A stability theory for lyophobic colloids was put forth in the 1940’s by Derjaguin, Landau, Verwey, and Overbeek. This theory, known as DLVO theory, has gone through the test of time and survived as a pillar of colloid science. In the present work, this theory has been used for describing the behavior of fine coal and silica particles in aqueous media. It has been found, however, that the classical DLVO theory is applicable only to weakly hydrophobic solids but not to very hydrophobic ones. The coagulation experiments conducted with very hydrophobic particles suggest that there exists a strong attractive force that has not been considered in the theory. This non-DLVO force has been estimated in the present work based on the data obtained from coagulation experiments.

Contributions from the non-DLVO force, which is referred to as hydrophobic interaction energy (V_H), have been related to the nondispersion component of work of adhesion of water on solids (W^nd_a). An expression for V_H which is now a function of W^nd_a, has been added as a third term in the DLVO equation in order to better describe the stability of colloidal suspensions regardless of the hydrophobicity of the particles involved.

A population balance model for a system of isotropic turbulent flow has been developed. Both aggregate growth and breakage have been considered in the model and their rate constants have been derived from a phenomenological approach. Numerical procedures have been proposed for solving the coagulation kinetic equations. Computer simulations show that the model is fairly flexible and the results are in reasonable agreement with experiment.