Adsorption of charged colloid particles to charged liquid surfaces

In this paper we present a thermodynamic model for the adsorption of charged colloidal particles to air-water and oil-water interfaces from water-based suspensions and derive the equations for the respective particle adsorption isotherms. The effects of electrolyte concentration, surface charge density of both the particles and the air-water (oil-water) interface, particle contact angle, and particle volume fraction are studied in detail. The model is based on a detailed account of the interfacial free energy of particles and electric double layer formation, as well as collective effects related to the free energy of mixing of the particles with the liquid phases (water and oil) and surface charge displacement. The effect of particle size on the adsorption at the air-water and the oil-water interfaces is discussed. An analytical expression for the distribution coefficient of particles between oil and water has been derived and discussed in terms of the effects of electrolyte, contact angle, surface charge, and oil-water interfacial tension. The predictions of the model are in accord with relevant experimental data. The results are directly relevant for understanding the behavior of solid particles as emulsifier agents and foam stabilizers and in the process of antifoaming and liquid-liquid extraction of minerals.