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Numerical Simulation of Electroosmotic Flow in Flat Microchannels with Lattice Boltzmann Method

  • Research Article - Mechanical Engineering
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Abstract

In the present work, a new Lattice Boltzmann model has been developed to study the electroosmotic flows in a 2-D flat microchannel. The governing equations are presented in the continuum model, while a set of equivalent equations in Lattice Boltzmann model is introduced and solved numerically. In particular, the Poisson and the Nernst–Planck (NP) equations are solved by two new lattice evolution methods. In the analysis of electroosmotic flows, when the convective effects are not negligible or the electric double layers have overlap, the NP equations must be employed to determine the ionic distribution throughout the microchannel. The results of this new model have been validated by available analytical and numerical results. The model has also been used to examine the electroosmotic flows in a heterogeneous flat microchannel. Furthermore, the predictions of the NP model are compared with those of the Poisson Boltzmann (PB) equation to identify the applicability of the PB equations for such flows, which can also serve as validations for the present model.

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Abbreviations

A :

Ratio of the externally applied voltage to the elementary voltage

B :

Ratio of ionic pressure to dynamic pressure

D :

Diffusion coefficient

e :

Elementary charge of an electron

E :

Electric field intensity

H :

Width of microchannel

K :

Debye–Huckel parameter

k :

Double layer thickness parameter, k = KH

k B :

Boltzmann constant

n + :

Concentration of positive ions

n − :

Concentration of negative ions

n 0 :

Bulk ion concentration

P :

Pressure

Re :

Reynolds number

Sc :

Schmidt number

T :

Absolute temperature

u *, v * :

Dimensionless velocity components

U ref :

Reference velocity

x *, y * :

Dimensionless Cartesian coordinates

z :

Valance number of positive and negative ions

\({\varepsilon _0}\) :

Permittivity of vacuum

\({\varepsilon _r}\) :

Dielectric constant of the solution

\({\phi}\) :

Applied electric potential

\({\mu}\) :

Dynamic viscosity of working fluid

\({\rho}\) :

Density of working fluid

\({\rho_{\rm e}}\) :

Net electrical charge density

\({\zeta}\) :

Zeta potential

\({\psi}\) :

EDL potential

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Authors and Affiliations

  1. Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran

    Omid Reza Mohammadipoor & Hamid Niazmand

  2. Mechanical Engineering Department, University of Birjand, Birjand, Iran

    Seyed Ali Mirbozorgi

Authors
  1. Omid Reza Mohammadipoor
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  2. Hamid Niazmand
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  3. Seyed Ali Mirbozorgi
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Corresponding author

Correspondence to Hamid Niazmand.

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Mohammadipoor, O.R., Niazmand, H. & Mirbozorgi, S.A. Numerical Simulation of Electroosmotic Flow in Flat Microchannels with Lattice Boltzmann Method. Arab J Sci Eng 39, 1291–1302 (2014). https://doi.org/10.1007/s13369-013-0679-x

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  • DOI: https://doi.org/10.1007/s13369-013-0679-x

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