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Unsteady electroosmotic channel flows with the nonoverlapped and overlapped electric double layers

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Abstract

In micro- and nanoflows, the Boltzmann distribution is valid only when the electric double layers (EDL’s) are not overlapped and the ionic distributions establish an equilibrium state. The present study has numerically investigated unsteady two-dimensional fully-developed electroosmotic flows between two parallel flat plates in the nonoverlapped and overlapped EDL cases, without any assumption of the Boltzmann distribution. For the study, two kinds of unsteady flows are considered: one is the impulsive application of a constant electric field and the other is the application of a sinusoidally oscillating electric field. For the numerical simulations, the ionic-species and electric-field equations as well as the continuity and momentum ones are solved. Numerical simulations are successful in accurately predicting unsteady electroosmotic flows and ionic distributions. Results show that the nonoverlapped and overlapped cases are totally different in their basic characteristics. This study would contribute to further understanding unsteady electroosmotic flows in micro- and nanofluidic devices.

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Abbreviations

C s ,C 0 :

Molar ionic concentrations

D s ,D :

Ionic diffusion coefficients

E i ,E 0 :

External electric fields

e f :

External electric-field mode

F :

Faraday constant

H(t) :

Heaviside function

h :

Channel half-width

k :

Parameter

M :

Grid resolution

p :

Pressure

R :

Gas constant

Sc :

Schmidt number

T :

Absolute temperature

t :

Time

U c ,U 0 :

Streamwise velocities

U eo :

Electroosmotic velocity

u i ,(u,v) :

Velocity components

x i , (x, y):

Cartesian coordinates

y’:

Normal distance from surface

Z s ,z :

Ionic valences

Δt :

Transient timescale

Δt c ,Δ te :

Transient timescales

Δtu,Δtω :

Transient timescales

δ:

Penetration depth

δ(y):

Dirac delta function

ε:

Fluid permittivity

ξ0 :

Zeta potential

ξ0 * :

Nondimensional zeta potential

κ:

Nondimensional EDL length

λ:

EDL length

ν:

Fluid kinematic viscosity

ξ:

Parameter

ρ:

Fluid density

ρe :

Volumetric electric-charge density

σ0 :

Surface electric-charge density

Ψ,Ψw :

Electric potentials

ω:

External electric-field frequency

•:

Spatial averaging

i :

Indices

m :

Anions

p :

Cations

s :

Indices (p, m)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Dong-A University, 604-714, Busan, Korea

    Sangmo Kang & Yong Kweon Suh

Authors
  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. Unsteady electroosmotic channel flows with the nonoverlapped and overlapped electric double layers. J Mech Sci Technol 20, 2250–2264 (2006). https://doi.org/10.1007/BF02916342

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  • DOI: https://doi.org/10.1007/BF02916342

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