Application of DLVO energy map to evaluate interactions between spherical colloids and rough surfaces.

This study theoretically evaluated interactions between spherical colloids and rough surfaces in three-dimensional space using Derjaguin-Landau-Verwey- Overbeek (DLVO) energy/force map and curve. The rough surfaces were modeled as a flat surface covered by hemispherical protrusions. A modified Derjaguin approach was employed to calculate the interaction energies and forces. Results show that more irreversible attachments in primary minima occur at higher ionic strengths, which theoretically explains the observed hysteresis of colloid attachment and detachment during transients in solution chemistry. Secondary minimum depths can be increased significantly in concave regions (e.g., areas aside of asperities or between asperities) due to sidewall interactions. Through comparing the tangential attractive forces from asperities and the hydrodynamic drag forces in three-dimensional space, we showed that attachment in secondary minima can be located on open collector surfaces of a porous medium. This result challenges the usual belief that the attachment in secondary minima only occurs in stagnation point regions of the porous medium and is absent in shear flow systems such as parallel plate flow chamber and impinging jet apparatus. Despite the argument about the role of secondary minima in colloid attachment remained, our study theoretically justified the existence of attachment in secondary minima in the presence of surface roughness. Further, our study implied that the presence of surface roughness is more favorable for attachment in secondary minima than in primary minima under unfavorable chemical conditions.