Research on quantitative method of particle segregation based on axial center nearest neighbor index
Graphical abstract
Introduction
Ball mills are widely used in the particle mixing industry, such as pharmaceutical, metallurgy, chemical, silicate and other industries. The mixing performance of particles has a great influence on the product quality and production efficiency of mixing equipment. However, due to the difference in density, size and shape of particles, the segregation of particulate matter generally occurs during mixing movement (Cui et al., 2014, Liao, 2019, Liao et al., 2015, Liao et al., 2014), resulting in a significant segregation structure in the particle system, which reduces the mixing quality. Particle mixing and segregation behavior is usually hard to predict, which makes the characterization and quantification of particle mixing and segregation degree a very important work, so as to become a topic of concern for researchers. Therefore, further research on the quantification of the degree of particle mixing and segregation will help to select appropriate parameters, design effective particle material mixing equipment, and solve potential problems related to production efficiency and product quality (Brück et al., 2018, Cleary and Morrison, 2016, He et al., 2019). This will provide great help for industrial applications of particle mixing equipment such as ball mills.
In recent years, many researchers have analyzed the mixing and segregation of particles in the rotating drum through experimental approach. However, the particle mixing process in a three-dimensional system is very complicated. Some techniques, such as the freeze cutting method and the probe method, can be used to study the overall mixing of the material bed, but these methods are invasive and destructive. Many non-invasive techniques are helpful for understanding and evaluating the particle movement and mixing behavior of rotating drums, mainly including velocity measurement, spectroscopic measurement and tomography (Finger et al., 2016, Liu et al., 2015, Mandal and Khakhar, 2017, Morgan and Heindel, 2017, Nadeem and Heindel, 2018, Rasouli et al., 2016), but some of these methods must be performed under high-standard laboratory conditions. One of the most commonly used methods, Optical image processing (OIP), is relatively simple and low-costly, while some defects, such as high sensitivity to external interference and lack of measurement of internal flow characteristics, limit its practicability.
In contrast, with the rapid development of high-performance computing technology, discrete element method (DEM) is becoming a powerful tool for studying the internal mixing and segregation characteristics of particle systems. For example, the DEM method first proposed by Cundall (Cundall and Strack, 1979), which can provide a visual trajectory of each particle, is conducive to the measurement of the characteristic variables of the mixing and segregation process (Arntz et al., 2014, Liu et al., 2017, Yang et al., 2017, Yazdani and Hashemabadi, 2019). At present, this method has been widely used to study the mixing and segregation of binary particles and their influencing factors in rotating drums (Hou et al., 2019, Xiao et al., 2017). However, most researchers still quantify the degree of particle mixing and segregation based on the well-known Lacey index (Lacey, 2007, Lacey, 1997). This method counts all the particle information by calculating average value within measurement range, thereby ignoring the local particle distribution changes.
In the second section of this study, we will propose an axial center nearest neighbor index (ACNN) to represent mixing and segregation characteristics according to the definitions of nearest neighbor method (Godlieb et al., 2009, Twente, 2007) and neighborhood distance method (Deen et al., 2010). This method takes the particle information (position) as a function with respect to time and characterize the evolution of the particle–particle positional relationship, reflecting the degree of spatial and temporal mixing and segregation. In the third section, we determine the discrete element model and parameters, and verify the ACNN method through the binary particle mixing experiment. In the fourth section, on the basis of the above research, we quantitatively compared the particle mixing and segregation processes of different shaft segments and the whole drum. And then we studied the mixing and segregation characteristics of particle under different particle size ratio, density ratio and drum’s L/D ratio.
Section snippets
Lacey index evaluation method
The Lacey index evaluation method defines the mixing index to describe the degree of mixing and segregation by measuring the sample-based mixing variance. This method analyzes the particle mixing variance according to the number of particles in a given sample. Combining the mixing index M to describe the degree of mixing and segregation, we can understand the distribution characteristics of the particles. The mixed index M can be calculated as follows,where S2 is the actual mixed
Discrete element method
Discrete element method (DEM) is a numerical method used to calculate mechanical behavior of granular systems. The basic idea of the DEM method is to treat each particle as an element, and give each element attributes such as mass, moment of inertia, speed, position, etc. During a given time step, the interaction of elements’ movement were calculated based on Newton's laws of mechanics. After multiple iterations, information such as the speed and position of all elements are updated to get
Results and discussion
On the basis of the axial center nearest neighbor index evaluation method proposed in Section 2 and the discrete element model verified by experiment in Section 3, the local mixing and the overall mixing are compared and analyzed from the two aspects of single axial section and overall drum. Further, using particle density (1, 250 kg/m3 and 2, 500 kg/m3), particle size (12 mm, 16 mm, 22 mm) and drum length (400 mm, 800 mm, 1200 mm) as variable parameters, the effects of particle size ratio σ,
Conclusion
This paper proposes a new ACNN method to quantify the degree of mixing and segregation using particle position information. ACNN is defined according to the state of the particles in the section of different shaft sections in the drum and the compensation distance from the section of the central shaft section. The method calculates the segregation index of particle segregation, providing a quantitative description of the segregation characteristics of the particle mixture. Through DEM
CRediT authorship contribution statement
Peng Huang: Conceptualization, Methodology, Software. Qiuhua Miao: Data curation, Writing - original draft, Writing - review & editing. Gao Sang: Investigation, Validation. Yuhang Zhou: Supervision. Minping Jia: Software, Validation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (No. 51775109) and Natural Science Foundation of Jiangsu Province (BK20181274).
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