FracVAL: An improved tunable algorithm of cluster-cluster aggregation for generation of fractal structures formed by polydisperse primary particles

In this study, the tunable algorithm of cluster-cluster aggregation developed by Filippov et al. (2000) for generating fractal aggregates formed by monodisperse spherical primary particles is extended to polydisperse primary particles. This new algorithm, termed FracVAL, is developed by using an innovative aggregation strategy. The algorithm is able to preserve the prescribed fractal dimension (D_f) and prefactor (k_f) for each aggregate, regardless of its size, with negligible error for lognormally distributed primary particles with the geometric standard deviation being as large as 3. In contrast, for polydisperse primary particles the direct use of Filippov et al. (2000) method, as is done by Skorupski et al. (2014), does not ensure the preservation of D_f and k_f for individual aggregates and it is necessary to generate a large number of aggregates to achieve the prescribed D_f and k_f on an ensemble basis. The performance of FracVAL is evaluated for aggregates consisting of 500 and 1000 monomers and for fractal dimension variation over the entire range of D_f between 1 and 3 and k_f between 0.1 and 2.7. Aggregates consisting of 500 monomers are generated on average in less than 2.4 min on a common laptop, illustrating the efficiency of the proposed algorithm.

在本研究中，Filippov 等人于 2000 年开发的针对由单分散球形初级粒子形成的分形聚集体可调算法，被扩展应用于多分散初级粒子。该新算法命名为 FracVAL，其开发基于一种创新的聚集策略。该算法能够保持每个聚集体预定的分形维度（D_f）和前因子（k_f），无论其大小如何，对于对数正态分布的初级粒子，其几何标准差可达 3，误差可忽略不计。相比之下，对于多分散初级粒子，直接应用 Filippov 等人（2000）的方法，如 Skorupski 等人（2014）所做的那样，并不能保证单个聚集体中 D_f 和 k_f 的保持，因此需要生成大量的聚集体才能在总体层面上达到预定的 D_f 和 k_f。FracVAL 的性能在由 500 和 1000 个单体组成的聚集体中进行了评估，并测试了分形维度在 1 到 3 以及 k_f 在 0.1 到 2.7 整个范围内的变化。由 500 个单体组成的聚集体在普通笔记本电脑上平均生成时间少于 2.4 分钟，这证明了所提算法的高效性。