Li Xiao-Yan, Zhang Jian-Jun
Department of Civil Engineering, University of Hong Kong, Pokfulam Road, Hong Kong, China.
J Colloid Interface Sci. 2003 Jun 1;262(1):149-61. doi: 10.1016/S0021-9797(03)00194-2.
Mathematical simulation of particle coagulation dynamics was carried out using improved sectional modeling techniques for a system with a pulsed input of primary particles. The methodological improvement included the modification of the size density function based on a realistic assumption of particle size distributions, the application of a new and comprehensive curvilinear collision model, and special adjustment for the mass transfer of a doublet of particles that were very different in size. The simulation results demonstrated that the rectilinear model over-predicted the rate of particle coagulation and that the degree of over-prediction increased as the particles increased in size and the system became more heterogeneous. The coagulation rate increased remarkably as the fractal dimension of the particle aggregates decreased. The curvilinear model and the fractal scaling relationship in place of the rectilinear model and the Euclidean sizing geometry are two important modifications to the conventional Smoluchowski modeling approach. However, both modifications, rather than only one of them, should be applied together to produce more accurate and realistic simulations of coagulation dynamics. As indicated by the simulation, the importance of fluid shear rate to particle coagulation is reduced according to the curvilinear model compared to that previously described with the rectilinear model. As particles increased in size, the role of shear rate in coagulation became even less significant according to the curvilinear view of particle collisions. The results of numerical simulations in terms of the evolution of particle size distributions compared reasonably well with the observations of the jar-test coagulation experiments, which suggested the applicability of the modeling system, including the modified curvilinear-fractal approach, established in the present study.
采用改进的分区建模技术，对具有初级粒子脉冲输入的系统进行了颗粒凝聚动力学的数学模拟。方法改进包括基于颗粒尺寸分布的实际假设修改尺寸密度函数、应用新的综合曲线碰撞模型以及对尺寸差异很大的粒子对的传质进行特殊调整。模拟结果表明，直线模型高估了颗粒凝聚速率，并且随着颗粒尺寸增加和系统变得更加不均匀，高估程度增加。随着颗粒聚集体的分形维数降低，凝聚速率显著增加。用曲线模型和分形标度关系代替直线模型和欧几里得尺寸几何形状是对传统斯莫卢霍夫斯基建模方法的两个重要修改。然而，这两种修改应一起应用，而不是仅应用其中一种，以产生更准确和现实的凝聚动力学模拟。如模拟所示，与先前用直线模型描述的情况相比，根据曲线模型，流体剪切速率对颗粒凝聚的重要性降低。随着颗粒尺寸增加，根据颗粒碰撞的曲线观点，剪切速率在凝聚中的作用变得更不重要。颗粒尺寸分布演变的数值模拟结果与搅拌试验凝聚实验的观察结果相当吻合，这表明本研究建立的包括改进的曲线 - 分形方法在内的建模系统具有适用性。
