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气溶胶粒子凝聚模型可以按初始粒子的形态特征、凝聚模拟方式、凝聚对象类型等方式进行分类。
气溶胶粒子凝聚模型按初始粒子的形态特征分为球形粒子凝聚模型与非球形粒子凝聚模型。目前球形粒子凝聚模型研究深入,应用简便。但因粒子的多样性和复杂性,其形成的凝聚体与球形粒子凝聚模型形成的凝聚体有一定的偏差。气溶胶粒子只有部分飞灰、粉煤灰等粒子具有球形形态[2],其余大多数粒子以类似圆柱形、椭球形和Chebyshev等[55]非球形形态存在。而非球形粒子凝聚模型模拟过程更接近现实气溶胶粒子凝聚过程,其产生的凝聚体逼真度更高。目前非球形气溶胶粒子凝聚模型多以椭球形或固定取向的非球形凝聚为主。非球形粒子结构复杂,其中不规则非球形粒子凝聚模型计算量较大、算法复杂,较难实现,目前针对该方向的凝聚模型及其应用还有待进一步研究。
粒子凝聚模型根据其模拟方式分为晶格(on-lattice) 模拟[56]和非晶格(off-lattice)模拟[57-58]。晶格和非晶格模拟只有在初始粒子数足够多时,相差不大,可忽略不计[57]。其在晶格模拟过程中,粒子的存在与运动受晶格的限制,粒子只能朝邻近晶格方向移动晶格单元的整数倍。当两个粒子所在的晶格相邻时,粒子发生凝聚现象。晶格模拟的自由性受维度影响,当晶格维度越大,其模拟空间划分越细,粒子运动方向和移动步长越精确,越接近现实运动模拟,通常晶格模拟更容易编程,效率更高[56, 59]。对于非晶格模拟,粒子的运动方式更接近现实模拟,其方向和步长不受约束,可自由运动,但模拟碰撞凝聚时需要考虑粒子凝聚的空间距离因素,算法复杂,计算量较大,耗时较长。
按参与凝聚的对象类型可大体分为粒子-团簇凝聚和团簇-团簇凝聚两种模型。粒子-团簇凝聚以粒子运动碰撞的方式参与凝聚过程,根据粒子运动的方式以及粒子碰撞成功的概率将其分为扩散限制凝聚模型、反应限制凝聚模型、弹道凝聚模型和弹道粒子-团簇凝聚模型。而团簇-团簇凝聚是粒子和团簇均可参与凝聚,其凝聚过程是粒子运动碰撞形成团簇后,粒子与团簇均做无规则运动,当满足碰撞凝聚条件时,发生凝聚,其更接近真实碰撞凝聚过程。团簇-团簇凝聚模型根据粒子和团簇移动凝聚方式和凝聚概率等凝聚条件分为扩散限制团簇凝聚、反应限制团簇凝聚、团簇-团簇凝聚和弹道团簇凝聚模型。
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气溶胶粒子凝聚模型模拟粒子以相切形式凝聚,即遍历团簇A(单个运动粒子或运动团簇)与团簇B(单个粒子或团簇)的位置关系,当团簇A和团簇B中的最小粒子间距等于对应的两个粒子半径之和时,满足粒子碰撞相切条件。文中按粒子-团簇凝聚和团簇-团簇凝聚分类为例,详细介绍两大类气溶胶粒子凝聚模型。
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自凝聚模型发展至今,扩散限制凝聚模型(Diffusion Limited Aggregation,DLA)一直是研究最多的一类模型,由Witten和 Sander在1981年为解决烟尘凝聚和枝晶非平衡生长问题而提出,之后被广泛改进应用在薄膜生长、粉末微粒凝聚、电化学沉积等现象中[45]。该模型的主要过程[45]是将设定的有限区域分成一定数量的固定网格,在其网格原点即区域中心放置一个初始静止粒子,在区域边缘(离原点很远的任意位置)添加第二个粒子,让其随机游走,直到它与初始粒子发生接触碰撞,形成团簇。然后以同样的步骤,引入其他粒子,如果粒子在其随机游走过程中碰到区域边界,即该粒子运动到与初始粒子之间的距离超过一定的数值时,则认为该粒子无法达成凝聚条件,应舍弃,从远处重新释放一个新的粒子[60]。以此类推,当所有达成条件的粒子凝聚在一起,该凝聚过程终止,其算法流程图如图1所示[61]。
1983年,Meakin[62]为模拟更实际的2~4维空间的粒子凝聚过程,提出了粘附概率一词并进行模拟,后续基于这一研究,考虑粒子碰撞后成功凝聚的概率因素问题,在DLA模型的基础上进行改进,加入粒子凝聚的概率条件,正式提出了反应限制凝聚模型 (Reaction Limited Aggregation, RLA),只有粒子大量接触碰撞,克服势垒才能凝聚成功,此时凝聚概率为1 [63]。该模型由于大量碰撞,其粒子更容易进入团簇内部,凝聚体结构比DLA更致密,分形维数更大。RLA模型具有粘附概率特性,广泛应用于气凝胶生成、材料生长、悬浮液凝聚等领域,其算法流程图如图2所示[61]。
