  In computational models of microchannel flows, the Helmholtz-Smoluchowski
slip velocity boundary condition is often used because it approximates the
motion of the electric double layer without resolving the charge density
profiles close to the walls while drastically reducing the computational effort
needed for the flow model to be solved. Despite working well for straight
channel flow of Newtonian fluids, the approximation does not work well for flow
involving complex fluids and spatially varying surface potential distribution.
To treat these effects using the slip velocity boundary condition, it is
necessary to understand how the surface potential and fluid properties affect
the slip velocity. The present analysis shows the existence of a modified
electroosmotic slip velocity for viscoelastic fluids, which is strongly
dependent upon Deborah number and viscosity ratio, and this modification
differs significantly from the slip velocity of Newtonian fluids. An
augmentation of fluid elasticity results in an asymmetric distribution of slip
velocity. Nonintuitively, the modulation wavelength of the imposed surface
potential contributes to changing the slip velocity magnitude and adding
periodicity to the solution. The proposed electroosmotic slip velocity for
viscoelastic fluid can be used in computational models of microchannel flows to
approximate the motion of the electric double layer without resolving the
charge density profiles close to the walls.

Fluid Dynamics