Collision efficiency factor for heteroaggregation: Extension to soft interactions

Abstract

An improved model for the collision efficiency factor of clusters of oppositely charged spheres has been developed, which accounts for repulsive and attractive interactions that occur at a finite distance from the colliding species, i.e., the so-called "soft" interactions. Trends in measured optimum dosages for rapid aggregation with increasing Debye length ͑a decrease at particle size ratios between 0.3 and 1 and an increase at particle size ratios less than 0.3͒ are explained qualitatively by employing the modified collision efficiency model. Several observations from the literature, specifically the formation of stringlike aggregates at low ionic strength and the uneven optimum dosage requirements of particles of equal size, are also explained in view of the model presented.

Dual pH-triggered physical gels prepared from mixed dispersions of oppositely charged pH-responsive microgels

“…Oppositely charged particles are good candidates for heteroaggregation. 18,19 Although heteroaggregation has received considerable attention, 20,21 heteroaggregation involving microgels has been less widely studied. [22][23][24][25] Heteroaggregation of microgels has been studied in the context of composite preparation.…”

Discrete bivariate population balance modelling of heteroaggregation processes

“…Introducing an excluded surface area to each adsorbed MF-RhB particle, is also physically traceable due to electrostatic repulsion to other MF-RhB particles on the PS surface. The exact extent caused by this remains uncertain though, since shielding effects due to cluster formation [35,36] also limit the average number of surface MF-RhB particles, but were not considered in the kernel.…”

“…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.…”

“…In the original publication, the kernel is limited in use to the dimer formation rate. It does not consider rotation of the clusters and shielding effects, as investigated in other contributions [35,36]. Here the kernel is used not restricted to the dimer formation rate.…”

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