Bi-modal hetero-aggregation rate response to particle dosage

The rate of flocculation of cationic polystyrene latex (PSL) particles by smaller, anionic PSL particles has been measured using a low-angle static light scattering technique. The rate of aggregate growth has been investigated as a function of particle size ratio and relative concentration of each particle species (for a constant dose of cationic particles). Contrary to many previous reports, two peaks in the flocculation rate were observed as a function of dose. It is speculated that the peak observed at the lower particle concentration coincides with the dose yielding maximum constant collision efficiency in the steady-state regime, a condition which is attained only after complete adsorption of the smaller particles onto the larger particle species. The peak at the higher particle concentration is believed to be related to the maximum collision rate constant upon reaching the steady-state regime, the value of which corresponds to maximum degree of aggregation and therefore the maximum mean collision efficiency prior to reaching this condition. From classical collision kinetics, the rate of aggregate growth may be represented as being proportional to the product of the collision rate constant and collision efficiency at any given time. Given then that the maximum value of these two variables coincides with different particle concentrations, the product of the response of each to particle dosage can in some cases yield a net bi-modal aggregation rate response to particle dosage.