Pore-Scale Simulations to Determine the Applied Hydrodynamic Torque and Colloid Immobilization

Values of the applied hydrodynamic torque (T-applied) and the resisting adhesive torque (T-adhesion) will determine whether a colloid will be immobilized (T-applied <= T-adhesion) or roll (T-applied > T-adhesion) on a solid water interface. Previous literature has demonstrated in 1-2 collector (grain) systems that the influence of T-applied on colloid retention can be significant under unfavorable attachment conditions and that only a fraction of the solid surface may contribute to retention. However, many questions remain on how to obtain, analyze, and upscale information on the forces and torques that act on colloids near solid surfaces in porous media. To address some of these gaps in knowledge, high resolution pore-scale water flow simulations were conducted for sphere packs (25 spheres) over a range of Darcy velocities, grain sizes and distributions, and porosities. The spatial variability of T-applied was calculated from this information, and successfully described using a lognormal cumulative density function (CDF). Linear interpolation and scaling techniques were subsequently used to predict the lognormal CDF of T-applied for various colloid sizes, grain sizes and distributions, and water velocities. The lognormal CDF of T-applied was then evaluated at select values of T-adhesion (i.e, interaction energy) to quantify the fraction and locations on the solid surface that contributes to colloid retention (S-f), and the theoretical maximum solid phase concentration of retained colloids (S-max).