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Research Papers: Flows in Complex Systems

# Combined Effect of Surface Roughness and Heterogeneity of Wall Potential on Electroosmosis in Microfluidic/Nanofuidic Channels

[+] Author and Article Information
S. Bhattacharyya1

Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, Indiasomnath@maths.iitkgp.ernet.in

A. K. Nayak

Department of Chemical Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

1

Corresponding author.

J. Fluids Eng 132(4), 041103 (Apr 15, 2010) (11 pages) doi:10.1115/1.4001308 History: Received March 23, 2009; Revised January 30, 2010; Published April 15, 2010; Online April 15, 2010

## Abstract

The motivation of the present study is to generate vortical flow by introducing channel wall roughness in the form of a wall mounted block that has a step-jump in $ζ$-potential on the upper face. The characteristics for the electrokinetic flow are obtained by numerically solving the Poisson equation, the Nernst–Planck equation, and the Navier–Stokes equations, simultaneously. A numerical method based on the pressure correction iterative algorithm (SIMPLE ) is adopted to compute the flow field and mole fraction of the ions. The potential patch induces a strong recirculation vortex, which in turn generates a strong pressure gradient. The strength of the vortex, which appears adjacent to the potential patch, increases almost linearly with the increase in $ζ$-potential. The streamlines follow a tortuous path near the wall roughness. The average axial flow rate over the block is enhanced significantly. We found that the ionic distribution follow the equilibrium Boltzmann distribution away from the wall roughness. The solutions based on the Poisson–Boltzmann distribution and the Nernst–Planck model are different when the inertial effect is significant. The combined effects due to geometrical modulation of the channel wall and heterogeneity in $ζ$-potential is found to produce a stronger vortex, and hence a stronger mixing, compared with either of these. Increase in $ζ$-potential increases both the transport rate and mixing efficiency. A novelty of the present configuration is that the vortex forms above the obstacle even when the patch potential is negative.

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## Figures

Figure 1

(a) Schematic diagram of the computational domain and (b) electric potential distribution of the external electric field when E0 corresponds to 106 V/m

Figure 2

Comparison of the present solutions in the fully developed region (x=−1.7) with that of Ramirez and Conlisk (13) when h=50 nm, g0=2.77×10−5, f0=2.54×10−6, and E0=1.7143 V/μm. (a) Axial velocity profile and (b) mole fractions. (◻) denote the results due to Ramirez and Conlisk (13). Grid size effect on the solution is shown in (a).

Figure 3

Comparison of axial velocity with different models and the results due to Wang (25) for various external electric fields in plane channels of height 0.8 μm with zeta potential as −50 mV and the ionic concentration is 10−4M

Figure 4

Comparison of our result for flow rates at different channel heights in a plane nanochannel with Ref. 29. The molarity of ions at the walls are Na+=9.6871M and Cl−=0.0009M. The external electric field E0 corresponds to 0.05 V over a channel of length 3.5 μm. Experimental results are as provided in Ref. 29.

Figure 7

Distribution of axial velocity, transverse velocity, mole fractions, potential, pressure, and lines of constant potential for nanochannel of height 60 nm with ionic species concentration at the wall is Na+=0.154M and Cl−=0.141M (strong electrolyte) and imposed electric field is 106 V/m and ϕp=0.2

Figure 8

Distribution of axial velocity, transverse velocity, mole fractions, potential for channel height h=60 nm with ionic species concentration at the wall is Na+=0.00154M, Cl−=0.00141M (weak electrolyte), and ϕp=0.2

Figure 5

Comparison of the ionic concentrations of cations and anions of the solution near a step-jump in ζ-potential (x=1.55) with the results due to Fu (20). The ionic strength of the solution (I) is 10−5M with h=50 μm, g0=2.7×10−5, f0=2.5×10−5, ϕp is −2.853, and E0=105 V/m.

Figure 6

Comparison of the axial velocity (N-P model and P-B model) at different sections of the channel with Ref. 22 (P-B model) in a channel with heterogeneous ζ-potential. Here, E0=104 V/m, h=30 μm, g0=2.7×10−6, f0=2.5×10−6, and ϕp is −2.853. Solid line, result due to the N-P model; dotted line, result due to the P-B model; ◼ (22).

Figure 9

Streamlines close to the block when the channel height is h=60 nm with block having overpotential ϕp=0.2 on the upper face. (a) Strong electrolyte g0=0.00276(Na+=0.154M), f0=0.00252(Cl−=0.141M). (b) Weak electrolyte g0=0.0000276(Na+=0.00154M), f0=0.0000252(Cl−=0.00141M).

Figure 10

Distribution of pressure and transverse velocity along the x-axis, at different y, when h=60 nm, g0=0.00276(Na+=0.154M), f0=0.00252(Cl−=0.141M), and ϕp=0.2. (a) Pressure and (b) transverse velocity.

Figure 11

Effect of channel height, ζ-potential, and overpotential of the patch on the circulation strength of the vortex. (a) Na+=0.154M, Cl−=0.141M (strong electrolyte), ϕp=0.2, and 20 nm≤h≤60 nm; (b) Cl−=0.141M and 0.154M≤Na+≤1.232M, ϕp=0.2, and h=20 nm; and (c) Na+=0.154M, Cl−=0.141M, and h=60 nm.

Figure 12

Results for streamlines for a strong electrolyte case at the channel height 20 nm. The electrical field corresponds to 106 V/m. The overpotential ϕp=0.0.

Figure 13

Comparison of the results for axial velocity at different sections of the channel above the obstacle obtained by the present model (N-P) and Poisson–Boltzmann model (P-B) at h=20 nm with ϕp=0.2. The species concentration at the wall are Na+=0.154M and Cl−=0.141M (strong electrolyte) with imposed electric field 106 V/m.

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