Research Papers: Multiphase Flows

Nonlinear Electroosmosis Pressure-Driven Flow in a Wide Microchannel With Patchwise Surface Heterogeneity

[+] Author and Article Information
S. Bhattacharyya

e-mail: somnath@maths.iitkgp.ernet.in

Subrata Bera

e-mail: subrata.br@gmail.com
Department of Mathematics,
Indian Institute of Technology,
Kharagpur 721302, India

1Corresponding author.

Manuscript received May 11, 2012; final manuscript received October 17, 2012; published online March 19, 2013. Assoc. Editor: Prashanta Dutta.

J. Fluids Eng 135(2), 021303 (Mar 19, 2013) (12 pages) Paper No: FE-12-1240; doi: 10.1115/1.4023446 History: Received May 11, 2012; Revised October 17, 2012

In this paper, we have studied the electrokinetics and mixing driven by an imposed pressure gradient and electric field in a charged modulated microchannel. By performing detailed numerical simulations based on the coupled Poisson, Nernst–Planck, and incompressible Navier–Stokes equations, we discussed electrokinetic transport and other hydrodynamic effects under the application of combined pressure and dc electric fields for different values of electric double layer thickness and channel patch potential. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field and mole fraction of the ions. Since electroosmotic flow depends on the magnitude and sign of wall potential, a vortex can be generated through adjusting the patch potential. The dependence of the vortical flow on imposed pressure gradient is investigated. Formation of vortex in electroosmotic flow has importance in producing solute dispersion. The circulation of vortex grows with the rise of patch potential, whereas the pressure-assisted electroosmotic flow produces a reduction in vortex size. However, the flow rate is substantially increased in pressure-assisted electroosmotic flow. Flow reversal and suppression of fluid transport is possible through an adverse pressure gradient. The ion distribution and electric field above the potential patch are distorted by the imposed pressure gradient. At higher values of the pressure gradient, the combined pressure electroosmotic-driven flow resembles the fully developed Poiseuille flow. Current density is found to increase with the rise of imposed pressure gradient.

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Grahic Jump Location
Fig. 1

Schematic diagram of the microchannel with patchwise surface heterogeneity in lower wall of the channel

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Fig. 2

Comparison of dimensional u-velocity with the results due to Wang et al. [34] for various values of external electric field in a plane channel of height h = 0.8 μm with ζ-potential as –60 mV and the ionic concentration I = 10-4 M

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Fig. 3

Comparison of our computed results for pure EOF case (G = 0). The (a) height of the vortex center from the patch (hp) with Chen and Conlisk [17] at different values of the over potential of the patch (φp = ζp-ζ) for h = 20 nm, E0 = 107 V/m, and ζ = -0.46 when electrolyte is 0.1 M NaCl solution; (b) circulation strength of the vortex (Γ) with Bhattacharyya and Nayak [16] at different values of φp when h = 30 nm, E0 = 106 V/m, and the concentration of ionic species along the homogeneous part of the wall is Na+ = 0.154 M and Cl-1 = 0.141 M. We have also presented Γ for h = 20 nm, 60 nm, 100 nm when ionic concentration and electric field are same as above.

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Fig. 4

Comparison of the mole fraction of cations and anions near a step jump in ζ-potential with Fu et al. [13] when the concentration of the bulk electrolyte I = 10-4 mol/m3, external electric field E0 = 105 V/m, and channel height h = 0.1 μm

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Fig. 5

Velocity profiles (u, v) at x = 0.0 (on the patch) at different Re when h = 10 μm, λ = 0.6 μm, ζ = -1, ζp = 1, and E0 = 104 V/m at different values of the imposed pressure gradient (G). (a) First row corresponds to G = −5, −3, −1, 0, 1, 3, 5. (b) Second row corresponds to G = 10, 20, 30, 50. Arrows are pointing in the increasing direction of G. Here, UHS = 1.8×10-4 m/s.

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Fig. 6

Streamlines for different values of Re when h = l = 10 μm, λ = 0.6 μm, ζ = -1, ζp = 1, and E0 = 104 V/m. (a) Re = 0.12×10-2(G = -1); (b) pure EOF, Re = 0.15×10-2(G = 0); (c) Re = 0.18×10-2(G = 1). The values of the nondimensional stream function are indicated.

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Fig. 7

Cross-sectional averaged pressure (Pavg) distribution along the channel length when both the channel height h and patch length l are 10 μm, λ = 0.6 μm, ζ = -1, ζp = 1, and E0 = 104 V/m at different vales of G = −5, 0, 5, 10. Arrow is along the direction in which G is increasing. Here, p0 = 0.018 Pa.

