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Research Papers

Nonlinear Electrokinetic Transport Under Combined ac and dc Fields in Micro/Nanofluidic Interface Devices

[+] Author and Article Information
Vishal V. R. Nandigana

e-mail: nandiga1@illinois.edu

N. R. Aluru

e-mail: aluru@illinois.edu
Department of Mechanical Science and Engineering,
Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

1Corresponding author.

Manuscript received March 22, 2012; final manuscript received July 6, 2012; published online March 19, 2013. Assoc. Editor: Sushanta K. Mitra.

J. Fluids Eng 135(2), 021201 (Mar 19, 2013) (10 pages) Paper No: FE-12-1141; doi: 10.1115/1.4023442 History: Received March 22, 2012; Revised July 06, 2012

The integration of micro/nanofluidic devices led to many interesting phenomena and one of the most important and complex phenomenon among them is concentration polarization. In this paper, we report new physical insights in micro/nanofluidic interface devices on the application of ac and dc electric fields. By performing detailed numerical simulations based on the coupled Poisson, Nernst–Planck, and incompressible Navier–Stokes equations, we discuss electrokinetic transport and other hydrodynamic effects under the application of combined ac and dc electric fields for different nondimensional electrical double layer (EDL) thicknesses and nanochannel wall surface charge densities. We show that for a highly ion-selective nanochannel, the application of the combined ac/dc electric field, at amplitudes greater than the dc voltage and at a low Strouhal number, results in large dual concentration polarization regions (with unequal lengths) at both the micro/nanofluidic interfaces due to large and unequal voltage drops at these junctions. The highly nonlinear potential distribution gives rise to an electric field and body force that changes the electrokinetic fluid velocity from that obtained on the application of only a dc source.

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Figures

Grahic Jump Location
Fig. 1

Simulation setup (not drawn to scale), consisting of a nanochannel of height (h = 30 nm) connected to two reservoirs of a 1 μm× 1 μm cross section

Grahic Jump Location
Fig. 2

(a) Numerical results of the time averaged nondimensional axial potential distribution for different α( = φac/φdc) at a fixed St = 4.65. Note: for the ac only case φacFz/RT = 386.84 and St = 4.65. The inset of the figure shows the nondimensional axial potential distribution for a large dc voltage φdcFz/RT = 193.419. At this voltage, there is a large voltage drop observed at the anodic junction of the micro/nanochannel due to the concentration polarization space charges induced at this junction. (b) Variation of the time averaged nondimensional axial potential distribution for different St( = fL0/U0) at a fixed α = 16. In all of these cases the applied dc voltage is φdcFz/RT = 19.3419, β = 0.0049, and σ* = -109.227.

Grahic Jump Location
Fig. 3

Schematic of the potential distribution along the length of the micro/nanochannel. The regions with large voltage drops near both the micro/nanofluidic interfaces are defined as concentration polarization regions. Here, CPL-I represents the polarization length at the right end (anodic end) of the nanochannel, while CPL-II indicates the polarization length at the cathodic end. The subscripts dc and ac + dc indicate the lengths when the corresponding fields are applied (the solid line and the dashed line indicate the approximate potential profile for the large dc voltage and large α (and low St) ac + dc field, respectively).

Grahic Jump Location
Fig. 4

Normalized dual concentration polarization lengths measured at a fixed β = 0.0049, σ* = -109.227 (a) as a function of α at a fixed St=4.65 and φdcFz/RT = 19.3419. The inset of the figure displays the dual concentration polarization lengths for a large dc voltage φdcFz/RT = 193.419 (b) as a function of St at a fixed α = 16 and φdcFz/RT = 19.3419. The resolution of the lengths measured is limited by the grid spacing.

Grahic Jump Location
Fig. 5

Nondimensional axial body force distribution (averaged over one time period and averaged across the cross section) for different electric fields at a fixed β = 0.0049, σ* = -109.227, and φdcFz/RT = 19.3419

Grahic Jump Location
Fig. 6

(a) Time averaged nondimensional axial pressure distribution for different α at a fixed St = 4.65. Note: for the ac only case φacFz/RT = 386.84 and St = 4.65. The inset of the figure shows the nondimensional axial pressure distribution for a large dc voltage φdcFz/RT = 193.419. At this voltage, there is a large induced pressure gradient near the anodic junction of the micro/nanochannel due to the concentration polarization space charges induced at this junction. (b) Variation of the time averaged nondimensional axial pressure distribution for different St at a fixed α = 16. In all of these cases β = 0.0049, σ* = -109.227, and φdcFz/RT-19.3419.

Grahic Jump Location
Fig. 7

The ratio of the total axial electrostatic body force (averaged over one time period) integrated over the entire channel under the combined ac/dc electric field to the total dc axial electrostatic body force for a fixed β = 0.0049, σ* = -109.227, and φdcFz/RT = 19.3419 (a) as a function of α at a fixed St = 4.65, and (b) as a function of St at a fixed α = 16

Grahic Jump Location
Fig. 8

Numerically calculated velocities (averaged over one time period) measured at the center of the nanochannel (x/L0 = 1) at a fixed St = 4.65, β = 0.0049, σ* = -109.227, and φdcFz/RT = 19.3419. (a) The ratio of the time averaged ac/dc axial electroosmotic velocity to the dc axial electroosmotic velocity as a function of α. The inset of the figure displays the velocity variation with α for a large dc voltage φdcFz/RT = 193.419. (b) The variation of the time averaged nondimensional axial electroosmotic velocity across the cross section of the nanochannel for different α. For the ac only case φacFz/RT = 386.84 and St = 4.65. Note: the negative sign indicates the flow direction from right to left.

Grahic Jump Location
Fig. 9

Numerically calculated velocities (averaged over one time period) measured at the center of the nanochannel (x/L0 = 1) at a fixed α = 16, β = 0.0049, σ* = -109.227, and φdcFz/RT = 19.3419. (a) The ratio of the time averaged ac/dc axial electroosmotic velocity to the dc axial electroosmotic velocity as a function of St. (b) The variation of the time averaged nondimensional axial electroosmotic velocity across the cross section of the nanochannel for different St.

Grahic Jump Location
Fig. 10

Effect of the dimensionless EDL thickness (β = λD/L0) and St on the ratio of the time averaged ac/dc axial electroosmotic velocity to the dc axial electroosmotic velocity. The velocity is measured at the center of the nanochannel (x/L0 = 1) at a fixed α = 6, σ* = -109.227, and φdcFz/RT = 19.3419. Here, β is varied by changing the bulk ionic concentration (c0) of the electrolyte.

Grahic Jump Location
Fig. 11

Effect of the normalized surface charge density (σ*) and St on the ratio of the time averaged ac/dc axial electroosmotic velocity to the dc axial electroosmotic velocity. The velocity is measured at the center of the nanochannel (x/L0 = 1) at a fixed α = 6, β = 0.0049, and φdcFz/RT = 19.3419.

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