Ultrafiltration of charge-stabilized dispersions at low salinity

TL;DR

This study combines theoretical modeling and experiments to analyze ultrafiltration of charge-stabilized colloidal suspensions at low salinity, highlighting the dominant role of collective diffusion and osmotic pressure in permeate flux.

Contribution

It introduces a comprehensive macroscopic model incorporating electro-hydrodynamic effects and validates it with experiments, revealing the weak influence of concentration polarization on permeate flux.

Findings

Permeate flux is mainly influenced by collective diffusion coefficient D_c.

Strong electro-hydrodynamic effects enhance D_c and osmotic pressure compared to hard-sphere suspensions.

Fouling observed is not due to filter cake formation by crystallization or vitrification.

Abstract

We present a comprehensive study of cross-flow ultrafiltration (UF) of charge-stabilized suspensions, under low-salinity conditions of electrostatically strongly repelling colloidal particles. The axially varying permeate flux, near-membrane concentration-polarization (CP) layer and osmotic pressure profiles are calculated using a macroscopic diffusion-advection boundary layer method, and are compared with filtration experiments on aqueous suspensions of charge-stabilized silica particles. The theoretical description based on the one-component macroion fluid model (OCM) accounts for the strong influence of surface-released counterions on the renormalized colloid charge and suspension osmotic compressibility, and for the influence of the colloidal hydrodynamic interactions and electric double layer repulsion on the concentration-dependent suspension viscosity $\eta$, and collective diffusion coefficient $D_c$. A strong electro-hydrodynamic enhancement of $D_c$ and $\eta$, and likewise of the osmotic pressure is predicted theoretically, as compared with their values for a hard-sphere suspension. We also point to the failure of generalized Stokes-Einstein relations describing reciprocal relations between $D_c$ and $\eta$. According to our filtration model, $D_c$ is of dominant influence, giving rise to an only weakly developed CP layer having practically no effect on the permeate flux. This prediction is quantitatively confirmed by our UF measurements of the permeate flux using an aqueous suspension of charged silica spheres as the feed system. The experimentally detected fouling for the largest considered transmembrane pressure values is shown not to be due to filter cake formation by crystallization or vitrification.