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Journal of Fluids Engineering | Volume 139 | Issue 8 | research-article
Research Papers: Fundamental Issues and Canonical Flows

Enhanced Electroosmotic Flow Through a Nanochannel Patterned With Transverse Periodic Grooves

[+] Author and Article Information
S. Bhattacharyya

Department of Mathematics,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: somnath@maths.iitkgp.ernet.in

Naren Bag

Department of Mathematics,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 3, 2016; final manuscript received February 28, 2017; published online May 18, 2017. Assoc. Editor: Moran Wang.

J. Fluids Eng 139(8), 081203 (May 18, 2017) (7 pages) Paper No: FE-16-1648; doi: 10.1115/1.4036265 History: Received October 03, 2016; Revised February 28, 2017
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In this paper, we have analyzed an enhanced electroosmotic flow (EOF) by geometric modulation of the surface of a charged nanochannel. Otherwise, flat walls of the channel are modulated by embedding rectangular grooves placed perpendicular to the direction of the applied electric field in a periodic manner. The modulated channel is filled with a single electrolyte. The EOF within the modulated channel is determined by computing the Navier–Stokes–Nernst–Planck–Poisson equations for a wide range of Debye length. The objective of the present study is to achieve an enhanced EOF in the surface modulated channel. A significant enhancement in average EOF is found for a particular arrangement of grooves with the width of the grooves much higher than its depth and the Debye length is in the order of the channel height. However, the formation of vortex inside the narrow grooves can reduce the EOF when the groove depth is in the order of its width. Results are compared with the cases in which the grooves are replaced by superhydrophobic patches along which a zero shear stress condition is imposed.
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Grahic Jump Location
Fig. 1

Schematic of the model geometry. The computational domain is marked by dotted lines.

+Schematic of the model geometry. The computational domain is marked by dotted lines.
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Schematic of the model geometry. The computational domain is marked by dotted lines.
Grahic Jump Location
Fig. 2

(a) Comparison of computed (lines) and analytical (symbols) axial velocity profiles with fixed ζ = −0.1 and κH = 1, 2, 3, 5, 10, 40, and 100 and (b) variation of average axial velocity with surface potential for various values of κH = 0.1, 0.5, 1, 2, 3, 5, and 10 when L/H = 100, Ls = Lns, E0 = 104 V/m, and channel height (H) = 50 nm

+(a) Comparison of computed (lines) and analytical (symbols) axial velocity profiles with fixed ζ = −0.1 and κH = 1, 2, 3, 5, 10, 40, and 100 and (b) variation of average axial velocity with surface potential for various values of κH = 0.1, 0.5, 1, 2, 3, 5, and 10 when L/H = 100, Ls = Lns, E0 = 104 V/m, and channel height (H) = 50 nm
View Large  |  Save Figure  |  Download Slide (.ppt)
(a) Comparison of computed (lines) and analytical (symbols) axial velocity profiles with fixed ζ = −0.1 and κH = 1, 2, 3, 5, 10, 40, and 100 and (b) variation of average axial velocity with surface potential for various values of κH = 0.1, 0.5, 1, 2, 3, 5, and 10 when L/H = 100, Ls = Lns, E0 = 104 V/m, and channel height (H) = 50 nm
Grahic Jump Location
Fig. 3

Streamline patterns near a groove embedded on the channel wall for different values of periodic length L/H = 1, 2, 10, and 100 with Ls = Lns when depth of the groove d/H = 1, κH = 0.5, ζ = −0.1, and E0 = 104  V/m and channel height (H) is 50 nm: (a) L/H = 1, (b) L/H = 2, (c) L/H = 10, and (d) L/H = 100

+Streamline patterns near a groove embedded on the channel wall for different values of periodic length L/H = 1, 2, 10, and 100 with Ls = Lns when depth of the groove d/H = 1, κH = 0.5, ζ = −0.1, and E0 = 104  V/m and channel height (H) is 50 nm: (a) L/H = 1, (b) L/H = 2, (c) L/H = 10, and (d) L/H = 100
View Large  |  Save Figure  |  Download Slide (.ppt)
Streamline patterns near a groove embedded on the channel wall for different values of periodic length L/H = 1, 2, 10, and 100 with Ls = Lns when depth of the groove d/H = 1, κH = 0.5, ζ = −0.1, and E0 = 104  V/m and channel height (H) is 50 nm: (a) L/H = 1, (b) L/H = 2, (c) L/H = 10, and (d) L/H = 100
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Fig. 4

Flow enhancement factor (Ef) as a function of the periodic length L = Ls + Lns, with Ls = Lns at different κH = 0.1, 0.5, 1, 2, 3, 5, and 10 and depth of the groove: (a) d/H = 0.25, (b) d/H = 0.5, (c) d/H = 0.75, and (d) d/H = 1. Here, square symbols present Ef corresponding to the PD flow and the circular symbols in (d) correspond to the superhydrophobic case.

