A diffusion model for the swelling of compacted Na-montmorillonite in water

A diffusion model, which considers the hydration force, is presented to predict Na-montmorillonite swelling in water. The swelling originates from the growth of the layer-to-layer distance in the montmorillonite layered structure. The hydration force controls the swelling when the montmorillonite has a layer-to-layer distance less than 100 angstrom. The layer separation increases because of the diffusion motion of the layers in water. The motion is controlled by a viscous drag force of liquids and four interaction forces between the layers, including hydration, van der Waals, repulsive electrostatic double-layer, and repulsive entropic forces. Based on the model, a diffusivity is defined for the compacted Na-montmorillonite over a wide concentration range of montmorillonite. The model predicted the volume fraction of the montmorillonite in the swelling process and agreed with the published experimental results from 60% to 0.001% volume fraction. Besides that, the result revealed that hydration force, repulsive electrostatic double-layer force, and repulsive entropic force, dominate crystalline swelling, osmotic swelling, and Brownian swelling respectively. The result explained the coexistence phenomenon of dense dispersion, concentrated dispersion, and dilute dispersion in the swelling process.