CFD analysis of electroviscous effects in electrolyte liquid flow through heterogeneously charged non-uniform microfluidic device

Abstract

In this work, the pressure-driven flow of symmetric electrolyte liquid through a heterogeneously charged contraction-expansion (4:1:4) microfluidic device has been investigated numerically. Total potential ($U$), ion concentrations ($n_\pm$), velocity (${V}$), and pressure ($P$) fields are obtained after solving the mathematical model consisting of the Poisson's, Nernst-Planck (NP), Navier-Stokes (NS), and continuity equations numerically using the finite element method (FEM). Results are presented for wide ranges of dimensionless parameters such as inverse Debye length ($2\le K\le 20$), surface charge density ($4\le S_\text{1}\le 16$), and surface charge-heterogeneity ratio ($0\le S_\text{rh}\le 2$). Results show that the total potential ($\Delta U$) and pressure ($\Delta P$) drops change maximally by 3511.45% \add{(0.2127 to 7.6801)} (at $S_1=4$, $K=20$) and 41.4% \add{(1.0941 to 1.5471)} (at $S_1=16$, $K=2$), respectively with overall enhancing charge-heterogeneity ($0\le S_\text{rh}\le 2$), over the ranges of $K$ and $S_1$. Electroviscous correction factor, $Y$ (i.e., ratio of apparent to physical viscosity) increases maximally by 24.39\% \add{(1.1158 to 1.3879)} (at $K=4$, $S_\text{rh}=1.75$), 37.52% \add{(1.0597 to 1.4573)} (at $S_1=16$, $S_\text{rh}=2$), and 41.4% \add{(1.0306 to 1.4573)} (at $S_1=16$, $K=2$) with the variation of $S_1$ from 4 to 16, $K$ from 20 to 2, and $S_\text{rh}$ from 0 to 2, respectively. Further, overall increment in $Y$ is noted as 45.73\% \add{(1 to 1.4573)} (at $K=2$, $S_1=16$, $S_\text{rh}=2$), relative to non-EVF ($S_1=0$ or $K=\infty$). Thus, charge-heterogeneity enhances electroviscous effects in microfluidic devices, which enables the use of present numerical results for designing reliable and essential micro-sized channels for practical microfluidic applications.