弹道凝聚模型(Ballistic Aggregation,BA)[64]是Bensimon等于1984年在Sutherland[65]和Vold[66]等提出的弾道学驱动凝聚(Ballistically Driven Aggrega-,tion BDA,又称Sutherland-Vold)模型基础上改进提出的,模型的主要思想:在某一区域内的原点位置产生一个初始粒子,随机生成第二个粒子坐标及其运动的终点坐标(围绕凝聚体粒子半径范围内的任一地方)并进行直线运动,如果接触碰撞到前一个粒子或者是团簇粒子,则认为该粒子凝聚成功,停止运动,以此类推,直至所有粒子凝聚完成。该模型粒子以固定方向直线运动,更容易进入团簇内部发生凝聚,其形成的凝聚体具有分形维数较大,结构紧密,其外形无固定的生长方向等特点[67-68]。BA模型初始应用于悬浮液中絮状物的胶体凝聚过程[69],后期在平面衬底上的薄膜生长[70]、尘埃气体粒子凝聚等领域得到广泛的应用,其算法流程图如图3所示[64]。
弹道粒子-团簇凝聚模型(Ballistic Particle-Cluster Aggregation,BPCA)[71]是Clague和Dickinson在1984年提出的模型,其主要思想:在固定区域内的坐标系原点生成一个静止粒子,从某个任意方向的区域边缘处(离原点无穷远)释放与静止粒子相同粒径的其他粒子,该粒子沿着释放位置到原点附近坐标的直线路径运动,直至其与静止粒子接触时停止,以此类推,直至所有粒子释放完毕。该模型最开始用来研究光散射特性,后期应用在星体尘埃观测、粉尘凝聚等方面,其生成的凝聚体结构类似树枝状,分形维数较大,其算法流程图如图4所示[71-72]。
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扩散限制团簇凝聚模型(Diffusion LimitedCluster Aggregation,DLCA)[73-74]是1983年Paul和Kolb等为模拟更真实的胶体凝聚,基于DLA模型提出的改进模型。该模型的主要思想[73-74]:在规定的形状区域内,随机产生一定数量的粒子,其中处于相邻位置或网格的粒子被认为是同一团簇,让粒子和粒子团簇均无规则移动。当移动的粒子与团簇接触时,形成一个更大的团簇,通过团簇与粒子的凝聚运动,直至最后只剩一个大团簇。该模型由扩散系数决定团簇的生长凝聚效率,其生成的凝聚体结构松散,分形维数小于DLA。该模型形成的胶体凝聚体分形维数随着粒子半径的增加而显著降低,其值约为1.75~1.85 [75],其算法流程图如图5所示[61]。
反应限制团簇凝聚模型(Reaction-Limited Cluster Aggregation,RLCA) 是Jullien[76]根据RLA模型与团簇的概念,在1984年提出的,相比于DLCA模型,考虑了粒子间存在排斥力时,粒子与团簇碰撞不一定发生凝聚,这点与RLA模型特征类似[77]。当粒子与团簇多次碰撞,克服排斥势垒后,此时粒子成功凝聚的概率为1,实现凝聚过程。该模型形成凝聚体的结构、分形维数等特征与碰撞概率、凝聚速率高度相关。碰撞概率越低,其粒子更容易进入团簇内部,结构更加致密紧凑。粒子凝聚速率越快,形成的凝聚体结构越松散,分形维数越小。与DLCA凝聚模型相比,RLCA凝聚模型凝聚速度更慢,凝聚体结构更紧密,其算法流程图如图6所示[61]。
团簇-团簇凝聚模型(Cluster-Cluster Aggregation,CCA)是Meakin等[78]提出的模型,该模型[78-79]随机产生一定数量的粒子,所有粒子均在体系内进行无规则的布朗运动,先接触的粒子形成小团簇,允许小团簇与粒子继续运动碰撞凝聚,直至最后剩下一个大的团簇,凝聚过程结束。该模型形成的凝聚体结构、凝聚速率等特点受扩散系数、碰撞概率等因素影响[80]。在模拟过程中需考虑粒子、团簇的大小和质量建立合适的扩散系数,根据扩散系数和粒子的运动特点,设置合适的碰撞概率。该模型应用广泛,可模拟胶体、土壤、气溶胶粒子凝聚等现象[81],其算法流程图如图7所示[82]。
弹道团簇-团簇凝聚模型(Ballistic Cluster-Cluster Aggregation,BCCA)是Meakin[83]提出的,其算法原理:在给定空间内随机产生$ {2}^{i} $个粒子,粒子和团簇沿任意方向直线运动,当产生碰撞双方的初始粒子数一致时,发生凝聚,否则继续运动,直至空间内只剩一个团簇,结束凝聚[84]。该模型适用于天体尘埃、生物气溶胶等特性研究,其分形维数约为1.8~1.9[85-86],其算法流程图如图8所示[87]。
