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.
Keywords: Aggregation in a mixing flow; Brownian aggregation; Critical coagulation concentration; DLVO theory; Schulze-Hardy rule.
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