  The present study deals with the effect of ionic advection on electroosmotic
flow over charge modulated surfaces in a generalized paradigm when the
classically restrictive "weak field" limit may be relaxed. Going beyond the
commonly portrayed weak field limit (i.e, the externally applied electric field
is over-weighed by the surface-induced electrical potential, towards charge
distribution in an electrified wall-adhering layer) for electroosmotic
transport, we numerically solve the coupled full set of Poisson-Nernst-Planck
(PNP) and Navier-Stokes equations, in a semi-infinite domain, bounded at the
bottom by a charged wall. Further, in an effort to obtain deeper physical
insight, we solve the simplified forms of the relevant governing equations for
low surface potential in two separate asymptotic limits: (i) a regular
perturbation solution for Low Ionic Peclet number (Pe), where Pe is employed as
the gauge function and (ii) a matched asymptotic solution for O(1) Pe in the
Thin Electric Double Layer (EDL) limit. We demonstrate that reasonably good
agreement is observed between the analytical and numerical solutions. Our
analysis reveals that the primary effect of Pe on the flow is to slow down the
"free stream velocity", adding to the periodicity of the flow, while it also
induces significant changes in the overall potential. We further show that the
electrical double layer thickness strongly dictates the "free stream velocity",
and a simple Smoluchowski type of slip boundary condition cannot be used, if
the effect of advection is taken into account. These results can be of
significant importance in designing microfluidic and nanofluidic systems with
surface charge modulation.
