size distributions
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L. Michels ◽  
A. J. F. Pires ◽  
C. A. S. Ribeiro ◽  
B. Kroka ◽  
E. G. Hoel ◽  

AbstractNon-metallic microparticles in spheroidal graphite irons are a product of the inoculation and the Mg-treatment of the liquid melt. Besides the influence on the mechanical properties of these iron–carbon–silicon alloys, they are also responsible for the nucleation and the morphology of the graphite phase. The present investigation is undertaken to study holding time effects of a (Ba, Ca, Al)–ferrosilicon (called Ba-inoculant) and (Ca, Al)–ferrosilicon (called Ca-inoculant) inoculants on the overall distribution of microparticles. Using the 2D to 3D conversions method, which is typically used for graphite nodules, the non-metallic microparticles’ statistical parameters, such as size distributions and number densities, are quantified. The total number of particles is similar after Mg-treatment and inoculation for Ca-inoculant but not for Ba-inoculated samples, which lose approximately 25 pct of microparticles after 1 minute of holding time. Iron treated with the Ca-inoculant loses about 37 pct of its nodules after 5 minutes, while the Ba-inoculated melts maintain their performance even after 10 minutes. Based on extrapolating the trend of the undercooling, Ba-inoculated samples would reach the uninoculated undercooling values in 48 minutes, while Ca-inoculated samples in only 11 minutes. By evaluating the size distributions of the non-metallic microparticles, the Ostwald ripening hypothesis or particle aggregation can be verified. The results suggest that sulfides are more critical for graphite nucleation since they can be correlated with the graphite number densities. However, due to the small difference in the microparticle population of the uninoculated sample with Ca-inoculated samples, other aspects of the fading mechanism need to be considered, such as transient metastable states, since the central hypothesis of loss of inclusions cannot alone explain the decrease in the nucleation frequency of graphite.

2022 ◽  
Vol 1049 ◽  
pp. 295-304
Vitaly Polosin

In the study of polydisperse materials, most of the experimental particle size distributions were obtained on bounded intervals. In these cases, it is also desirable to use bounded models with different shapes to simulate the results of studying polydisperse and powder materials. The beta distribution is often used to approximate results due to the fact that this distribution contains many forms for displaying realizations on a limited interval. With the development of computer technology, there has been an increased interest in the use of beta distribution in the modern practice of analyzing results. Meanwhile, there remains a limitation in the use of the beta distribution that is associated with the choice of distribution shape. The possibilities of using known shape measures for mapping beta distribution in this paper is discusses. On the example of the space of shape measure of kurtosis and skewness, the limited use of only probabilistic measures of shapes is illustrated. It is proposed to use the entropy coefficients as an additional informational parameter of the beta distribution shape. On the base of a features comparison of the entropy coefficients for biased and unbiased beta distributions, recommendations for their application are given. By using the example of beta distributions mapping in the space of asymmetry and the entropy coefficient, it is shown that the synergistic combination of probabilistic and informational measures of the shape allows expanding the possibilities of estimating the shape parameters beta distributions. Two methods to display the positions of realizations of beta distributions is proposed. There are trajectories on a constant ratio of shape and realizations position curve on equal values of one parameter. In particular, the features of the choice of beta distributions with negative skewness are discussed.

Fluids ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 29
Miguel Panão

In particle engineering, spray drying is an essential technique that depends on producing sprays, ideally made of equal-sized droplets. Ultrasonic sprays appear to be the best option to achieve it, and Faraday waves are the background mechanism of ultrasonic atomization. The characterization of sprays in this atomization strategy is commonly related to the relation between characteristic drop sizes and the capillary length produced by the forcing frequency of wavy patterns on thin liquid films. However, although this atomization approach is practical when the intended outcome is to produce sprays with droplets of the same size, drop sizes are diverse in real applications. Therefore, adequate characterization of drop size is paramount to establishing the relations between empirical approaches proposed in the literature and the outcome of ultrasonic atomization in actual operating conditions. In this sense, this work explores new approaches to spray characterization applied to ultrasonic sprays produced with different solvents. The first two introduced are the role of redundancy in drop size measurements to avoid resolution limitation in the measurement technique and compare using regular versus variable bin widths when building the histograms of drop size. Another spray characterization tool is the Drop Size Diversity to understand the limitations of characterizing ultrasonic sprays solely based on representative diameters or moments of drop size distributions. The results of ultrasonic spray characterization obtained emphasize: the lack of universality in the relation between a characteristic diameter and the capillary length associated with Faraday waves; the variability on drop size induced by both liquid properties and flow rate on the atomization outcome, namely, lower capillary lengths produce smaller droplets but less efficiently; the higher sensibility of the polydispersion and heterogeneity degrees in Drop Size Diversity when using variable bin widths to build the histograms of drop size; the higher drop size diversity for lower flow rates expressed by the presence of multiple clusters of droplets with similar characteristics leading to multimodal drop size distributions; and the gamma and log-normal mathematical probability functions are the ones that best describe the organization of drop size data in ultrasonic sprays.

Gels ◽  
2022 ◽  
Vol 8 (1) ◽  
pp. 39
Varuzhan Sarkisyan ◽  
Roman Sobolev ◽  
Yuliya Frolova ◽  
Irina Vorobiova ◽  
Alla Kochetkova

Beeswax and beeswax hydrocarbon-based oleogels were studied to evaluate the quantitative relationship between their yield strength and crystal size distribution. With this aim, oleogels were prepared using four different cooling regimes to obtain different crystal size distributions. The microstructure was evaluated by polarized light microscopy. The yield strength is measured by the cone penetration test. Oleogels were characterized by average grain size, microstructure entropy, grain boundary energy per unit volume, and microstructure temperature. We have provided the theoretical basis for interpreting the microstructure and evaluating the microstructure-based hardening of oleogels. It is shown that the microstructure entropy might be used to predict the yield strength of oleogels by the Hall-Petch relationship.

2022 ◽  
Giuseppe Battaglia ◽  
Salvatore Romano ◽  
Antonello Raponi ◽  
Daniele Marchisio ◽  
Michele Ciofalo ◽  

Magnesium is a raw material of great importance, which attracted increasing interest in the last years. A promising route is to recover magnesium in the form of Magnesium Hydroxide via precipitation from highly concentrated Mg2+ resources, e.g. industrial or natural brines and bitterns. Several production methods and characterization procedures have been presented in the literature reporting a broad variety of Mg(OH)2 particle sizes. In the present work, a detailed experimental investigation is aiming to shed light on the characteristics of produced Mg(OH)2 particles and their dependence upon the reacting conditions. To this purpose, two T-shaped mixers were employed to tune and control the degree of homogenization of reactants. Particles were analysed by laser static light scattering with and without an anti-agglomerant treatment based on ultrasounds and addition of a dispersant. Zeta potential measurements were also carried out to further assess Mg(OH)2 suspension stability.

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