Transient Electroosmotic Flow of Maxwell Fluids Through Soft Channels with High Surface Potentials

This study analyzes the combined effects of non-Newtonian rheology and electrostatics on the transient electroosmotic flow of Maxwell fluids in soft channels. The walls of the rigid channels are hydrophobic, ionically charged, and coated with a polyelectrolyte layer (PEL). This design is intended to regulate both the surface electric potential and the flow velocity. The mathematical model is based on modified Poisson–Boltzmann and momentum equations, which are solved numerically using a one-dimensional (1D) approach. The results indicate that high potentials, exceeding the Debye–Hückel limit, are achieved under conditions of thick polyelectrolyte layers, high surface charge density, and a higher concentration of fixed charges compared to the electrolyte ionic concentration. In this regime, steric effects increase the electric potential; however, this potential increase is limited by the formation of a Donnan potential. The hydrodynamic analysis demonstrates that the velocity magnitude is influenced not only by the wall potential but also by the spatial distribution of free charge density and electroosmotic force, which, in turn, are affected by steric effects. Additionally, changing the polarity and concentration of fixed charge in the PEL produces asymmetric flows, and while hydrodynamic slip enhances velocity, the drag parameter reduces it. Finally, the dimensionless parameters that control the time required to dampen the oscillatory flow induced by viscoelastic effects and reach steady-state are mainly the relaxation time, the drag parameter, the PEL thickness, and the electrokinetic parameter of the PEL, while the surface charge density and the external pressure gradient exert a comparatively minor influence.