An improved collision efficiency model for particle aggregation

Abstract

A generalized geometric model is presented which describes the collision efficiency factor of aggregation ͑the probability of a binary particle or aggregate collision resulting in adhesion͒ for systems comprised of two oppositely charged species. Application of the general model to specific systems requires calculation of the area of each species available for collision with a second species. This is in contrast to previous models developed for polymer-particle flocculation that are based on the fractional surface coverage of adsorbed polymer. The difference between these approaches is suggested as an explanation for previously observed discrepancies between theory and observation. In the current work the specific case of oppositely charged nondeformable spherical particles ͑heteroaggregation͒ is quantitatively addressed. The optimum concentration of oppositely charged particles for rapid aggregation ͑maximum collision efficiency͒ as a function of relative particle size is calculated and an excellent correlation is found with data taken from literature.

Collision efficiency factor for heteroaggregation: Extension to soft interactions

“…This is in agreement with the collision efficiency model presented by Olsen et al 2 However, Puertas et al found that if the surface potential of one species is lower than that of the other, a greater relative fraction of the less charged species is required to achieve the maximum aggregation rate. This change in optimum dosage should be due to a change in collision efficiency factor but the geometric model 2 of E makes no allowances for variation in surface potential.…”

“…The work presented here attempts to modify the collision efficiency model presented previously 2 to allow for soft interactions, i.e., particle interactions for which the Debye length is significant relative to the particle size. Correction factors are incorporated to account for interactions at a finite distance from the surface of the interacting species, and a number of trends observed from experiment and literature are explained qualitatively using the modified model.…”

Discrete bivariate population balance modelling of heteroaggregation processes

“…While the collision frequency is generally agreed upon in the literature, a multitude of modelling approaches were published for the collision efficiency over the past years [2,[31][32][33][34][35][36]. In the following sections suitable literature models for the calculation of collision frequencies and efficiencies are introduced.…”

“…property state space. The development of appropriate kernels is an area of ongoing research [31][32][33][34][35][36].…”

Dispersion of Colloidal Suspensions and Their Stability

“…Eq. 4.1), which is described as reactivity, sticking probability, or flocculation efficiency (Smellie and La Mer 1958;Hogg 1999;Sandkühler et al 2005;Oolsen et al 2006;.…”