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Research Papers: Flows in Complex Systems

Electroosmotic Flow in Hydrophobic Microchannels of General Cross Section

[+] Author and Article Information
Morteza Sadeghi

Center of Excellence in Energy
Conversion (CEEC),
School of Mechanical Engineering,
Sharif University of Technology,
Tehran 11155-9567, Iran
e-mail: sadeghi_morteza@mech.sharif.edu

Arman Sadeghi

Department of Mechanical Engineering,
University of Kurdistan,
Sanandaj 66177-15175, Iran
e-mail: a.sadeghi@eng.uok.ac.ir

Mohammad Hassan Saidi

Center of Excellence in Energy
Conversion (CEEC),
School of Mechanical Engineering,
Sharif University of Technology,
Tehran 11155-9567, Iran
e-mail: saman@sharif.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 2, 2015; final manuscript received August 17, 2015; published online October 1, 2015. Assoc. Editor: Prashanta Dutta.

J. Fluids Eng 138(3), 031104 (Oct 01, 2015) (9 pages) Paper No: FE-15-1230; doi: 10.1115/1.4031430 History: Received April 02, 2015; Revised August 17, 2015

Adopting the Navier slip conditions, we analyze the fully developed electroosmotic flow in hydrophobic microducts of general cross section under the Debye–Hückel approximation. The method of analysis includes series solutions which their coefficients are obtained by applying the wall boundary conditions using the least-squares matching method. Although the procedure is general enough to be applied to almost any arbitrary cross section, eight microgeometries including trapezoidal, double-trapezoidal, isosceles triangular, rhombic, elliptical, semi-elliptical, rectangular, and isotropically etched profiles are selected for presentation. We find that the flow rate is a linear increasing function of the slip length with thinner electric double layers (EDLs) providing higher slip effects. We also discover that, unlike the no-slip conditions, there is not a limit for the electroosmotic velocity when EDL extent is reduced. In fact, utilizing an analysis valid for very thin EDLs, it is shown that the maximum electroosmotic velocity in the presence of surface hydrophobicity is by a factor of slip length to Debye length higher than the Helmholtz–Smoluchowski velocity. This approximate procedure also provides an expression for the flow rate which is almost exact when the ratio of the channel hydraulic diameter to the Debye length is equal to or higher than 50.

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Figures

Grahic Jump Location
Fig. 1

Geometries of the ducts being considered; the bold dot shows the origin of the coordinate system for each geometry

Grahic Jump Location
Fig. 2

Schematic diagram of a typical geometry along with the coordinate system

Grahic Jump Location
Fig. 3

Dimensionless velocity distribution considering K = 20 and L* = 0.05 for (a) a double-trapezoidal duct with σ = 1 and α = 0.5; (b) an elliptical duct with σ = 0.5; (c) an isotropically etched duct with σ = 1; and (d) a rhombic duct with σ = 1; (e) a semi-elliptical duct with σ = 0.5 l; (f) a trapezoidal duct with σ = 1 and α = 0.5; (g) an isosceles triangular duct with σ = 1; and (h) a rectangular duct with σ = 0.5.

Grahic Jump Location
Fig. 4

Dimensionless velocity distribution in a double-trapezoidal duct with σ = 1 and α = 0.5 considering L* = 0.05 and (a) K = 5 (b) K = 50

Grahic Jump Location
Fig. 5

Dimensionless velocity distribution at the symmetry line of a double-trapezoidal duct for different values of K and L* considering σ = 1 and α = 0.5

Grahic Jump Location
Fig. 6

Plots of Q* versus K for (a) a double-trapezoidal duct, (b) an elliptical duct, (c) an isotropically etched duct, (d) a rhombic duct, (e) a semi-elliptical duct, (f) a trapezoidal duct, (g) an isosceles triangular duct, and (h) a rectangular duct

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