Application of the DLVO theory for particle deposition problems

Abstract

Implications of the DLVO theory for problems associated with colloid particle adsorption and deposition at solid/liquid interfaces were reviewed. The electrostatic interactions between two planar double-layers described by the classical Poisson–Boltzmann (PB) equation were first discussed. Then, the approximate models for calculating interactions of curved interfaces (e.g. spheres) were exposed in some detail, inter alia the extended Derjaguin summation method and the linear superposition approach (LSA). The results stemming from these models were compared with the exact numerical solution for two dissimilar spheres (including the case of sphere/plane interactions) obtained in bispherical coordinate system. The electrostatic interaction energy was used in combination with dispersion interactions for constructing the DLVO energy profiles discussed next. The influence of surface roughness and charge heterogeneity on energy profiles was also discussed. It was demonstrated that in particle deposition problems the monotonically changing profiles determined by the electrostatic interactions played the most important role. In further part of the review the role of these electrostatic interactions in adsorption and deposition of colloid particles was discussed. The governing continuity equation was exposed incorporating the convective transport in the bulk and the specific force dominated transport at the surface. Approximate analytical models aimed at decoupling of these transfer steps were described. It was demonstrated that the surface boundary layer approximation (SFBLA) was the most useful one for describing the effect of electrostatic interaction at initial adsorption stages. A procedure of extending this model for non-linear adsorption regimes, governed by the steric barrier due to adsorbed particles, was also presented. The theoretical results were then confronted with experimental evidences obtained in the well-defined systems, e.g. the impinging-jet cells and the packed-bed columns of monodisperse spherical particles. The experiments proved that the initial adsorption flux of particles was considerably increased in dilute electrolytes due to attractive electrostatic interactions. This was found in a quantitative agreement with the convective diffusion theory. On the other hand, the rate of later adsorption stages was diminished by the electrostatic lateral interactions between adsorbed and adsorbing particles. Similarly, the experimental data obtained by various techniques (AFM, reflectometry, optical microscopy) demonstrated that these interactions reduced significantly the maximum monolayer coverages at low ionic strength. This behaviour was found in good agreement with theoretical MC-RSA simulation performed by using the DLVO energy profiles. The extensive experimental evidences seem, therefore, to support the thesis that the electrostatic interactions play an essential role in adsorption phenomena of colloid particles.