  This work investigates electroviscous effects in presence of charge-dependent
slip in steady pressure-driven laminar flow of a symmetric (1:1) electrolyte
liquid through a uniformly charged slit contraction - expansion (4:1:4)
microfluidic device. The mathematical model comprising Poisson's,
Nernst-Planck, Navier-Stokes, and current continuity equations are solved
numerically using finite element method (FEM). The flow fields (electrical
potential, charge, induced electric field strength, pressure drop, and
electroviscous correction factor) have been obtained and presented for a wide
range of parameters like inverse Debye length (K=2-20), surface charge density
(S=4-16) and slip length ($0\le B_0\le 0.20$) at fixed Schmidt number (Sc=1000)
and low Reynolds number (Re=0.01). The flow fields have shown complex
dependence on governing parameters. The charge-dependent slip has further
enhanced complexity of dependency in comparison to no-slip condition. The total
electrical potential ($|\Delta U|$) maximally increases by 78.68%, and pressure
drop ($|\Delta P|$) maximally decreases by 63.42%, relative to no-slip flow,
over the ranges of conditions. The electroviscous correction factor ($Y=$ ratio
of apparent to physical viscosity) increases by 33.58% under the no-slip
($B_0=0$) condition. It ($Y$) increases maximally by 72.10% for
charge-dependent slip than in no-slip flow for considered ranges of the
conditions. A simple analytical model to estimate the pressure drop in the
electroviscous flow has been developed based on the Poiseuille flow in
individual uniform sections and pressure loss due to thin orifice. The model
overpredicts pressure drop by 2 - 4% from the numerical values. Finally, the
predictive relations, depicting the functional dependence of numerical results
on governing parameters, are presented for their practical use in design and
engineering of microfluidic devices.
