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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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References

1
Choi, C.-H. , and Kim, C.-J. , 2006, “ Large Slip of Aqueous Liquid Flow Over a Nanoengineered Superhydrophobic Surface,” Phys. Rev. Lett., 96(6), p. 066001. [CrossRef] [PubMed]
2
Lee, C. , Choi, C.-H. , and Kim, C.-J., 2008, “ Structured Surfaces for a Giant Liquid Slip,” Phys. Rev. Lett., 101(6), p. 064501. [CrossRef] [PubMed]
3
Rothstein, J. P. , 2010, “ Slip on Superhydrophobic Surfaces,” Annu. Rev. Fluid Mech., 42(1), pp. 89–109. [CrossRef]
4
Schönecker, C. , and Hardt, S. , 2014, “ Electro-Osmotic Flow Along Superhydrophobic Surfaces With Embedded Electrodes,” Phys. Rev. E, 89(6), p. 063005. [CrossRef]
5
Wang, C. , 2003, “ Flow Over a Surface With Parallel Grooves,” Phys. Fluids, 15(5), pp. 1114–1121. [CrossRef]
6
Lauga, E. , and Stone, H. A. , 2003, “ Effective Slip in Pressure-Driven Stokes Flow,” J. Fluid Mech., 489(6), pp. 55–77. [CrossRef]
7
Belyaev, A. V. , and Vinogradova, O. I. , 2010, “ Effective Slip in Pressure-Driven Flow Past Super-Hydrophobic Stripes,” J. Fluid Mech., 652, pp. 489–499. [CrossRef]
8
Viswanath, P. , 2002, “ Aircraft Viscous Drag Reduction Using Riblets,” Prog. Aerosp. Sci., 38(6–7), pp. 571–600. [CrossRef]
9
Jovanović, J. , Frohnapfel, B. , and Delgado, A. , 2010, “ Viscous Drag Reduction With Surface-Embedded Grooves,” Turbulence and Interactions, Springer, Berlin, pp. 191–197.
10
Mohammadi, A. , and Floryan, J. M. , 2015, “ Numerical Analysis of Laminar-Drag-Reducing Grooves,” ASME J. Fluids Eng., 137(4), p. 041201. [CrossRef]
11
DeGroot, C. T. , Wang, C. , and Floryan, J. M. , 2016, “ Drag Reduction Due to Streamwise Grooves in Turbulent Channel Flow,” ASME J. Fluids Eng., 138(12), p. 121201. [CrossRef]
12
Bahga, S. S. , Vinogradova, O. I. , and Bazant, M. Z. , 2010, “ Anisotropic Electro-Osmotic Flow Over Super-Hydrophobic Surfaces,” J. Fluid Mech., 644, pp. 245–255. [CrossRef]
13
Squires, T. M. , 2008, “ Electrokinetic Flows Over Inhomogeneously Slipping Surfaces,” Phys. Fluids, 20(9), p. 092105. [CrossRef]
14
Ng, C.-O. , and Chu, H. C. , 2011, “ Electrokinetic Flows Through a Parallel-Plate Channel With Slipping Stripes on Walls,” Phys. Fluids, 23(10), p. 102002. [CrossRef]
15
Papadopoulos, P. , Deng, X. , Vollmer, D. , and Butt, H.-J. , 2012, “ Electrokinetics on Superhydrophobic Surfaces,” J. Phys. Condens. Matter, 24(46), p. 464110. [CrossRef] [PubMed]
16
Zhao, H. , 2010, “ Electro-Osmotic Flow Over a Charged Superhydrophobic Surface,” Phys. Rev. E, 81(6), p. 066314. [CrossRef]
17
Belyaev, A. V. , and Vinogradova, O. I. , 2011, “ Electro-Osmosis on Anisotropic Superhydrophobic Surfaces,” Phys. Rev. Lett., 107(9), p. 098301. [CrossRef] [PubMed]
18
Steffes, C. , Baier, T. , and Hardt, S. , 2011, “ Enabling the Enhancement of Electroosmotic Flow Over Superhydrophobic Surfaces by Induced Charges,” Colloids Surf. A, 376(1), pp. 85–88. [CrossRef]
19
Maduar, S. , Belyaev, A. , Lobaskin, V. , and Vinogradova, O. , 2015, “ Electrohydrodynamics Near Hydrophobic Surfaces,” Phys. Rev. Lett., 114(11), p. 118301. [CrossRef] [PubMed]
20
