Aggregation always occurs in industrial processes with fractal-like particles, especially in dense systems (the volume fraction, ϕ>1%). However, the classic aggregation theory, established by Smoluchowski in 1917, cannot sufficiently simulate the particle dynamics in dense systems, particularly those of generat ed fractal-like particles. In this article, the Langevin dynamic was applied to study the collision rate of aggregations as well as the structure of aggregates affected by different volume fractions. It is shown that the collision rate of highly concentrated particles is progressively higher than that of a dilute concentration, and the SPSD (self-preserving size distribution) is approached (σg,n≥1.5). With the increase in volume fraction, ϕ, the SPSD broadens, and the geometric standard is 1.54, 1.98, and 2.73 at ϕ= 0.1, 0.2, and 0.3. When the volume fraction, ϕ, is higher, the radius of gyration is smaller with the same cluster size (number-based), which means the particle agglomerations are in a tighter coagulation. The fractal-like property D_f is in the range of 1.60–2.0 in a high-concentration system. Knowing the details of the collision progress in a high-concentration system can be useful for calculating the dynamics of coagulating fractal-like particles in the industrial process.

中文翻译：

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布朗凝聚的高浓度聚合和碰撞

聚集总是发生在具有分形状颗粒的工业过程中，尤其是在密集系统中（体积分数，φ>1%）。然而，由 Smoluchowski 于 1917 年建立的经典聚集理论不能充分模拟稠密系统中的粒子动力学，尤其是那些生成的分形状粒子。本文应用朗之万动力学研究了聚集体的碰撞率以及不同体积分数对聚集体结构的影响。结果表明，高浓度粒子的碰撞率逐渐高于低浓度粒子的碰撞率，并接近SPSD（自保尺寸分布）（σg，n≥1.5）。随着体积分数 ϕ 的增加，SPSD 变宽，并且在 ϕ= 0.1、0.2 和 0.3 时几何标准为 1.54、1.98 和 2.73。当体积分数 ϕ 较高时，在相同簇大小（基于数量）的情况下，回转半径较小，这意味着颗粒团聚更紧密。分形性质 D在高浓度系统中，_f在 1.60-2.0 的范围内。了解高浓度系统中碰撞过程的细节对于计算工业过程中凝结分形粒子的动力学非常有用。