DLVO interaction energy between spheroidal particles and a flat surface

Abstract

The orientation dependent interaction energy between a spheroidal particle and an infinite planar surface is determined using the surface element integration (SEI) technique. The interaction energy predictions of SEI are shown to be considerably more accurate than the corresponding predictions based on Derjaguin’s approximation (DA). Comparison with the Hamaker approach for evaluating the non-retarded van der Waals interaction energy reveals that SEI predicts the orientation dependent interaction energy for spheroidal particles with remarkable accuracy. It is further shown that both SEI and DA give nearly identical predictions of the electrostatic double layer interaction energy between a spheroidal particle and a flat plate at high electrolyte concentrations. However, at low electrolyte concentrations, considerable deviations are noted between the predictions of SEI and DA, particularly for very small aspect ratios of the particle (aspect ratio=length of minor axis/length of major axis). It is also noted that when the spheroidal particle is oriented with its major axis parallel to the planar surface, DA incorrectly predicts the interaction energy as that of a spherical particle with a radius equal to the semi-major axis of the spheroid. This limitation of DA is avoided in SEI, which accounts for the dependence of the interaction energy on the actual shape (aspect ratio) of the particle at any orientation. Predictions of the DLVO interaction energy based on SEI indicate that, at high electrolyte concentrations, the orientation dependence of the interaction energy is not significant at large separation distances, and assumption of an equivalent spherical particle may be sufficient. However, significant deviation of the interaction energy from that of a spherical particle is observed at small separation distances, particularly at low electrolyte concentrations. At these small separation distances, where the correct orientation dependence of the interaction energy must be considered for proper calculations of particle interaction phenomena with flat surfaces (e.g. particle deposition), SEI provides a facile route to perform such calculations.