Implications of inhomogeneous distribution of concentration polarization for interpretation of pressure-driven membrane measurements

Abstract

A number of CFD studies have demonstrated that there is a considerable inhomogeneity of extent of Concentration Polarization (CP) over the membrane surface especially in spacer-filled feed channels. However, the consequences of this inhomogeneity for the interpretation of measurements of solute rejection in pressure-driven membrane processes have received little attention. This study uses a simple model of locally-1D CP combined with a postulated probability distribution of unstirred-layer thickness over the membrane thickness. In this way, we obtain transparent analytical results and can consider qualitative consequences of inhomogeneous distribution of CP over membrane surface. Our analysis shows that disregarding the CP distribution underestimates the CP of strongly positively-rejected solutes and overestimates the CP for the negatively-rejected ones. This observation is especially important for the interpretation of ion rejection from multi-ion solutions in nanofiltration where strong positive and pronounced negative rejections can occur simultaneously for solutes of different charges. We conclude that for reliable interpretation of pressure-driven membrane measurements it is desirable to reduce the inhomogeneity of CP distribution to a minimum in membrane-testing devices.

Ion separations with membranes

“…Fundamental studies using devices such as rotating membranes that give well-controlled CP could prove useful in this regard. [206] Another experimental challenge is assessment of selectivities in very small membranes. Fabrication of membranes with well-controlled pores is often not yet possible at large scales, so researchers examine selectivity using conductivity measurements with different salt solutions.…”

“…Fundamental studies using devices such as rotating membranes that give well‐controlled CP could prove useful in this regard. [ 206 ]…”

Toward Incorporation of Membrane Properties Non-Uniformity in Spiral Wound Module Performance Simulators—Effect of Non-Uniform Permeability on Fouling Layer Evolution

“…This means that the fouling layer, and its evolution, can be described by its probability density function (PDF) instead of its detailed shape. In the same spirit, very recently, the use of the PDF of mass transfer coefficient (computed by CFD codes) is proposed for the computation of permeate concentration without incorporating wall flow in CFD simulations [23]. Dealing with the evolution of PDF is computationally much easier than with the evolution of the detailed layer shape.…”

Nanofiltration of Multi-Ion Solutions: Quantitative Control of Concentration Polarization and Interpretation by Solution-Diffusion-Electro-Migration Model

“…In a major part of testing devices for pressure membrane processes the extent of CP is inhomogeneous. Disregarding this fact can lead to considerable underestimation or overestimation of the impact of CP depending on the sign of the solute rejection [ 16 ]. Therefore, CP inhomogeneity can have a considerable impact on the interpretation of experimental measurements, particularly in multi-ion solutions experiencing very different simultaneous rejections in multi-ion solutions.…”