凝聚模型都有其适用性与局限性。DLA和DLCA模型适用于满足拉普拉斯方程的无规则扩散现象,其形成的凝聚体结构存在屏蔽效应[88];RLA和RLCA模型适用于粒子需要多次碰撞才能发生凝聚过程的现象,其形成的凝聚体结构克服了屏蔽效应[89];BA、BPCA和BCCA适用于以线性轨迹扩散的平均自由程远大于团凝聚体尺寸的粒子凝聚现象[90],其形成的凝聚体结构因线性运动而更致密。其中DLA和RLA模型存在中心固定粒子,限定了凝聚体的位置,计算简单。而CCA、DLCA和RLCA模型运动粒子更多元,粒子与团簇均随机运动,计算较复杂。此外,BPCA模型的初始粒径一致,BCCA模型碰撞双方的初始粒子数量一致,才能发生凝聚,与实际粒子凝聚现象存在一定误差。气溶胶粒子凝聚仿真模型的关系如图9所示,各个模型的比较具体如表1所示。
图 9 气溶胶粒子凝聚仿真模型的分类示意图
Figure 9. Schematic illustration of classification of aerosol particles aggregation simulation model
表 1 气溶胶粒子凝聚仿真模型的比较
Table 1. Comparison of simulation models for aerosol particles aggregation
Simulation model Movement mechanism Structure features Application scope DLA Brownian motion Dendritic structure, insensitive to adhesion probability Film growth, powder particle aggregation,
electrochemical deposition, etc.RLA Brownian motion Compact structure, high dependence on cohesion probability Aerogel synthesis, material growth, colloidal particles aggregation, etc. BA Linear motion Compact structure, no fixed trend of growth direction and large fractal dimension Colloidal particles aggregation, film growth, dust particles aggregation, etc. BPCA Linear motion Compact structure and large fractal dimension Dust particle aggregation, powder aggregation, etc. DLCA Brownian motion Dendritic structure, small correlation between fractal dimension and cluster size when a large number of particles are simulated Material growth, electrochemical deposition,
aerosol aggregation, etc.RLCA Brownian motion More compact structure than DLCA model, high dependence on coalescence probability Aerogel synthesis, material growth, colloidal particles aggregation, etc. CCA Brownian motion Compact structure, fractal dimension size is related to adhesion probability and collision efficiency Colloid, soil, aerosol aggregation, etc. BCCA Linear motion Compact structure and large fractal dimension Aerosol particles(dust and microbial particles) aggregation, etc.
