  This study has numerically investigated the charge-heterogeneity effects in
the electroviscous flow of symmetric ($1$:$1$) electrolyte liquid through a
uniform slit microfluidic device. The Poisson's, Nernst-Planck (N-P),
Navier-Stokes (N-S), and continuity equations are solved using the finite
element method (FEM) to obtain the flow fields, such as total electrical
potential ($U$), excess charge ($n^\ast$), induced electric field strength
($E_\text{x}$), and pressure ($P$) fields for following conditions: inverse
Debye length ($2\le K\le 20$), surface charge density ($4\le
\mathit{S_\text{1}}\le 16$), and surface charge-heterogeneity ratio ($0\le
\mathit{S_\text{rh}}\le 2$). Results have shown that the total potential
($|\Delta U|$) and pressure ($|\Delta P|$) drop maximally increase by 99.09%
(at $K=20$, $\mathit{S_\text{1}}=4$) and 12.77% (at $K=2$,
$\mathit{S_\text{1}}=8$), respectively with overall charge-heterogeneity ($0\le
\mathit{S_\text{rh}}\le 2$). Electroviscous correction factor (i.e., the ratio
of effective to physical viscosity) maximally enhances by 12.77% (at $K=2$,
$\mathit{S_\text{1}}=8$), 40.98% (at $\mathit{S_\text{1}}=16$,
$\mathit{S_\text{rh}}=1.50$), and 41.35% (at $K=2$,
$\mathit{S_\text{rh}}=1.50$), with the variation of $\mathit{S_\text{rh}}$
(from 0 to 2), $K$ (from 20 to 2), and $\mathit{S_\text{1}}$ (from 0 to 16),
respectively. Further, a simple pseudo-analytical model is developed to
estimate the pressure drop in the electroviscous (EV) flow, accounting for the
influence of charge-heterogeneity based on the Poiseuille flow in the uniform
channel. This model predicts the pressure drop $\pm$2-4% within the numerical
results. The robustness and simplicity of this model enable the present
numerical results for engineering and design aspects of microfluidic
applications.
