Adsorption isotherms from aqueous liquid phase of H+ and/or OH- ions onto Si3N4 solid surface agglomerates have been derived through titration measurements (Beruto et al., J. Chem. Sec., Faraday Trans, 91(2), 323 (1995)), The isotherms exhibit S-shape and can be fitted with Freundlich as well as with Langmuir type isotherms, In order to explain the agglomeration process based on the decrease of total solid-liquid interfacial energy, a model (ISD) has been developed. The agreement between numerical data derived by this model and the experimental data is quite good, Isotherm equation and agglomeration law should obey also the dispersion thermodynamic stability criterion, This condition yields an extra equation to select the pair of functions, thus providing a criterion to choose between the several equations that fit adsorption and agglomeration data fairly well, The solution of the problem mentioned above, from the mathematical point of view, is based on the Dini implicit function theorem (Mezzasalma and Oliva, Appl. Math, Lett., submitted), The results indicate that Van der Waals adsorption isotherm coupled with the ISD model are compatible with the thermodynamic stability of the aqueous Si3N4 dispersions,