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Pressure effects on electroosmotic flow of power-law fluids in rectangular microchannels

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Abstract

In this paper, the fully developed electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient is analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. A complete parametric study reveals that the pressure effects are more pronounced at higher values of the channel aspect ratio and smaller values of the flow behavior index. The Poiseuille number is found to be an increasing function of the channel aspect ratio for pressure assisted flow and a decreasing function of this parameter for pressure opposed flow. It is also observed that the Poiseuille number is increased by increasing the zeta potential. Furthermore, the results show that an increase in the flow behavior index results in a lower flow rate ratio, defined to be the ratio of the flow rate to that of a Newtonian fluid at the same conditions. Moreover, whereas the flow rate ratio in the presence of an opposed pressure gradient is smaller than that of a favorable pressure force for shear thinnings, the opposite is true for shear-thickening fluids.

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Abbreviations

e :

Proton charge (C)

E x :

Electric field in the axial direction (Vm−1)

f :

Friction factor \({\left[=2\tau_{w,{\rm av}} /\rho u_{\rm HS}^2\right]}\)

F :

Component of body force vector (Nm−3)

F :

Body force vector (Nm−3)

H :

Half channel height (m)

k B :

Boltzmann constant (JK−1)

m :

Flow consistency index (Pasn)

n :

Flow behavior index

n 0 :

Ion density at neutral conditions (m−3)

p :

Pressure (Pa)

Q :

Volumetric flow rate (m3 s−1)

r :

Radial coordinate (m)

R :

Channel radius (m)

Re :

Reynolds number \({\left[=\rho u_{\rm HS}^{2-n} H^{n}/m\right]}\)

t :

Time (s)

T :

Absolute temperature (K)

u :

Axial velocity (ms−1)

u HS :

Helmholtz–Smoluchowski velocity [Eq. (20)]

u PD :

Pressure-driven velocity [Eq. (24)]

u :

Velocity vector (ms−1)

W :

Half channel width (m)

x, y, z :

Coordinates (m)

Z :

Valence number of ions in solution

α:

Channel aspect ratio [ = W/H]

\({\dot{\gamma}}\) :

Magnitude of the strain rate tensor (s−1)

\({{\mathbf{\dot{\gamma}}}}\) :

Strain rate tensor (s−1)

Γ:

Velocity scale ratio [Eq. (23)]

\({\varepsilon }\) :

Fluid permittivity (CV−1 m −1)

ζ :

Zeta potential (V)

K :

Dimensionless Debye–Hückel parameter \({\left[=H/\lambda_{\rm D}\right]}\)

K′:

Dimensionless Debye–Hückel parameter for circular geometry \({\left[=R/\lambda_{\rm D}\right]}\)

λ D :

Debye length (m)

μ :

Effective viscosity (Pas)

ρ :

Fluid density (kgm−3)

ρ e :

Net electric charge density (Cm−3)

τ :

Stress tensor component (Pa)

\({\boldsymbol{\tau}}\) :

Stress tensor (Pa)

φ :

Electrostatic potential (V)

Φ :

Externally imposed electrostatic potential (V)

ψ :

EDL potential (V)

av:

Average

c :

Circular

m :

Mean

r :

Rectangular

w :

Wall

0:

Reference

*:

Dimensionless variable

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Authors and Affiliations

  1. Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, P.O. Box: 11155-9567, Tehran, Iran

    Mohammad Ali Vakili, Arman Sadeghi & Mohammad Hassan Saidi

Authors
  1. Mohammad Ali Vakili
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  2. Arman Sadeghi
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  3. Mohammad Hassan Saidi
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Correspondence to Arman Sadeghi.

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Communicated by Oleg Zikanov.

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Vakili, M.A., Sadeghi, A. & Saidi, M.H. Pressure effects on electroosmotic flow of power-law fluids in rectangular microchannels. Theor. Comput. Fluid Dyn. 28, 409–426 (2014). https://doi.org/10.1007/s00162-014-0325-6

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