基于分形学的絮凝理论研究进展

絮凝过程中形成的絮体具有自相似性和标度不变性等特点，是一个典型的分形体。但传统的絮凝理论并未考虑絮体的分形结构，因而存在一定的缺陷。本文主要介绍了引入分形理论后，絮凝形态学和絮凝动力学的发展状况，重点阐述了絮体分形结构与其粒径、强度、密度、沉降速度等之间的关系，以及分形理论对Smoluchowski方程、传统絮体生长模式理论的改进。此外，本文同时指出分形学与絮凝理论的结合在很多方面尚未总结出系统的普适规律，尤其是非线性絮凝动力学仍需进一步完善。

A review of flocculation theories incorporating fractal geometry

Flocs formed during flocculation process have the characteristics of self-similarity and scale invariance, and are recognized as typical fractal objects. However, the conventional flocculation theories did not involve the effects of floc fractal structure. This paper, the advances in flocculation morphology and flocculation dynamics incorporating fractal theories were reviewed. The relations between floc fractal structure and floc size, strength, density and settling velocity, as well as the improvement in Smoluchowski equation and conventional floc growth model by incorporating fractal theories, were elaborated. In addition, it was pointed out that general conclusions in some respects haven’t be drawn in the case of fractal theory applications in flocculation process, and that especially the nonlinear flocculation kinetics still needs to be further developed.