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Fig. 8

Variation of height of the vortex center from the patch (hp) with the imposed pressure gradient (G) for different values of EDL thickness (λ = 0.6 μm,0.3 μm,0.1 μm) when h = l = 10 μm, ζ = -1.0, ζp = 1.0, and E0 = 104 V/m

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Fig. 9

(a) Critical value of the patch potential (ζp) for the onset of vortex at different Reynolds number (Re). (b) Height of the vortex center (hp) as a function of patch potential (ζp) when Re = 0.12×10-2(G = -1), Re = 0.15×10-2(G = 0), Re = 0.18×10-2(G = +1). Here, h = l = 10 μm, λ = 0.6 μm, ζ = -1, and E0 = 104 V/m.

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Fig. 10

Variation of the circulation strength of the vortex with Re at different values of patch potential (ζp). Here, h = l = 10 μm, λ = 0.6 μm, ζ = -1, E0 = 104 V/m, and G varies from −5 to 8.

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Fig. 11

Contour plots for the nondimensional cation (g) and anion (f) concentration near a potential patch when h = l = 10 μm, λ = 0.6 μm, ζ = -1, ζp = 1, and E0 = 104 V/m. First row corresponds to pure EOF case, i.e., G = 0 (Re = 1.56×10-3). Second row corresponds to G = 50 (Re = 1.65×10-2). The nondimensional values of the ionic concentration, nondimensionalized by the bulk ionic concentration I = 0.5×10-4 mole/m3, is indicated on each contour.

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Fig. 12

Profiles for distribution of nondimensional ionic concentration (g,f) at different sections of the channel for different values of the imposed pressure gradient (G) when ζ = -1 and ζp = 1. Solid lines, g, and broken lines, f. The first row corresponds to h = l = 20 nm, λ = 4 nm (I = 11.5 mol/m3), and E0 = 106 V/m. Second row corresponds to h = l = 10 μm, λ = 0.6 μm (I = 0.5×10-4 mol/m3), and E0 = 104 V/m. (a) Near inlet of the channel (x = -1.75); (b) on the patch x = 0.0. Arrow is along the direction in which G is increasing. Here, ionic concentration is scaled by I, the bulk value.

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Fig. 13

Contour plots for the nondimensional induced potential (φ/φ0) when channel height h = l = 10 μm, λ = 0.6 μm, ζ = -1, ζp = 1, and E0 = 104 V/m for EOF with and without imposed convection. (a) Pure EOF case, Re = 1.56×10-3(G = 0); (b) mixed EOF case, Re = 1.65×10-2(G = 50). The nondimensional vales of φ/φ0 are indicated on each contour.

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Fig. 14

Variation of the electrostatic body force factor (Ff = F/FEOF) with the imposed pressure gradient (G) when ζ = -1 and ζp = 1. Results are presented for both micro- and nanochannel cases, i.e., h = 10 μm, λ = 0.6 μm, and E0 = 104 V/m and h = 20 nm, λ = 4.0 nm, and E0 = 106 V/m.

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Fig. 15

Distribution of the cross-sectional, averaged current density along the channel when h = l = 10 μm, λ = 0.6 μm, ζ = -1, ζp = 1, and E0 = 104 V/m for different values of the imposed pressure gradient, G = 0, 1, 3, 5, 10, 20, 30, 50. Arrow is along the direction in which G is increasing. Here, j0 = 6.27×10-4 A/m2.

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Fig. 16

Plots for the concentration of solute, scaled by the reference concentration C0, within the channel at two different patch potentials ζp = 1,2 when h = l = 10 μm, λ = 0.6 μm, ζ = -1, and E0 = 104 V/m for pure EOF Re = 0.15×10-2(G = 0) and mixed EOF case with Re = 0.21×10-2(G = 2). The Peclet number based on the diffusivity of the uncharged solute is Pes = 13.83. (a) ζp = 1; (b) ζp = 2. The color bar indicates the nondimensional concentration (red lower left is high and blue upper left is low). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of the article.)

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Fig. 17

Profiles of nondimensional solute concentration at inlet and outlet region of the channel at different ζp = 1,2 and Re when h = 10 μm, λ = 0.6 μm, ζ = -1, E0 = 104 V/m, and Pes = 13.83. Here, Re = 0.15×10-2(G = 0), Re = 0.18×10-2 (G = 1), and Re = 0.21×10-2(G = 2). Arrow points the increasing direction of Re.



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