Gravity as a factor of aggregative stability and coagulation

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.