Goudeli Eirini, Eggersdorfer Maximilian L, Pratsinis Sotiris E
Particle Technology Laboratory, Institute of Process Engineering, Department of Mechanical and Process Engineering, Eidgenössische Technische Hochschule Zürich , Sonneggstrasse 3, CH-8092 Zürich, Switzerland.
Langmuir. 2015 Feb 3;31(4):1320-7. doi: 10.1021/la504296z. Epub 2015 Jan 20.
Agglomeration occurs in environmental and industrial processes, especially at low temperatures where particle sintering or coalescence is rather slow. Here, the growth and structure of particles undergoing agglomeration (coagulation in the absence of coalescence, condensation, or surface growth) are investigated from the free molecular to the continuum regime by discrete element modeling (DEM). Particles coagulating in the free molecular regime follow ballistic trajectories described by an event-driven method, whereas in the near-continuum (gas-slip) and continuum regimes, Langevin dynamics describe their diffusive motion. Agglomerates containing about 10-30 primary particles, on the average, attain their asymptotic fractal dimension, D(f), of 1.91 or 1.78 by ballistic or diffusion-limited cluster-cluster agglomeration, corresponding to coagulation in the free molecular or continuum regimes, respectively. A correlation is proposed for the asymptotic evolution of agglomerate D(f) as a function of the average number of constituent primary particles, n̅(p). Agglomerates exhibit considerably broader self-preserving size distribution (SPSD) by coagulation than spherical particles: the number-based geometric standard deviations of the SPSD agglomerate radius of gyration in the free molecular and continuum regimes are 2.27 and 1.95, respectively, compared to ∼1.45 for spheres. In the transition regime, agglomerates exhibit a quasi-SPSD whose geometric standard deviation passes through a minimum at Knudsen number Kn ≈ 0.2. In contrast, the asymptotic D(f) shifts linearly from 1.91 in the free molecular regime to 1.78 in the continuum regime. Population balance models using the radius of gyration as collision radius underestimate (up to about 80%) the small tail of the SPSD and slightly overpredict the overall agglomerate coagulation rate, as they do not account for cluster interpenetration during coagulation. In the continuum regime, when a recently developed agglomeration rate is used in population balance equations, the resulting SPSD is in excellent agreement with that obtained by DEM.
团聚现象发生在环境和工业过程中，特别是在低温下，此时颗粒烧结或聚结相当缓慢。在此，通过离散元建模（DEM）从自由分子态到连续介质态研究了团聚颗粒（在没有聚结、凝聚或表面生长情况下的凝聚）的生长和结构。在自由分子态下凝聚的颗粒遵循由事件驱动方法描述的弹道轨迹，而在近连续介质（气体滑移）和连续介质态下，朗之万动力学描述它们的扩散运动。平均而言，包含约10 - 30个初级颗粒的团聚体通过弹道或扩散限制的簇 - 簇团聚分别达到其渐近分形维数D(f)为1.91或1.78，分别对应于自由分子态或连续介质态下的凝聚。提出了团聚体D(f)作为组成初级颗粒平均数量n̅(p)的函数的渐近演化的相关性。与球形颗粒相比，团聚体通过凝聚表现出明显更宽的自保持尺寸分布（SPSD）：在自由分子态和连续介质态下，基于数量的SPSD团聚体回转半径的几何标准差分别为2.27和1.95，而球体约为1.45。在过渡态下，团聚体表现出准SPSD，其几何标准差在克努森数Kn≈0.2时通过最小值。相比之下，渐近D(f)从自由分子态下的1.91线性转变为连续介质态下的1.78。使用回转半径作为碰撞半径的群体平衡模型低估了（高达约80%）SPSD的小尾巴，并略微高估了整体团聚体凝聚速率，因为它们没有考虑凝聚过程中的簇相互渗透。在连续介质态下，当在群体平衡方程中使用最近开发的团聚速率时，得到的SPSD与通过DEM获得的结果非常吻合。