+Flow enhancement factor (Ef) as a function of the periodic length L = Ls + Lns, with Ls = Lns at different κH = 0.1, 0.5, 1, 2, 3, 5, and 10 and depth of the groove: (a) d/H = 0.25, (b) d/H = 0.5, (c) d/H = 0.75, and (d) d/H = 1. Here, square symbols present Ef corresponding to the PD flow and the circular symbols in (d) correspond to the superhydrophobic case.
View Large  |  Save Figure  |  Download Slide (.ppt)
Flow enhancement factor (Ef) as a function of the periodic length L = Ls + Lns, with Ls = Lns at different κH = 0.1, 0.5, 1, 2, 3, 5, and 10 and depth of the groove: (a) d/H = 0.25, (b) d/H = 0.5, (c) d/H = 0.75, and (d) d/H = 1. Here, square symbols present Ef corresponding to the PD flow and the circular symbols in (d) correspond to the superhydrophobic case.
Grahic Jump Location
Fig. 5

Ratio of shear stress at groove–channel interface (τM) and plane channel wall (τEO) as a function of groove width fordifferent values of groove depth d/H = 0.25, 0.5, 0.75, and 1when κH = 0.1, E0 = 104  V/m, Ls = Lns, and H = 50 nm: (a) L/H = 10H and (b) L/H = 100H

+Ratio of shear stress at groove–channel interface (τM) and plane channel wall (τEO) as a function of groove width fordifferent values of groove depth d/H = 0.25, 0.5, 0.75, and 1when κH = 0.1, E0 = 104  V/m, Ls = Lns, and H = 50 nm: (a) L/H = 10H and (b) L/H = 100H
View Large  |  Save Figure  |  Download Slide (.ppt)
Ratio of shear stress at groove–channel interface (τM) and plane channel wall (τEO) as a function of groove width fordifferent values of groove depth d/H = 0.25, 0.5, 0.75, and 1when κH = 0.1, E0 = 104  V/m, Ls = Lns, and H = 50 nm: (a) L/H = 10H and (b) L/H = 100H
Grahic Jump Location
Fig. 6

Flow enhancement factor (Ef) as a function of (a) and (b) groove depth (d) and (c) Ls/Lns when κH = 0.1, 0.5, 1, 2, 3, 5, and 10 and ζ = −0.1. Here, circular symbols represent Ef corresponding to the superhydrophobic case; square symbols represent Ef corresponding to the pressure driven flow.

+Flow enhancement factor (Ef) as a function of (a) and (b) groove depth (d) and (c) Ls/Lns when κH = 0.1, 0.5, 1, 2, 3, 5, and 10 and ζ = −0.1. Here, circular symbols represent Ef corresponding to the superhydrophobic case; square symbols represent Ef corresponding to the pressure driven flow.
View Large  |  Save Figure  |  Download Slide (.ppt)
Flow enhancement factor (Ef) as a function of (a) and (b) groove depth (d) and (c) Ls/Lns when κH = 0.1, 0.5, 1, 2, 3, 5, and 10 and ζ = −0.1. Here, circular symbols represent Ef corresponding to the superhydrophobic case; square symbols represent Ef corresponding to the pressure driven flow.
Grahic Jump Location
Fig. 7

(a) Axial velocity and (b) net charge density as a function of channel height for various values of κH = 0.1, 0.5, 1, 2, 3, 5, and 10 at x = L/2 when E0 = 104 V/m, L/H = 200, Ls = Lns, d/H = 1 and H = 50 nm

+(a) Axial velocity and (b) net charge density as a function of channel height for various values of κH = 0.1, 0.5, 1, 2, 3, 5, and 10 at x = L/2 when E0 = 104 V/m, L/H = 200, Ls = Lns, d/H = 1 and H = 50 nm
View Large  |  Save Figure  |  Download Slide (.ppt)
(a) Axial velocity and (b) net charge density as a function of channel height for various values of κH = 0.1, 0.5, 1, 2, 3, 5, and 10 at x = L/2 when E0 = 104 V/m, L/H = 200, Ls = Lns, d/H = 1 and H = 50 nm

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