dimensional numerical simulations can capture the flame structure and predict soot formation quite satisfactorily. The predicted particle size distribution function (PSDF) is in reasonable agreement with experimental results, but the model only partially reproduces the distinct separation between nucleation and coagulation modes observed experimentally. This leads to some discrepancies in the prediction of soot number density, while the predicted soot volume fraction, which is dominated by the large particles of the PSDF, is in generally good agreement with the experimental data. There is an overestimation of the initial soot volume fraction in the flame region close to the burner, which is a consequence of the over-prediction of the amount of young particles. Therefore, the prediction of PAHs formation and their condensation on soot, which controls the nucleation rate, will require further attention. The comparison between the temperature-dependent model and the model neglecting the temperature dependency showed that the temperature-dependent model could improve the prediction of soot number density, which is controlled by small particles.

Predictive population balance model development and validation of the effect of high shear wet granulation process parameters on granule properties

In this work, a population balance model has been developed and calibrated with experimental data to be used as a predictive tool to replace or reinforce experimental studies of high shear wet granulation. The system studied also involves dry binder addition necessitating the incorporation of dissolution calculations, viscosity-binder correlations and drop penetration calculations to address some of the heterogeneities arising from the dry addition of binder. To address inhomogeneous liquid distribution in the powder bed, the granulator has been divided into two compartments, one with more liquid, less solid and the other one with the opposite. 27 wet granulation experiments were performed by varying liquid addition amount, liquid addition rate, impeller speed and wet massing time. Geometric mean diameter (GMD) in one case and d10 along with d50 in the other case for the 9 of these experiments were used to estimate the tuning parameters in the model. With the estimated parameters, GMD and d10, d50 were predicted for the remaining 18 experiments using the model and compared with experimental results. The model was able to predict the GMD of 8 experiments with a deviation of <10 μm and 4 more with <20 μm deviation. The model was also able to predict the d10 of 6 batches within 10 μm and 9 more batches within 20 μm. For d50 prediction, the deviation was <10 μm for 12 batches and <20 μm for 4 more batches. The model predicted particle size distribution (PSD) was also compared with the experimental PSD for two of the predicted sets as an example. It was seen that the model was able to replicate the PSD fairly well with the exception of the presence of some big granules seen in the experiments.

Formation of Silicate and Titanium Clouds on Hot Jupiters

Abstract We present the first application of a bin-scheme microphysical and vertical transport model to determine the size distribution of titanium and silicate cloud particles in the atmospheres of hot Jupiters. We predict particle size distributions from first principles for a grid of planets at four representative equatorial longitudes, and investigate how observed cloud properties depend on the atmospheric thermal structure and vertical mixing. The predicted size distributions are frequently bimodal and irregular in shape. There is a negative correlation between the total cloud mass and equilibrium temperature as well as a positive correlation between the total cloud mass and atmospheric mixing. The cloud properties on the east and west limbs show distinct differences that increase with increasing equilibrium temperature. Cloud opacities are roughly constant across a broad wavelength range, with the exception of features in the mid-infrared. Forward-scattering is found to be important across the same wavelength range. Using the fully resolved size distribution of cloud particles as opposed to a mean particle size has a distinct impact on the resultant cloud opacities. The particle size that contributes the most to the cloud opacity depends strongly on the cloud particle size distribution. We predict that it is unlikely that silicate or titanium clouds are responsible for the optical Rayleigh scattering slope seen in many hot Jupiters. We suggest that cloud opacities in emission may serve as sensitive tracers of the thermal state of a planet’s deep interior through the existence or lack of a cold trap in the deep atmosphere.