Representation of Heterogeneity in "Single Collector Efficiency" Equation for Multi Walled Carbon Nanotubes

Abstract

Carbon nanotubes (type of engineered nanoparticles) are identified as a group of new and emerging contaminants. Because of their unique characteristics, novel models need to be developed in order to forecast their transport and fate in the saturated porous media. The movement of nanoparticles through saturated porous media has been previously modelled by clean-bed filtration theory. In this theory single collector efficiency (SCE) evaluates the fraction of transported particles that come into contact with the collector grain and can be removed from the aqueous phase. This equation assumes spherical geometry for nanoparticles. This assumption was identified as a short coming concerning carbon nanotubes (CNTs). To address this limitation, single collector efficiency equation was modified to accommodate the cylindrical shape of Multi-Walled Carbon Nanotubes (MWCNT), however, the underlying assumption for this empirical model is uniformity and homogeneity of the porous media. In this paper, further modification of the abovementioned equation is suggested in order to represent the heterogeneity of a natural porous media through replacing the “collector diameter”. This was achieved through utilising field measured properties such as hydraulic conductivity, porosity, and grain-size distribution. The resulting equation overcomes the limitations of current approaches and shows remarkable agreement with exact theoretical predictions of the single collector efficiency over a range of conditions commonly encountered in natural groundwater systems. Furthermore, the theoretical effect of natural heterogeneity on the movement of CNTs in saturated porous media is assessed. It was established that the use of an average grain size can greatly over-estimate the movement of CNTs while representing heterogeneity through the modified equation reduces the modelled mobility of CNTs. In addition, increasing heterogeneity (smaller uniformity coefficient) resulted in mobility reduction for CNTs.