Normalization and extension of the single-collector efficiency correlation equation for predicting transport of (nano)particles

The colloidal transport and deposition are important phenomena involved in many engineering problems. In the environmental engineering field the use of micro- and nano-scale zerovalent iron (M-NZVI) is one of the most promising technologies for groundwater remediation. Colloid deposition is normally studied from a micro scale point of view and the results are then implemented in macro scale models that are used to design field-scale applications. The single collector efficiency concept predicts particles deposition onto a single grain of a complex porous medium in terms of probability that an approaching particle would be retained on the solid grain. In literature, many different approaches and equations exist to predict it, but most of them fail under specific conditions (e.g. very small or very big particle size and very low fluid velocity) because they predict efficiency values exceeding unity. By analysing particle fluxes and deposition mechanisms and performing a mass balance on the entire domain, the traditional definition of efficiency was reformulated and a new definition was proposed. This new formulation is valid for a wide range of parameters and it never predicts efficiency values exceeding unity because of its formulation. Moreover a new traditional single collector contact efficiency correlation equation was formulated starting from the fitting of the mass flow on the collector. This equation shows that there are important deposition terms, neglected by previous correlation equations present in literature, but that are essential to extend the definition of single collector contact efficiency to a wider range of parameters (e.g. very small Peclet numbers).