  The electroviscous effects in the pressure-driven flow of electrolyte liquid
through an asymmetrically charged contraction-expansion (4:1:4) slit
microfluidic device have been investigated numerically. The mathematical model
(i.e., Poisson's, Navier-Stokes, and Nernst-Planck equations) is solved using
the finite element method to obtain the electrical potential, velocity,
pressure, ion concentration fields, excess charge, an induced electric field
strength for the following ranges of parameters: Reynolds number (${Re=0.01}$),
Schmidt number (${\mathit{Sc}=1000}$), inverse Debye length (${2\le K\le 20}$),
top wall surface charge density (${4\le S_t\le 16}$), surface charge ratio
(${0\le S_r\le 2}$) and contraction ratio (${d_{\text{c}}=0.25}$). Results show
that the charge asymmetry at the different walls of the microfluidic device
plays a significant role in the induced electric field development and
microfluidic hydrodynamics. The total potential (${|\Delta U|}$) and pressure
drop (${|\Delta P|}$) maximally increase by 197.45\% and 25.46\%, respectively,
with asymmetry of the charge. {The electroviscous correction factor (ratio of
apparent to physical viscosity) maximally increases by 20.85\% (at ${K=2}$,
${S_t=16}$ for ${0\le S_r\le 2}$), 25.46\% (at ${S_t=16}$, ${S_r=2}$ for ${2\le
K\le 20}$), and 39.13\% (at ${K=2}$, ${S_r=2}$ for ${0\le S_t\le16}$).}
Further, a simpler analytical model is developed to predict the pressure drop
in electroviscous flow considering asymmetrically charged surface, based on the
Poiseuille flow in the individual uniform sections and pressure losses due to
orifice, estimates the pressure drop 1--2\% within the numerical results. The
robustness of this model enables the use of present numerical results for
design aspects in microfluidic applications.
