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Recently, the use of nanoparticles in extraction columns has gained increasing attention due to their potential to enhance mass transfer processes. Most of the reported work, however, has been concerned with mass transfer enhancement in gas–liquid systems in the presence of nanoparticles, while limited studies of liquid–liquid systems have been reported. Liquid–liquid extraction is an extensively employed separation method that has taken on a substantial role in engineering and industrial applications for recovery processes. Therefore, the aim of this review article is to provide an overview of the state-of-the-art from the available literature on the effect of nanoparticles on the hydrodynamic behavior and mass transfer performance of liquid–liquid systems. Attention is also given to providing an understanding of the mechanisms responsible for the improvements in mass transfer with the use of nanoparticles. In the majority of studies, the presence of nanoparticles was found to be beneficial and to lead to improved mass transfer, although a few investigations reported a detrimental impact of nanoparticles. The literature does not clearly describe the conditions under which the addition of nanoparticles would be unfavorable. Moreover, the addition of nanoparticles always introduces potential drawbacks, such as sedimentation, accumulation, or clogging inside extraction columns, as well as the need to separate the nanoparticles at the outlets. These drawbacks have not been considered in the literature, limiting the practical employment of nanoparticles in this industry. [ABSTRACT FROM AUTHOR]

In this work, a two-phase mixture model for evaluation of flow and heat transfer performance of SiO 2 /water nanofluids under turbulent flow was proposed by considering the heterogeneity of concentration due to crossed effect and the influences of shear rate, viscosity gradient, thermophoresis and Brownian motion on the diffusion of the nanoparticles. The effects of Peclet number, Reynolds number, nanoparticle size and nanofluid mean concentration on the distribution of nanoparticles have been evaluated. The values of thermal conductivity and viscosity as the main thermophysical properties of nanofluids changed across different layers of the liquid due to the heterogeneous distribution of concentration. It was observed that an increase in the Peclet number caused heterogeneity in the distribution of the properties. The achieved nanoparticle distribution has been implemented for analysis of nanofluid using two-phase mixture model. It was found that the effect of nanofluid concentration on the Nusselt number was more noticeable in lower Reynolds numbers due to the insignificant effect of flow momentum on heat transfer. The maximum of 43.9% enhancement in convection heat transfer was achieved by dispersion of 4% SiO 2 nanoparticles inside DI-water at Re = 25,000. [ABSTRACT FROM AUTHOR]