A New Method of Moments for the Bimodal Particle System in the Stokes Regime

Abstract and Applied Analysis, Nov 2013

The current paper studied the particle system in the Stokes regime with a bimodal distribution. In such a system, the particles tend to congregate around two major sizes. In order to investigate this system, the conventional method of moments (MOM) should be extended to include the interaction between different particle clusters. The closure problem for MOM arises and can be solved by a multipoint Taylor-expansion technique. The exact expression is deduced to include the size effect between different particle clusters. The collision effects between different modals could also be modeled. The new model was simply tested and proved to be effective to treat the bimodal system. The results showed that, for single-modal particle system, the results from new model were the same as those from TEMOM. However, for the bimodal particle system, there was a distinct difference between the two models, especially for the zero-order moment. The current model generated fewer particles than TEMOM. The maximum deviation reached about 15% for and 4% for . The detailed distribution of each submodal could also be investigated through current model.

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A New Method of Moments for the Bimodal Particle System in the Stokes Regime

A New Method of Moments for the Bimodal Particle System in the Stokes Regime Yan-hua Liu1 and Zhao-qin Yin2 1College of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022, China 2China Jiliang University, Hangzhou 310018, China Received 22 September 2013; Accepted 30 October 2013 Academic Editor: Jianzhong Lin Copyright © 2013 Yan-hua Liu and Zhao-qin Yin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The current paper studied the particle system in the Stokes regime with a bimodal distribution. In such a system, the particles tend to congregate around two major sizes. In order to investigate this system, the conventional method of moments (MOM) should be extended to include the interaction between different particle clusters. The closure problem for MOM arises and can be solved by a multipoint Taylor-expansion technique. The exact expression is deduced to include the size effect between different particle clusters. The collision effects between different modals could also be modeled. The new model was simply tested and proved to be effective to treat the bimodal system. The results showed that, for single-modal particle system, the results from new model were the same as those from TEMOM. However, for the bimodal particle system, there was a distinct difference between the two models, especially for the zero-order moment. The current model generated fewer particles than TEMOM. The maximum deviation reached about 15% for ? 0   and 4% for ? 2 . The detailed distribution of each submodal could also be investigated through current model. 1. Introduction The particulate matter has become one of the most dangerous pollutants to the atmospheric environment and the health of human beings. It will reduce the visibility of the atmosphere and cause the traffic crowding and serious accidents. The fine particles (PM2.5) will also be breathed into the bronchus of human beings, followed by several kinds of respiratory diseases. The lungs will absorb the fine particles and cardiovascular disease will come into being [1]. However, the mechanism of the generation and evolution of the particulate matter still remains to be clarified. Hence, it has both theoretical and realistic senses to study the dynamics of the particulate matter. Previous study on the aerosol dynamics usually supposes that the particle system is monodispersed (i.e., the system has only one scale) or multidispersed (i.e., the system has multiscales) but is in a log-normal distribution in size [2]. Such kinds of assumptions will greatly simplify the problems, and a series of approximate or precise solutions will be obtained. However, these assumptions are based on the experimental measurement and cannot be applied to all the cases. There is another type of particle size distribution, namely, bimodal or multimodal distribution. For example, the newborn particles together with the background particles compose the bimodal distribution system. Furthermore, the newborn particles may also exhibit a multimodal or bimodal distribution [3]. Pugatshova et al. [4] and Lonati et al. [5] measured the particulate matter in the urban on-road atmosphere in different cities and times. The multimodal distribution was observed. At this time, unacceptable error may appear using mono-dispersed or log-normal assumption. Take the bimodal system, for example: the particles gather around two independent particle sizes. In order to study such a system, the particle size distribution should be separated into two sub-PSDs [6]. The dynamics of the system may be obtained according to the two subparticle clusters. Under this description, the governing equations of the particle system should be modified to represent the additional coagulation effect [7]; that is, the collision of particles is artificially separated into two kinds: internal coagulation and external coagulation. Because the typical particle diameter of the bimodal system is 5 nm to 2.5 μm, which means that particles lie in different dynamic regimes (free molecular regime, transition regime and continuum regime), the coagulation in such a wide range should also be treated separately. The current study will focus on the continuum (Stokes) regime. Generally, the particle balance equation (PBE) governs the detailed evolution process of PSD and can be numerically solved. However, because of its huge computation resource to solve the PBE directly, the method of moment (MOM) [2, 8, 9] is often taken into account as an alternation. It takes several moments of PSD in particle volume space and converts PBE into moment equations. Each moment has its physical meaning: zero-order moment represents the number concentration, first-order moment represents the volume concentration, and second-order moment is related to the polydis (...truncated)


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Yan-hua Liu, Zhao-qin Yin. A New Method of Moments for the Bimodal Particle System in the Stokes Regime, Abstract and Applied Analysis, 2013, 2013, DOI: 10.1155/2013/840218