Colloid migration in symmetrical non-uniform fractures: particle tracking in three dimensions

A three-dimensional model for the migration of colloids in a saturated fracture is presented, which considers the motion of colloids as a result of advection and diffusion, as well as colloid-surface interactions at the fracture walls. This model is successfully incorporated into a three-dimensional particle tracking algorithm that tracks particles within a continuum and allows consideration of the migration of colloids in symmetrical, three-dimensional, non-uniform fractures. The framework is general enough to incorporate non-local interactions that provide colloid motion relative to the fluid. The algorithm is verified against classical Taylor dispersion, and its generalization to a sorbing phase, in a uniform fracture and shows excellent agreement with theory. A simple, non-uniform fracture that has an analytically tractable velocity field is also considered, and both quantitative and qualitative comparisons are made with the uniform fracture case. The modelling of more complex fracture geometries is also discussed and a particular case is implemented within the particle tracking framework.