Electroosmotic flow in a concentrated suspension of polyelectrolyte-grafted solid cylindrical particles: a particle-in-cell approach

Abstract

The present study attempts to deal with electrokinetic and hydrodynamic characteristics of mixed electroosmotic and pressure-driven flow through a membrane composed of a swarm of poly-electrolyte-coated solid cylindrical particles. The unit cell model approach is utilized to analyze the hydrodynamic interactions between particles of the multiparticle system. The electroosmotic flow is generated under the influence of an externally applied electric field, and a pressure gradient is assumed in the axial direction of the cylinder. The poly-electrolyte coating over the solid cylindrical particle is considered as a heterogeneous porous medium having variable permeability characteristics. The electrolyte fluid contains charged ions, which can be present and migrate in both inside and outside of the poly-electrolyte layer (PEL). Hence, PEL acts as a semi-permeable porous layer. The PEL is referred to as a fixed charged layer (FCL) owing to an extra number density of immobilized charged ions, fixed on the poly-electrolyte fibers. In order to derive the electric potential distribution in the membrane, the Debye–Hückel approximation is used to linearize the Poisson–Boltzmann equation, which is further used in hydrodynamic governing equations to investigate the electrokinetic effects in the membrane. The flow domain is divided into two subdomains: the FCL region, governed by the Brinkmann–Forchheimer equation, and the clear fluid region, governed by the Stokes equation. The effect of electroosmotic parameters such as electric double layer (EDL) thickness, thickness ratio parameter, and zeta potential, and the membrane parameters such as viscosity ratio, particle volume fraction, stress-jump parameter, Forchheimer number, and variable permeability parameter are analyzed on the flow profile as well as hydrodynamic quantities of the membrane such as hydrodynamic permeability and the Kozeny constant. It is observed that the increasing thickness of the EDL and equivalent EDL reduce the hydrodynamic permeability of the membrane; however, the membrane becomes more hydrodynamic permeable with the enhancement of the zeta potential.