Sadeghi, M. , Sadeghi, A. , and Saidi, M. H. , 2016, “ Electroosmotic Flow in Hydrophobic Microchannels of General Cross Section,” ASME J. Fluids Eng., 138(3), p. 031104. [CrossRef]
21
De, S. , Bhattacharyya, S. , and Hardt, S. , 2015, “ Electroosmotic Flow in a Slit Nanochannel With Superhydrophobic Walls,” Microfluid. Nanofluid., 19(6), pp. 1465–1476. [CrossRef]
22
Barrat, J. L. , and Bocquet, L. , 1999, “ Large Slip Effect at a Nonwetting Fluid-Solid Interface,” Phys. Rev. Lett., 82(23), p. 4671. [CrossRef]
23
Huang, D. M. , Cottin-Bizonne, C. , Ybert, C. , and Bocquet, L. , 2008, “ Aqueous Electrolytes Near Hydrophobic Surfaces: Dynamic Effects of Ion Specificity and Hydrodynamic Slip,” Langmuir, 24(4), pp. 1442–1450. [CrossRef] [PubMed]
24
Stone, H. A. , Stroock, A. D. , and Ajdari, A. , 2004, “ Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-A-Chip,” Annu. Rev. Fluid Mech., 36(1), pp. 381–411. [CrossRef]
25
Ou, J. , Perot, B. , and Rothstein, J. P. , 2004, “ Laminar Drag Reduction in Microchannels Using Ultrahydrophobic Surfaces,” Phys. Fluids, 16(12), pp. 4635–4643. [CrossRef]
26
Ou, J. , and Rothstein, J. P. , 2005, “ Direct Velocity Measurements of the Flow Past Drag-Reducing Ultrahydrophobic Surfaces,” Phys. Fluids, 17(10), p. 103606. [CrossRef]
27
Kasiteropoulou, D. , Karakasidis, T. , and Liakopoulos, A. , 2013, “ Mesoscopic Simulation of Fluid Flow in Periodically Grooved Microchannels,” Comput. Fluids, 74, pp. 91–101. [CrossRef]
28
Dilip, D. , Jha, N. K. , Govardhan, R. N. , and Bobji, M. , 2014, “ Controlling Air Solubility to Maintain Cassie State for Sustained Drag Reduction,” Colloids Surf. A, 459, pp. 217–224. [CrossRef]
29
Jing, D. , and Bhushan, B. , 2015, “ The Coupling of Surface Charge and Boundary Slip at the Solid-Liquid Interface and Their Combined Effect on Fluid Drag: A Review,” J. Colloid Interface Sci., 454, pp. 152–179. [CrossRef] [PubMed]
30
Bhattacharyya, S. , Zheng, Z. , and Conlisk, A. T. , 2005, “ Electro-Osmotic Flow in Two-Dimensional Charged Micro- and Nanochannels,” J. Fluid Mech., 540, pp. 247–267. [CrossRef]
31
Baldessari, F. , 2008, “ Electrokinetics in Nanochannels—Part I: Electric Double Layer Overlap and Channel-to-Well Equilibrium,” J. Colloid Interface Sci., 325(2), pp. 526–538. [CrossRef] [PubMed]
32
Zangle, T. A. , Mani, A. , and Santiago, J. G. , 2009, “ On the Propagation of Concentration Polarization From Microchannel–Nanochannel Interfaces—Part II: Numerical and Experimental Study,” Langmuir, 25(6), pp. 3909–3916. [CrossRef] [PubMed]
33
Fletcher, C. A. , 1991, Computational Techniques for Fluid Dynamics, 2nd ed., Vol. 2, Springer, Berlin.
34
Patankar, S. , 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishers, New York.
35
Masliyah, J. H. , and Bhattacharjee, S. , 2006, Electrokinetic and Colloid Transport Phenomena, Wiley, Hoboken, NJ.
36
Schönecker, C. , and Hardt, S. , 2013, “ Longitudinal and Transverse Flow Over a Cavity Containing a Second Immiscible Fluid,” J. Fluid Mech., 717, pp. 376–394. [CrossRef]

Figures

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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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
Grahic Jump Location
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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