A numerical study of electro-viscous effects by using Poisson-Nernst-Planck equation in a disk cone system

Abstract

This paper investigates the formation of electrical double layers by ionic species in a rotating disk–cone geometry filled with an incompressible ternary nanofluid. Understanding EDL formation in rotating flows is crucial for miniaturized cooling devices, electrochemical reactors and energy-harvesting systems, where fluid momentum and charge transport are strongly coupled. The governing Navier–Stokes equations are coupled with the Poisson–Nernst–Planck equations to describe the interplay between fluid inertia, viscous stresses and electrokinetic forces. By introducing similarity variables, the system of partial differential equations is reduced to a set of ordinary differential equations, which are solved numerically for a range of dimensionless parameters. Radial and tangential velocity profiles, as well as the distributions of positive and negative ions, are obtained for different Schmidt numbers, Reynolds numbers, thermal diffusivities and rotation rates. The results reveal that increasing the Schmidt number from 0.5 to 1.5 leads to about a 40 % rise in the steady-state concentration of negative ions near the cone surface, whereas increasing the Reynolds number from 100 to 500 suppresses the accumulation of negative ions by roughly 30 %. The tangential velocity is enhanced by up to 25 % when the rotation rate of the disk is doubled, while higher thermal diffusivity increases the concentration of positive ions and improves heat transport. The results indicate that stronger centrifugal forces substantially accelerate the radial fluid flow, and that the electro-viscous force can be manipulated to alter the thickness of the electrical double layer. The results indicate that electro-viscous effects together with nanofluid characteristics in the disk–cone configuration creates a viable pathway to enhance heat conduction and regulating ion dispersion. The problem is novel as it couples the Poisson-Nernst-Plank equation with the momentum equation by considering the electrokinetic distribution and momentum of ionic species.