A Novel Numerical Procedure to Estimate the Electric Charge in the Pore from Filtration of Single-Salt Solutions.

Patrick Dutournié,Sébastien Déon,T Jean Daou

doi:10.3390/membranes11100726

Abstract

The assessment of physicochemical parameters governing the transport of ions through nanoporous membranes is a major challenge due to the difficulty in experimental estimation of the dielectric constant of the solution confined in nanopores and the volumetric membrane charge. Numerical identification by adjusting their values to fit experimental data is a potential solution, but this method is complicated for single-salt solutions due to the infinite number of couples that can describe a rejection curve. In this study, a novel procedure based on physical simplifications which allows the estimation of a range of values for these two parameters is proposed. It is shown here that the evolution of the interval of membrane charge with salt concentration can be described in all the experimental conditions by the Langmuir–Freundlich hybrid adsorption isotherm. Finally, it is highlighted that considering the mean dielectric constant and the adsorption isotherms assessed from a range of concentrations allowed a good prediction of rejection curves, irrespective of the salt and membrane considered.

Highlights

Pressure-driven membrane processes are often used to solve environmental issues such as desalination, wastewater treatment, drinking water production, etc
The vision of the transfer at the membrane/solution interfaces is usually improved by considering the dielectric exclusion due to a solvation energy barrier induced by changes in the dielectric constant of the solvent inside pores
This model, which was initially proposed by Bowen et al [7], has proved a good ability to describe the experimental ion rejections obtained in many experimental conditions [8,9,10,11], provided that four parameters are known or adjusted

Summary

Introduction

Pressure-driven membrane processes are often used to solve environmental issues such as desalination, wastewater treatment, drinking water production, etc. The vision of the transfer at the membrane/solution interfaces is usually improved by considering the dielectric exclusion due to a solvation energy barrier induced by changes in the dielectric constant of the solvent inside pores This model, which was initially proposed by Bowen et al [7], has proved a good ability to describe the experimental ion rejections obtained in many experimental conditions [8,9,10,11], provided that four parameters are known or adjusted. The estimation of the volumetric membrane charge Xd and the dielectric constant of the solution inside pores εp is more problematic and the way to assess them represents the key for a better understanding of transport mechanisms and the development of a predictive numerical tool These parameters are very complicated to assess experimentally, even if recent studies have shown that it is not completely unrealistic to develop original techniques to do so. These methods are not completely satisfying at the present time and a numerical way is often required [21]

Objectives

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Conclusion