Orthokinetic aggregation of charged colloidal particles in the presence of repulsive double layer force: A trajectory analysis with the solution of non-linear Poisson–Boltzmann equation

Effects of ionic valence on aggregation kinetics of colloidal particles with and without a mixing flow

HYPOTHESIS

The classical Schulze-Hardy rule states that the critical coagulation concentration (CCC) of colloidal particles is inversely proportional to the counter-ionic valence at powers ranging from 2 to 6. However, the inverse Schulze-Hardy rule has recently been proposed, suggesting that the CCC can also be inversely proportional to the co-ionic valence. Previous studies on these rules did not consider the effect of flow on aggregation kinetics and the CCC. This study aims to investigate the effect of multivalent counter-ions and co-ions on aggregation kinetics and the CCCs in systems with and without a mixing flow.

EXPERIMENTS

We measured the aggregation rate coefficients of polystyrene sulfate latex particles as a function of the salt concentration with different ionic species. Furthermore, we analyzed these measurements using theoretical models based on hydrodynamic pair-diffusion in a random flow and trajectory analysis in two steady flows. The analysis was conducted using zeta potentials determined through electrophoretic measurements.

FINDINGS

Although the trajectory analysis underestimates the CCCs, the hydrodynamic pair-diffusion model can capture the shift of critical coagulation concentrations in the mixing flow to higher values than those in Brownian aggregation and also shows a better agreement with the experimental results. This result suggests that combining random flow and Brownian diffusion is crucial for developing a consistent framework for predicting both Brownian aggregation and aggregation in a mixing flow.

The Relationship between Gelation Behavior and the Amount of Polymer Dose per Silica Surface Area of "Shake-Gels" Consisting of Silica Nanoparticles and Poly(Ethylene Oxide)

The understanding and control of the rheological behaviors of colloids and polymer mixtures is an important issue for scientific interests and industrial applications. Aqueous mixed suspensions of silica nanoparticles and poly(ethylene oxide) (PEO) under certain conditions are interesting systems called "shake-gels", whose states vary reversibly between sol-like and gel-like under repeated shaking and being left to stand. Previous studies have indicated that the amount of PEO dose per silica surface area (C_p) is a crucial parameter for the formation of shake-gels and the relaxation time from gel-like to sol-like states. However, the relationship between the gelation dynamics and the C_p values has not been fully investigated. To determine how the gelation dynamics are affected by the C_p, we measured the time taken for silica and PEO mixtures to gelate from the sol-like to gel-like states as a function of the C_p under different shear rates and flow types. Our results show that the gelation time decreased with increasing shear rates and depended on the C_p values. Moreover, the minimum gelation time was found around a certain C_p (=0.03 mg/m²) for the first time. The finding suggests that there is an optimum C_p value at which the bridging of silica nanoparticles using PEO is significant, and thus, the shake-gels and stable gel-like states are most likely to form.