Research progress of aerosol particle aggregation model (invited)
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摘要: 气溶胶粒子凝聚模型作为研究大气中的粒子运动过程和凝聚体形貌特征的重要手段,在光学、天体物理学和材料学等领域有着重要应用。文中根据气溶胶粒子凝聚相关理论及影响因素,分析了气溶胶粒子的凝聚机理,阐述了几种主要的气溶胶粒子凝聚模型,介绍了凝聚模型在光学、天体物理学和动力学等领域的应用,总结了主要凝聚模型的优化现状,结合目前气溶胶粒子凝聚模型的应用现状及挑战,从实现非球形粒子凝聚、多因素耦合及凝聚体实时空间分布仿真等方面进行了展望。Abstract:
Significance Aerosol particles refer to the solid, liquid or solid-liquid mixture particles suspended in the atmosphere caused by naturally formed or artificial factors, which are composed of metal powder, bioparticle, dust particle and so on. The analysis of the spatial structure and motion status of aerosol particles is of great significance for ecological environmental protection, climate change control and functional materials development. As an important means to study the spatial structure and motion status of aerosol particles, the aggregation model of aerosol particles is used to simulate the aggregated procedure of aerosol particles under different conditions, which is employed to explain its aggregation and physical mechanism. Aggregation models are widely used in optics, astronomical physics, dynamics and so on. The investigation on the mechanism, influential factors and application of aerosol particles aggregation model is beneficial to the optimization of aerosol particles aggregation model and the preparation of novel extinction materials. Progress Firstly, the mechanism and main influential factors of aerosol particle aggregations are analyzed, such as particle spatial structure characteristics, the interaction of particles, and atmospheric environment. The theory of fractal, mathematical statistics and molecular simulation used in the study of aerosol particle aggregation are summarized. Secondly, based on the implementation methods of aerosol particle aggregation simulation, the classifications and characteristics of aggregation models are described. In addition, the application of the aerosol particle aggregation model in optics, astrophysics, and dynamics is mentioned. The model optimization such as algorithm efficiency, simulation modes, and application errors reduction is analyzed. Finally, in view of the current application status and challenges faced by aerosol particle aggregation models, the trend of aggregation models is proposed, such as the construction of a non-spherical particle aggregation model, application of multi-factor coupled aggregation model and simulation of real-time spatial distribution of aggregation particles, etc. Conclusions and Prospects In recent years, the aerosol particle aggregation models have been used in a variety of areas. The aerosol particle aggregation model can be used to simulate the visual procedure of particle aggregation, study the formation mechanism and aggregation dynamics of particles, and carry out an in-depth analysis of aggregation characteristics. The aerosol particle aggregation model is important to analyze dynamics, morphology and other properties of aggregates. These models can be used to explain the phenomena such as gas mixture explosions and comet polarization. It can also provide a means for the screening and controllable preparation of extinction materials. However, there are still some shortcomings. Firstly, the complex morphology and structures of non-spherical particles are an important part of simulating and analyzing more realistic aerosol particle applications. The aggregation model of randomly oriented non-spherical aerosol particles with controllable particle shape and size has not yet been established. Secondly, the analysis of the aggregation mechanism of the model is relatively simple. To improve the accuracy of the simulation, the influence of multiple factors on the aggregation procedure needs to be considered. In addition, the simulation of real-time spatial distribution of the particles is acquired to further investigate in future. Therefore, the model can be optimized as followings. On the one hand, the aggregation models for of randomly oriented non-spherical aerosol particles can be analytically established. On the other hand, it can be revised in terms of multi-factor coupling and real-time spatial distribution of particles. -
Key words:
- aerosol /
- aggregation model /
- aggregation mechanism /
- aggregation dynamics /
- model optimization
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表 1 气溶胶粒子凝聚仿真模型的比较
Table 1. Comparison of simulation models for aerosol particles aggregation
Simulation model Movement mechanism Structure features Application scope DLA Brownian motion Dendritic structure, insensitive to adhesion probability Film growth, powder particle aggregation,
electrochemical deposition, etc.RLA Brownian motion Compact structure, high dependence on cohesion probability Aerogel synthesis, material growth, colloidal particles aggregation, etc. BA Linear motion Compact structure, no fixed trend of growth direction and large fractal dimension Colloidal particles aggregation, film growth, dust particles aggregation, etc. BPCA Linear motion Compact structure and large fractal dimension Dust particle aggregation, powder aggregation, etc. DLCA Brownian motion Dendritic structure, small correlation between fractal dimension and cluster size when a large number of particles are simulated Material growth, electrochemical deposition,
aerosol aggregation, etc.RLCA Brownian motion More compact structure than DLCA model, high dependence on coalescence probability Aerogel synthesis, material growth, colloidal particles aggregation, etc. CCA Brownian motion Compact structure, fractal dimension size is related to adhesion probability and collision efficiency Colloid, soil, aerosol aggregation, etc. BCCA Linear motion Compact structure and large fractal dimension Aerosol particles(dust and microbial particles) aggregation, etc. -
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