The purpose of this study is to investigate the flow of viscoelastic fluid through a slit polyelectrolyte-grafted (PE-grafted) nanochannel under applied alternating current (AC) electric field. The PE-grafted nanochannel (also called a soft nanochannel) is represented by a rigid surface coated by a polyelectrolyte layer (PEL) in a brush-like configuration. By solving linearized Poisson–Boltzmann equations and momentum equations, analytical solutions regarding electrical potentials and transient electroosmotic flow (EOF) velocities are derived under appropriate boundary conditions in the decoupled regime of the PE-grafted nanochannel, where the thickness of the PEL is independent of the electrostatic effects triggered by polyelectrolyte charges. We compare the distributions of EOF velocities between PE-grafted and rigid nanochannels. A good agreement with each other is found when the thickness of the PEL is very small. However, the velocity for PE-grafted nanochannels is larger than that for rigid ones. The influences of pertinent dimensionless parameters on the EOF velocities in PE-grafted nanochannels are discussed in detail. The results indicate that the EOF velocity amplitude for PE-grafted nanochannels increases with the thickness of the PEL. Increasing the relaxation time enhances the oscillation of the EOF velocity profiles, yet increasing the retardation time dampens the oscillation. Furthermore, increasing the oscillating Reynolds number Re results in a more obvious oscillating phenomenon of the EOF velocity, together with a weakening amplitude of oscillation. The conclusions have theoretical significance for biofluid-based microfluidic transport systems.
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