Dukhin A S, Dukhin S S, Goetz P J
Electrokinetic Technology, Goldens Bridge, NY 10526, USA.
Adv Colloid Interface Sci. 2007 Oct 31;134-135:35-71. doi: 10.1016/j.cis.2007.04.006. Epub 2007 Apr 29.
Gravity is a potential factor of aggregative stability and/or coagulation for any heterogeneous system having a density contrast between the dispersed phase and its dispersion medium. However, gravity becomes comparable to other stability factors only when the particle size becomes large enough. Since the particle size may grow in time due to various other instabilities, even nano-systems may eventually become susceptible to gravity. There have been many attempts in the last century to incorporate gravity in the overall theory of aggregative stability, but the relevant papers are scattered over a wide variety of journals, some of which are very obscure. Reviews on this subject in modern handbooks are scarce and inadequate. No review describes the role of gravity at all three levels introduced by DLVO theory for characterizing aggregative stability, namely: particle pair interaction, collision frequency and population balance equation. Furthermore, the modern tendency towards numerical solutions overshadows existing analytical solutions. We present a consistent review at each DLVO level. First we describe the role of gravity in particle pair interactions, including both available analytical solutions as well as numerical stability diagrams. Next we discuss a number of works on collision frequency, including works for both charged and non-charged particles. Finally, we present analytical solutions of the population balance equation that takes gravity into account and then compare these analytical solutions with numerical solutions. In addition to the traditional aggregate model we also discuss work on a fractal model and its relevance to gravity controlled stability. Finally, we discuss many experimental works and their relationship to particular theoretical predictions.
对于任何在分散相与其分散介质之间存在密度差异的非均相系统而言，重力是聚集稳定性和/或凝聚作用的一个潜在因素。然而，只有当粒径变得足够大时，重力才会与其他稳定性因素相当。由于粒径可能因各种其他不稳定性而随时间增长，所以即使是纳米系统最终也可能受到重力影响。在上个世纪，人们曾多次尝试将重力纳入聚集稳定性的整体理论中，但相关论文分散在各种各样的期刊上，其中一些期刊非常晦涩难懂。现代手册中关于这个主题的综述既稀少又不充分。没有一篇综述描述重力在由DLVO理论引入的用于表征聚集稳定性的所有三个层面上的作用，即：颗粒对相互作用、碰撞频率和群体平衡方程。此外，现代倾向于数值解的趋势掩盖了现有的解析解。我们在DLVO理论的每个层面进行了连贯的综述。首先，我们描述重力在颗粒对相互作用中的作用，包括现有的解析解以及数值稳定性图。接下来，我们讨论一些关于碰撞频率的研究工作，包括带电和不带电颗粒的相关研究。最后，我们给出考虑重力的群体平衡方程的解析解，然后将这些解析解与数值解进行比较。除了传统的聚集体模型，我们还讨论了分形模型的相关工作及其与重力控制稳定性的关系。最后，我们讨论了许多实验工作及其与特定理论预测的关系。
