Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size
Effective density (<i>ρ<sub>e</sub></i>) is universally used in atmospheric science as an alternative measure of the density (<i>ρ</i>) of aerosol particles, and its definitions can be expressed in terms of the particle mass (<i>m<sub>p</sub><...
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MDPI AG
2022-03-01
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| Series: | Atmosphere |
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| Online Access: | https://www.mdpi.com/2073-4433/13/4/564 |
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| author | Long Peng Yonglin Liu |
| author_facet | Long Peng Yonglin Liu |
| author_sort | Long Peng |
| collection | DOAJ |
| description | Effective density (<i>ρ<sub>e</sub></i>) is universally used in atmospheric science as an alternative measure of the density (<i>ρ</i>) of aerosol particles, and its definitions can be expressed in terms of the particle mass (<i>m<sub>p</sub></i>), <i>ρ</i>, mobility diameter (<i>D<sub>m</sub></i>), vacuum aerodynamic diameter (<i>D<sub>va</sub></i>), and dynamic shape factor (<i>χ</i>), as <i>ρ<sub>e</sub><sup>I</sup></i> = 6<i>m<sub>p</sub></i>/(<i>π</i>∙<i>D<sub>m</sub></i><sup>3</sup>), <i>ρ<sub>e</sub><sup>II</sup></i> = <i>ρ</i>/<i>χ</i>, and <i>ρ<sub>e</sub><sup>III</sup></i> = <i>D<sub>va</sub></i>/<i>D<sub>m</sub></i>. However, the theoretical foundation of these three definitions of <i>ρ<sub>e</sub></i> is still poorly understood before their application. Here, we explore the relationship between <i>ρ<sub>e</sub></i> and aerosol size through theoretical calculation. This study finds, for the first time, that <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> inherently decrease with increasing size for aspherical particles with a fixed <i>ρ</i> and <i>χ</i>. We further elucidate that these inherent decreasing tendencies are governed by <i>χ</i>, and the ratio of the Cunningham Slip Correction Factor of the volume-equivalent diameter to that of the mobility diameter (<i>C<sub>c</sub></i>(<i>D<sub>ve</sub></i>)/<i>C<sub>c</sub></i>(<i>D<sub>m</sub></i>)), but not by <i>ρ</i>. Taking the variable <i>χ</i> into consideration, the relationships of <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> to particle size become more complicated, which suggests that the values of <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> have little indication of the size-resolved physicochemical properties of particles. On the contrary, <i>ρ<sub>e</sub><sup>II</sup></i> is independent on size for fixed <i>χ</i> and <i>ρ</i>, which indicates that the change in <i>ρ<sub>e</sub><sup>II</sup></i> with size can better indicate the change in morphology and the transformation of the chemical compositions of particles. Our new insights into the essence of three <i>ρ<sub>e</sub></i>s provide an accurate and crucial theoretical foundation for their application. |
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| institution | Directory Open Access Journal |
| issn | 2073-4433 |
| language | English |
| last_indexed | 2024-03-09T11:10:36Z |
| publishDate | 2022-03-01 |
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| series | Atmosphere |
| spelling | doaj.art-f942772e4a7e4be295857ec38066c0ef2023-12-01T00:46:41ZengMDPI AGAtmosphere2073-44332022-03-0113456410.3390/atmos13040564Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle SizeLong Peng0Yonglin Liu1Institute for Environmental and Climate Research, Jinan University, Guangzhou 511443, ChinaInstitute for Environmental and Climate Research, Jinan University, Guangzhou 511443, ChinaEffective density (<i>ρ<sub>e</sub></i>) is universally used in atmospheric science as an alternative measure of the density (<i>ρ</i>) of aerosol particles, and its definitions can be expressed in terms of the particle mass (<i>m<sub>p</sub></i>), <i>ρ</i>, mobility diameter (<i>D<sub>m</sub></i>), vacuum aerodynamic diameter (<i>D<sub>va</sub></i>), and dynamic shape factor (<i>χ</i>), as <i>ρ<sub>e</sub><sup>I</sup></i> = 6<i>m<sub>p</sub></i>/(<i>π</i>∙<i>D<sub>m</sub></i><sup>3</sup>), <i>ρ<sub>e</sub><sup>II</sup></i> = <i>ρ</i>/<i>χ</i>, and <i>ρ<sub>e</sub><sup>III</sup></i> = <i>D<sub>va</sub></i>/<i>D<sub>m</sub></i>. However, the theoretical foundation of these three definitions of <i>ρ<sub>e</sub></i> is still poorly understood before their application. Here, we explore the relationship between <i>ρ<sub>e</sub></i> and aerosol size through theoretical calculation. This study finds, for the first time, that <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> inherently decrease with increasing size for aspherical particles with a fixed <i>ρ</i> and <i>χ</i>. We further elucidate that these inherent decreasing tendencies are governed by <i>χ</i>, and the ratio of the Cunningham Slip Correction Factor of the volume-equivalent diameter to that of the mobility diameter (<i>C<sub>c</sub></i>(<i>D<sub>ve</sub></i>)/<i>C<sub>c</sub></i>(<i>D<sub>m</sub></i>)), but not by <i>ρ</i>. Taking the variable <i>χ</i> into consideration, the relationships of <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> to particle size become more complicated, which suggests that the values of <i>ρ<sub>e</sub><sup>I</sup></i> and <i>ρ<sub>e</sub><sup>III</sup></i> have little indication of the size-resolved physicochemical properties of particles. On the contrary, <i>ρ<sub>e</sub><sup>II</sup></i> is independent on size for fixed <i>χ</i> and <i>ρ</i>, which indicates that the change in <i>ρ<sub>e</sub><sup>II</sup></i> with size can better indicate the change in morphology and the transformation of the chemical compositions of particles. Our new insights into the essence of three <i>ρ<sub>e</sub></i>s provide an accurate and crucial theoretical foundation for their application.https://www.mdpi.com/2073-4433/13/4/564effective densitydynamic shape factorchemical compositionsize |
| spellingShingle | Long Peng Yonglin Liu Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size Atmosphere effective density dynamic shape factor chemical composition size |
| title | Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size |
| title_full | Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size |
| title_fullStr | Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size |
| title_full_unstemmed | Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size |
| title_short | Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size |
| title_sort | theoretical foundation of the relationship between three definitions of effective density and particle size |
| topic | effective density dynamic shape factor chemical composition size |
| url | https://www.mdpi.com/2073-4433/13/4/564 |
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