Critical coagulation ionic strengths for heteroaggregation in the presence of multivalent ions

We have obtained the analytical expression for the critical coagulation ionic strengths (CCIS) to be applicable for repulsive heteroaggregation by using the DLVO interaction potential energy between different particles. In addition, we have developed a simple numerical scheme and derived an approximated analytical equation to estimate the CCIS for attractive heteroaggregation, where the double layer attraction between oppositely charged particles can be negligible, particularly in the range of the attraction. We have shown that our approach can nicely describe the experimental CCISs for both repulsive and attractive heteroaggregation as a function of the product of the charge densities characterizing the strength and acing range of double layer interaction.