Correlation Equation for Predicting Single-Collector Efficiency in Physicochemical Filtration in Saturated Porous Media

TLDR

The study introduces a new equation to predict single‑collector contact efficiency in physicochemical filtration of saturated porous media. The equation is derived by regressing dimensionless deposition parameters against theoretical efficiencies obtained from a rigorous numerical solution of the convective‑diffusion equation that incorporates hydrodynamic interactions and van der Waals forces, assuming the overall efficiency equals the sum of Brownian diffusion, interception, and sedimentation contributions. The resulting equation outperforms existing approaches, showing excellent agreement with theoretical predictions across a wide range of conditions and aligning more closely with experimental data than other expressions.

Abstract

A new equation for predicting the single-collector contact efficiency (η0) in physicochemical particle filtration in saturated porous media is presented. The correlation equation is developed assuming that the overall single-collector efficiency can be calculated as the sum of the contributions of the individual transport mechanismsBrownian diffusion, interception, and gravitational sedimentation. To obtain the correlation equation, the dimensionless parameters governing particle deposition are regressed against the theoretical value of the single-collector efficiency over a broad range of parameter values. Rigorous numerical solution of the convective−diffusion equation with hydrodynamic interactions and universal van der Waals attractive forces fully incorporated provided the theoretical single-collector efficiencies. The resulting equation overcomes the limitations of current approaches and shows remarkable agreement with exact theoretical predictions of the single-collector efficiency over a wide range of conditions commonly encountered in natural and engineered aquatic systems. Furthermore, experimental data are in much closer agreement with predictions based on the new correlation equation compared to other available expressions.