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Electroviscous effects in electrolyte liquid flow through an oppositely-charged contraction-expansion microfluidic slit device

Jitendra Dhakar, Ram Prakash Bharti

TL;DR

This paper addresses electroviscous flows in oppositely charged, non-uniform contraction–expansion micro-slits by solving the coupled Poisson–Nernst–Planck–Navier–Stokes equations with a finite element method framework. It explores a broad parametric space defined by $K$, $S_t$, $S_r$, $Re=10^{-2}$, $Sc=10^3$, and a contraction ratio $d_c=0.25$, and develops a pseudo-analytical model to predict pressure drop and the electroviscous correction factor $Y$. Key findings show large enhancements in total potential $|\Delta U|$ (up to 296.82%), pressure drop $|\Delta P|$ (up to 14.57%), and $Y$ (up to 15.13%), with opposite-charge asymmetry significantly altering EVF, though generally weaker than similar-charge asymmetry. The work also provides parity-based comparisons between Case A and Case B, and delivers predictive correlations for engineering design and optimization of microchips and microfluidic devices under electrokinetic control.

Abstract

Electrokinetic flows in microchannels with opposite charge asymmetry, i.e., unequal and contrasting surface charges on opposing channel walls, significantly influence microfluidic hydrodynamics and can be exploited for enhanced control of mass transfer, mixing, and heat transport in microfluidic applications. This study numerically investigates electroviscous flow of a liquid electrolyte through an oppositely charged non-uniform microslit. The governing Poisson, Nernst-Planck, and Navier-Stokes equations are solved using the finite element method to determine the coupled electrokinetic fields for a wide range of dimensionless parameters: Reynolds number (Re = 0.01), Schmidt number (Sc = 1000), inverse Debye length (K = 2-20), top-wall surface charge density (St = 4-16), surface charge density ratio (Sr = -2 to 0), and contraction ratio (dc = 0.25). For completeness, results for like-charged devices, where both walls carry surface charges of the same sign (Sr = 0-2), are also included. The results show that maximum enhancement in total electrical potential (|ΔU|) and pressure drop (|ΔP|) reaches 296.82% at K = 20, St = 4, -2 \le Sr \le -1.25, and 14.57% at St = 16, Sr = 0, K = 2-20, respectively. The electroviscous correction factor Y exhibits maximum increases of 14.02% at K = 2, St = 16; 11.81% at K = 2, Sr = 0; and 14.57% at Sr = 0, St = 16, when Sr increases (-0.75 to 0), St increases (4 to 16), and K decreases (20 to 2), respectively. The overall maximum increment in Y is 15.13% at K = 2, Sr = 0, St = 16, relative to the non-electroviscous flow case. These findings demonstrate that opposite charge asymmetry, though weaker than similar asymmetry, still strongly influences electroviscous flow in non-uniform microchannels.

Electroviscous effects in electrolyte liquid flow through an oppositely-charged contraction-expansion microfluidic slit device

TL;DR

This paper addresses electroviscous flows in oppositely charged, non-uniform contraction–expansion micro-slits by solving the coupled Poisson–Nernst–Planck–Navier–Stokes equations with a finite element method framework. It explores a broad parametric space defined by , , , , , and a contraction ratio , and develops a pseudo-analytical model to predict pressure drop and the electroviscous correction factor . Key findings show large enhancements in total potential (up to 296.82%), pressure drop (up to 14.57%), and (up to 15.13%), with opposite-charge asymmetry significantly altering EVF, though generally weaker than similar-charge asymmetry. The work also provides parity-based comparisons between Case A and Case B, and delivers predictive correlations for engineering design and optimization of microchips and microfluidic devices under electrokinetic control.

Abstract

Electrokinetic flows in microchannels with opposite charge asymmetry, i.e., unequal and contrasting surface charges on opposing channel walls, significantly influence microfluidic hydrodynamics and can be exploited for enhanced control of mass transfer, mixing, and heat transport in microfluidic applications. This study numerically investigates electroviscous flow of a liquid electrolyte through an oppositely charged non-uniform microslit. The governing Poisson, Nernst-Planck, and Navier-Stokes equations are solved using the finite element method to determine the coupled electrokinetic fields for a wide range of dimensionless parameters: Reynolds number (Re = 0.01), Schmidt number (Sc = 1000), inverse Debye length (K = 2-20), top-wall surface charge density (St = 4-16), surface charge density ratio (Sr = -2 to 0), and contraction ratio (dc = 0.25). For completeness, results for like-charged devices, where both walls carry surface charges of the same sign (Sr = 0-2), are also included. The results show that maximum enhancement in total electrical potential (|ΔU|) and pressure drop (|ΔP|) reaches 296.82% at K = 20, St = 4, -2 \le Sr \le -1.25, and 14.57% at St = 16, Sr = 0, K = 2-20, respectively. The electroviscous correction factor Y exhibits maximum increases of 14.02% at K = 2, St = 16; 11.81% at K = 2, Sr = 0; and 14.57% at Sr = 0, St = 16, when Sr increases (-0.75 to 0), St increases (4 to 16), and K decreases (20 to 2), respectively. The overall maximum increment in Y is 15.13% at K = 2, Sr = 0, St = 16, relative to the non-electroviscous flow case. These findings demonstrate that opposite charge asymmetry, though weaker than similar asymmetry, still strongly influences electroviscous flow in non-uniform microchannels.

Paper Structure

This paper contains 14 sections, 14 equations, 19 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Physical modelling
  3. Mathematical modelling
  4. Numerical approach
  5. Results and discussion
  6. Total electrical potential ($U$)
  7. Excess charge ($n^\ast$)
  8. Induced electric field strength ($E_{\text{x}}$)
  9. Velocity ($\mathbf{V}$)
  10. Pressure ($P$)
  11. Electroviscous correction factor ($Y$)
  12. Pseudo-analytical model for pressure drop and electroviscous correction factor
  13. Comparative analysis of electrokinetic flow characteristics in the similar and opposite asymmetrically charged micro-slits
  14. Concluding remarks

Figures (19)

  • Figure 1: Schematic of electroviscous flow (EVF) through oppositely charged non-uniform contraction-expansion microfluidic slit.
  • Figure 2: Distribution of total electrical potential ($U$) in the oppositely charged microfluidic contraction-expansion slit for $-2\le S_{\text{r}}\le 0$, $K=2$ and $S_{\text{t}}=8$.
  • Figure 3: Centreline profiles of the total electrical potential ($U$) in the oppositely charged micro-slit.
  • Figure 4: Influence of dimensionless parameters (${K,S_{\text{t}},S_{\text{r}}}$) on scaled total electrical potential (${U_\text{n}}$) variation on the contraction (${P_1}$, first column), expansion (${P_2}$, second column), and outlet (${P_3}$, third column) centreline points of the oppositely charged micro slit.
  • Figure 5: Distribution of excess charge ($n^{\ast}$) in the oppositely charged micro slit for $-2\le S_{\text{r}}\le 0$, $K=2$ and $S_{\text{t}}=8$.
  • ...and 14 more figures