On the collision efficiency in polymer flocculation of colloidal particles

The applicability of the conventional collision efficiency approach for the case where the collision of colloidal particles is not necessary for the rate-determining step is examined. On the basis of a dynamical treatment, we show that the fundamental assumption made in the conventional analysis may lead to a significant error. Depending upon the ratio of the number of sites on the colloidal surfaces to the number of polymer molecules, and the relative magnitudes of the desorption rate constant and the adsorption rate constant, the collision efficiency calculated by the conventional analysis may be either underestimated or overestimated. The present approach yields the temporal variation of the distribution of the fractional surface coverage. It can be shown that if the number of colloidal particles is large, using the mean fractional surface coverage instead of the exact distribution of the fractional surface coverage is sufficient for the evaluation of the collision efficiency.