Collision efficiency factor for heteroaggregation: extension to soft interactions

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 0.3) 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.