Polymerization and Collision in High Concentrations for Brownian Coagulation
Aggregation always occurs in industrial processes with fractal-like particles, especially in dense systems (the volume fraction,<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><mi&...
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MDPI AG
2021-07-01
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| author | Xiaoyue Wang Yueyan Liu Taiquan Wu Mingzhou Yu |
| author_facet | Xiaoyue Wang Yueyan Liu Taiquan Wu Mingzhou Yu |
| author_sort | Xiaoyue Wang |
| collection | DOAJ |
| description | Aggregation always occurs in industrial processes with fractal-like particles, especially in dense systems (the volume fraction,<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><mi>ϕ</mi><mo>></mo><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula>). However, the classic aggregation theory, established by Smoluchowski in 1917, cannot sufficiently simulate the particle dynamics in dense systems, particularly those of generat ed fractal-like particles. In this article, the Langevin dynamic was applied to study the collision rate of aggregations as well as the structure of aggregates affected by different volume fractions. It is shown that the collision rate of highly concentrated particles is progressively higher than that of a dilute concentration, and the SPSD (self-preserving size distribution) is approached (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>≥</mo><mn>1.5</mn></mrow></semantics></math></inline-formula>). With the increase in volume fraction, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>, the SPSD broadens, and the geometric standard is 1.54, 1.98, and 2.73 at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo>=</mo><mn>0.1</mn><mo>,</mo><mo> </mo><mn>0.2</mn><mo>,</mo><mrow><mo> </mo><mi>and</mi><mo> </mo></mrow><mn>0.3</mn></mrow></semantics></math></inline-formula>. When the volume fraction, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>, is higher, the radius of gyration is smaller with the same cluster size (number-based), which means the particle agglomerations are in a tighter coagulation. The fractal-like property <i>D<sub>f</sub></i> is in the range of 1.60–2.0 in a high-concentration system. Knowing the details of the collision progress in a high-concentration system can be useful for calculating the dynamics of coagulating fractal-like particles in the industrial process. |
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| spelling | doaj.art-2199b4d70b084c26a2cea3e9f21c468f2023-11-22T05:20:00ZengMDPI AGApplied Sciences2076-34172021-07-011115681510.3390/app11156815Polymerization and Collision in High Concentrations for Brownian CoagulationXiaoyue Wang0Yueyan Liu1Taiquan Wu2Mingzhou Yu3Laboratory of Aerosol Science and Technology, China Jiliang University, Hangzhou 310000, ChinaCollege of Modern Science and Technology, China Jiliang University, Yiwu 322000, ChinaCollege of Modern Science and Technology, China Jiliang University, Yiwu 322000, ChinaLaboratory of Aerosol Science and Technology, China Jiliang University, Hangzhou 310000, ChinaAggregation always occurs in industrial processes with fractal-like particles, especially in dense systems (the volume fraction,<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><mi>ϕ</mi><mo>></mo><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula>). However, the classic aggregation theory, established by Smoluchowski in 1917, cannot sufficiently simulate the particle dynamics in dense systems, particularly those of generat ed fractal-like particles. In this article, the Langevin dynamic was applied to study the collision rate of aggregations as well as the structure of aggregates affected by different volume fractions. It is shown that the collision rate of highly concentrated particles is progressively higher than that of a dilute concentration, and the SPSD (self-preserving size distribution) is approached (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>≥</mo><mn>1.5</mn></mrow></semantics></math></inline-formula>). With the increase in volume fraction, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>, the SPSD broadens, and the geometric standard is 1.54, 1.98, and 2.73 at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo>=</mo><mn>0.1</mn><mo>,</mo><mo> </mo><mn>0.2</mn><mo>,</mo><mrow><mo> </mo><mi>and</mi><mo> </mo></mrow><mn>0.3</mn></mrow></semantics></math></inline-formula>. When the volume fraction, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>, is higher, the radius of gyration is smaller with the same cluster size (number-based), which means the particle agglomerations are in a tighter coagulation. The fractal-like property <i>D<sub>f</sub></i> is in the range of 1.60–2.0 in a high-concentration system. Knowing the details of the collision progress in a high-concentration system can be useful for calculating the dynamics of coagulating fractal-like particles in the industrial process.https://www.mdpi.com/2076-3417/11/15/6815collisionBrownian motionaggregationmolecular dynamics |
| spellingShingle | Xiaoyue Wang Yueyan Liu Taiquan Wu Mingzhou Yu Polymerization and Collision in High Concentrations for Brownian Coagulation Applied Sciences collision Brownian motion aggregation molecular dynamics |
| title | Polymerization and Collision in High Concentrations for Brownian Coagulation |
| title_full | Polymerization and Collision in High Concentrations for Brownian Coagulation |
| title_fullStr | Polymerization and Collision in High Concentrations for Brownian Coagulation |
| title_full_unstemmed | Polymerization and Collision in High Concentrations for Brownian Coagulation |
| title_short | Polymerization and Collision in High Concentrations for Brownian Coagulation |
| title_sort | polymerization and collision in high concentrations for brownian coagulation |
| topic | collision Brownian motion aggregation molecular dynamics |
| url | https://www.mdpi.com/2076-3417/11/15/6815 |
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