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The effect of heterogeneous surface charges on mixing in a combined electroosmotic/pressure-driven micromixer

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Abstract

This paper presents a numerical investigation of electro-osmotic flow in heterogeneous microchannels employing the approximate Helmholtz-Smoluchowski model in which the effect of the electric field force is modeled as a velocity slip boundary condition on the fluid flow. The performance of mixing in such microchannels with implemented heterogeneous zeta-potential on their walls is examined through solving the concentration equation both qualitatively and quantitatively. This numerical study illustrates that merging two electro-osmotic and pressure-driven flows in a single microchannel with a suitable arrangement of heterogeneities can easily lead to devising an electro-osmotic micromixer with adjustable mixing performance. The behavior of such micromixers is mainly influenced by the arrangement of zeta-potential distribution and the amount of the applied external pressure drop. This paper introduces the relative mixing efficiency and mixing capacity and the well-discussed criterion of mixing performance to achieve a comprehensive mixing analysis. These factors show that heterogeneities do not significantly improve mixing under circumstances of an extremely small or large pressure drop. Therefore, the performance of micromixers with a combination of electro-osmotic and pressure-driven flows has an optimum point. It is also observed that the asymmetric degree of the charge pattern on the microchannel wall has a notable impact on the mixing efficiency of the micromixer compared to the absolute values of wall charges. This matter ensures that proper mixing can be achieved even with conventional/moderate zeta-potential surfaces in a micromixer.

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Abbreviations

\(C\) :

Concentration (\({\text{mol m}}^{ - 3}\))

\(C_{m}\) :

Mean concentration at each cross-section (\({\text{mol m}}^{ - 3}\))

\(D\) :

Molecular diffusion coefficient (\({\text{m}}^{2} {\text{ s}}^{ - 1}\))

\(E\) :

Electric field strength (\({\text{v m}}^{ - 1}\))

\(E_{{{\text{ext}}}}\) :

Applied electric field strength (\({\text{v m}}^{ - 1}\))

\({\text{E}}_{{{\text{Ch}},{\text{ r}}}}\) :

Relative mixing efficiency (−)

\(H\) :

Microchannel height (\({\text{m}}\))

\(L\) :

Channel length (\({\text{m}}\))

\(P\) :

Pressure (\({\text{kg m}}^{ - 1} {\text{ s}}^{ - 2}\))

\(Q_{{{\text{mix}}}}\) :

Mixing capacity (\({\text{nanoliter s}}^{ - 1}\))

\({\text{Re}}\) :

Reynolds number (−)

\({\text{Sc}}\) :

Schmidt number (−)

\(u_{{{\text{wall}}}}\) :

Velocity on the wall (\({\text{m s}}^{ - 1}\))

\(\vec{V}\) :

Velocity vector (\({\text{m s}}^{ - 1}\))

\(\in_{{{\text{ms}}}}\) :

Mixing efficiency based on the concentration (−)

\(\varepsilon\) :

Electrolyte permittivity coefficient (\({\text{c v}}^{ - 1} {\text{ m}}^{ - 1}\))

\(\mu\) :

Dynamic viscosity (\({\text{kg m}}^{ - 1} {\text{ s}}^{ - 1}\))

\(\zeta\) :

Zeta-potential (\({\text{v}}\))

\(\zeta_{p}\) :

Zeta-potential in pumping section (\({\text{v}}\))

\(\zeta_{m}\) :

Zeta-potential in middle section (\({\text{v}}\))

\(\Psi_{0}\) :

Solid-liquid interface surface potential (\({\text{v}}\))

\(\sigma\) :

Concentration deviation without weight function (\({\text{mol m}}^{ - 3}\))

\(\sigma_{w}\) :

Concentration deviation with weight function (\({\text{mol m}}^{ - 3}\))

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Acknowledgments

The authors gratefully acknowledge the mechanical engineering departments at the Ferdowsi University of Mashhad and the University of Saskatchewan for providing us the research facilities. The research is also made possible to the first author by the Devolved Graduate Scholarships and NSERC Discovery Grant to WJ.

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This research work is not supported by any funding agency.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK, S7N 5A9, Canada

    A. Farahinia & Wenjun Zhang

  2. Department of Mechanical Engineering, Razi University, 6714414971, Kermanshah, Iran

    J. Jamaati

  3. Department of Mechanical Engineering, Ferdowsi University of Mashhad, 9177948974, Mashhad, Iran

    H. Niazmand

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  1. A. Farahinia
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Correspondence to A. Farahinia.

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Farahinia, A., Jamaati, J., Niazmand, H. et al. The effect of heterogeneous surface charges on mixing in a combined electroosmotic/pressure-driven micromixer. J Braz. Soc. Mech. Sci. Eng. 43, 497 (2021). https://doi.org/10.1007/s40430-021-03215-x

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