A general criterion based on the implicit function theorem to model aggregation and adsorption in colloidal dispersions

This paper, which may interest not only colloid scientists and physical chemists but also applied mathematicians, completes some previous results on aqueous silicon nitride dispersions. Experimental data on adsorption from liquid solution were first obtained by a titration method and then used to derive the number of solid particles from an equilibrium constraint. To discuss the complex mechanisms affecting simultaneous solid particle aggregation and small ion adsorption at the solid/liquid interface, the Dini implicit function theorem (DT) has been applied to the equilibrium condition for a former suspension Gibbs free energy. It was able to relate the average particle number to the ion concentration adsorbed, but not to unequivocally specify their dependence on the liquid phase pH. We attempt here to model aggregation both through bulk and interfacial quantities. The generalized DT-based criterion has first been formulated in all generality, and then adopted according to a wider investigation. The results obtained confirm the original guess, i.e., to regard solid aggregation as dominated by interfacial mechanisms.