A dynamic force balance model for colloidal expansion and its DLVO-based application.

A force balance model that describes the dynamic expansion of colloidal bentonite gels/sols is presented. The colloidal particles are assumed to consist of one or several thin sheets with the other dimensions much larger than their thickness. The forces considered include van der Waals force, diffuse double layer force, thermal force giving rise to Brownian motion, gravity, as well as friction force. The model results in an expression resembling the instationary diffusion equation but with an immensely variable diffusivity. This diffusivity is strongly influenced by the concentration of counterions as well as by the particle concentration in the colloid gel/sol. The properties of the model are explored and discussed, exemplified by the upward expansion of an originally highly compacted bentonite tablet in a test tube. Examples are presented for a number of cases with ionic concentrations varying between very dilute waters up to several molar of counterions. The volume fraction of particles ranges from 40% to very dilute sols.