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Numerical analysis on electroosmotic flows in a microchannel with rectangle-waved surface roughness using the Poisson–Nernst–Planck model

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Abstract

The present study has numerically investigated two-dimensional electroosmotic flows in a microchannel with dielectric walls of rectangle-waved surface roughness to understand the roughness effect. For the study, numerical simulations are performed by employing the Nernst–Planck equation for the ionic species and the Poisson equation for the electric potential, together with the traditional Navier–Stokes equation. Results show that the steady electroosmotic flow and ionic-species transport in a microscale channel are well predicted by the Poisson–Nernst–Planck model and depend significantly on the shape of surface roughness such as the amplitude and periodic length of wall wave. It is found that the fluid flows along the surface of waved wall without involving any flow separation because of the very strong normal component of EDL (electric double layer) electric field. The flow rate decreases exponentially with the amplitude of wall wave, whereas it increases linearly with the periodic length. It is mainly due to the fact that the external electric-potential distribution plays a crucial role in driving the electroosmotic flow through a microscale channel with surface roughness. Finally, the present results using the Poisson–Nernst–Planck model are compared with those using the traditional Poisson–Boltzmann model which may be valid in these scales.

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Abbreviations

C p , C m :

nondimensional concentrations

C 0 :

molar ionic concentration in the bulk region (mol/m3)

D p , D m , D :

ionic diffusion coefficients (m2/s)

E i :

nondimensional total electric field component

E ϕ,i :

nondimensional external electric field component

E ψ,i :

nondimensional EDL electric field component

E 0 :

mean external streamwise electric field (V/m)

F :

Faraday constant (=96,485.338,3 C/mol)

F e,i :

nondimensional total electric force component

F e,ϕ,i :

nondimensional external electric force component

F e,ψ,i :

nondimensional EDL electric force component

H :

channel half-width (m)

h :

nondimensional amplitude of wall wave

L :

nondimensional periodic length of wall wave

Pe :

Peclet number (=U eo H/D)

p :

nondimensional pressure

Q :

nondimensional flow rate

Q * :

real flow rate (m3/s)

R :

gas constant (=8.314 J K−1 mol−1)

Re :

Reynolds number (=U eo H/ν)

Sc :

Schmidt number (=ν/D)

T :

absolute temperature (K)

t :

nondimensional time

U eo :

electroosmotic velocity (=ɛζ0 E 0/ρν, m/s)

u i :

nondimensional velocity components

x i :

nondimensional Cartesian coordinates

z p , z m , z :

ionic valences

β:

nondimensional parameter (=PeΩ)

Δ:

increment

ɛ:

fluid permittivity (C V−1 m−1 )

ζ0 :

reference zeta potential (V)

ζ *0 :

nondimensional reference zeta potential (=−zFζ0/RT)

κ:

nondimensional EDL thickness (=λ/H)

λ:

EDL thickness [=(ɛRT/2F 2 z 2 C 0)1/2, m]

ν:

fluid kinematic viscosity (m2/s)

ρ:

fluid density (kg/m3)

ρ e :

nondimensional volumetric electric-charge density

σ0 :

surface electric-charge density (C/m2)

Φ:

nondimensional total electric potential

ϕ:

nondimensional external electric potential

ψ:

nondimensional EDL electric potential

Ω:

nondimensional parameter (=ζ0/E 0 H)

i, j :

coordinate indices (1,2)

m :

anions

n :

wall-normal direction

p :

cations

t :

wall-tangential direction

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Acknowledgments

This work has been supported by the NRL (National Research Laboratory) Program of the Ministry of Education, Science and Technology, Korea.

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Authors and Affiliations

  1. Division of Mechanical Engineering, Dong-A University, 840, Hadan2-dong, Saha-gu, Busan, 604-714, South Korea

    Sangmo Kang & Yong Kweon Suh

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  1. Sangmo Kang
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  2. Yong Kweon Suh
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Correspondence to Sangmo Kang.

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Kang, S., Suh, Y.K. Numerical analysis on electroosmotic flows in a microchannel with rectangle-waved surface roughness using the Poisson–Nernst–Planck model. Microfluid Nanofluid 6, 461–477 (2009). https://doi.org/10.1007/s10404-008-0321-5

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  • DOI: https://doi.org/10.1007/s10404-008-0321-5

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