Electrokinetic diffusioosmosis of viscoelastic Phan-Thien–Tanner liquids in slit microchannels

Abstract

This research presents a theoretical/numerical investigation on electrokinetic diffusioosmotic flows of viscoelastic Phan-Thien–Tanner liquids in slit microchannels subjected to general wall zeta potentials. Based on a unidirectional lubricating flow analysis, numerical solutions to the effective viscosity, first normal stress difference, flow velocity field, and volume flow rate are obtained and expressed in terms of the spatial coordinate, half channel width to Debye length ratio, diffusivity difference parameter, wall zeta potential, and a combined elongation viscosity and Deborah number parameter (in short, Deborah number). Results of our parametric studies show that the respective strengths of the shear thinning and normal stress effects can be increased as the Deborah number is increased. Moreover, the respective strengths of the flow velocity and volume flow rate are increased as the Deborah number is increased regardless of the flow velocity and flow rate being directed towards upstream or downstream. Finally, based on the diffusivity difference parameter and zeta potential parametric pairs, the parametric regimes available for the volume flow rate to be directed towards downstream (upstream) are increased (reduced) as the value of the Deborah number parameter is reduced.