Analytical solutions for monodisperse and polydisperse colloid transport in uniform fractures

Abstract

Analytical solutions are derived describing the transport of suspensions of monodisperse as well as polydisperse colloid plumes of neutral buoyancy within a fracture with uniform aperture. Various initial and boundary conditions are considered. It is shown that both the finite colloid size and the characteristics of the colloid diameter distribution significantly affect the shape of colloid concentration breakthrough curves. Furthermore, increasing the standard deviation of the colloid diameter enhances colloid spreading and increases the number of attached colloids when colloid–wall interactions are taken into account. Excellent agreement between available experimental data and the analytical solution for the case of an instantaneous release of monodisperse colloids in a natural fracture is observed.