Analysis of an observed relationship between colloid collision efficiency and mean collector grain size

Previous investigators have attempted to use filtration theory to deconvolute the physical and chemical factors that influence colloid filtration in porous media. In the classic single-collector approach, bulk physical properties of the colloids and the medium are assumed to control the rate of colloid–collector collisions, while solution and surface chemical properties are assumed to control the probability of attachment. However, this assumed separation of physical and chemical variables will not apply when collector surface properties also vary with grain size. In recent work, we conducted column experiments with identical colloids and solution conditions, but with sand fractions of different mean grain size. The results indicated that both physical and chemical parameters varied with the collector grain size. However, this analysis was dependent on the particular model used to calculate the rate of colloid–collector collisions (the collector efficiency). To demonstrate that the variation of chemical parameters with grain size is not dependent on a particular physical transport model, in this work we apply and compare three different models for colloid filtration. The assumption of a constant attachment probability (collision efficiency) was found to be inconsistent with the experimental results. Instead, good results were obtained by considering that the collision efficiency varies linearly with the natural logarithm of the hydraulic conductivity of the collector medium. A linear relationship of this type was found for all three colloid filtration models. This analysis confirms that our data show a relationship between collector grain size, hydraulic conductivity, and attachment probability, and that the existence of such a relationship is not dependent on any particular model for colloid filtration.