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Electrokinetic ion transport at micro–nanochannel interfaces: applications for desalination and micromixing

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Abstract

The ion concentration polarization (ICP) phenomenon occurs widely near nano-channel/membrane interfaces. Due to its extraordinary selective ion transport ability, ICP has been applied in many fields, such as desalination, molecular preconcentration and biomolecular separation. This paper is devoted to describing the transport mechanism of buffer ions at micro–nanochannel interfaces. Here, a multiphysics coupling model is proposed, where the boundary condition for the fixed surface voltage is introduced to describe the effect of nanochannel networks. The effectiveness of the proposed model and the calculation process is confirmed through comparative simulations. Comparing the simulations with experimental ICP results shows that the proposed model can effectively describe the nonlinear distribution of electric fields and a typical vortex pair from flow phenomena. An analytic scaling law for the propagating ion depletion zone (IDZ) is proposed, and a theoretical analysis and numerical results confirm its existence. For transient evolution, the IDZ spreads as \({\sqrt t }\) due to diffusion for t < 0.01 s and as t due to convection from 0.01 s < t < 0.1 s. Furthermore, detailed studies are performed to elucidate the ICP mechanism for desalination. The factors affecting desalination are investigated, including the buffer concentration, length and performance of the nanochannel network, height of the microchannel and the tangential electric field. Finally, the proposed research confirms that this device also has excellent potential as a micromixer pump. The rapid mixing of neutral particles can be realized using nonlinear electrokinetic flows with a mixing efficiency reaching 91%. The presented results provide some important guidance and physical insights into the design and optimization for this kind of chip and other related applications.

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Abbreviations

C 0 :

Buffer concentration (M)

C i :

Ion concentrations (M)

C m :

Nanochannel surface concentration (M)

C max :

Maximum in concentration mixture (M)

D :

Diffusion coefficient (m2/s)

E :

Electric field (V/m)

e :

Elementary charge (C)

F :

Faraday’s number (C/mol)

g :

Gravitational acceleration (m/s2)

H :

Characteristic length (m)

J i :

Ion flux (mol/m2 s)

L :

Microchannel length (m)

L m :

Nanochannel network length (m)

P :

Pressure (Pa)

R :

Gas constant (J/(mol K))

r :

Index of mixing

T :

Absolute temperature (K)

U :

Fluid velocity (m/s)

V L :

Voltage at the left end of the channel (V)

V sur :

Surface voltage (V)

V R :

Voltage at the right end of the channel (V)

V T :

Thermal voltage (V)

Z i :

Ion valence

\(\sigma_{ - }\) :

Negatively charged density (mC/m2)

\(\beta\) :

Coefficient of expansion (kg/mol)

\(\varepsilon_{0}\) :

Vacuum permittivity (F/m)

\(\varepsilon_{\text{r}} (c)\) :

Solvent permittivity (F/m)

\(\varepsilon_{\text{W}}\) :

Relative dielectric constant (1)

\(\zeta (c)\) :

Zeta potential (V)

\(\eta (c)\) :

Dynamic viscosity (Pa s)

\(\rho (c)\) :

Concentration-dependent density (kg/m3)

\(\rho_{0}\) :

Initial fluid density (kg/m3)

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

Space charged density (C/m3)

\(\varPhi\) :

Electric potential (V)

1:

Cations

2:

Anions

3:

Particles

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Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant Nos. 11972257, 11802225 and 11472193) and Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2019JQ-261). The authors gratefully acknowledge these supports. We also thank anonymous reviewers for their helpful comments on an earlier draft of this paper.

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, People’s Republic of China

    Wei Liu & Yueting Zhou

  2. School of Civil Engineering and Institute of Mechanics and Technology, Xi’an University of Architecture and Technology, Xi’an, 710055, Shaanxi, People’s Republic of China

    Pengpeng Shi

  3. State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Research Center of NDT and Structural Integrity Evaluation, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Pengpeng Shi

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  1. Wei Liu
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Correspondence to Yueting Zhou or Pengpeng Shi.

Appendix A: Numerical verification

Appendix A: Numerical verification

See Fig. 8.

Fig. 8
figure 8

Comparison of our presented results and the previous results. a Previous numerical results (Jia and Kim 2014). b Our presented numerical results

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By neglecting the surface voltage boundary and no-slip boundary caused by the nanochannel network, the presented theoretical model can be directly compared to the simple model presented by Jia and Kim (2014) to prove the correctness of the numerical process. For this simplified case, an excellent agreement between the prediction from the present results and the previous simulation results is achieved. As a result, the present numerical calculation process has been validated.

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Liu, W., Zhou, Y. & Shi, P. Electrokinetic ion transport at micro–nanochannel interfaces: applications for desalination and micromixing. Appl Nanosci 10, 751–766 (2020). https://doi.org/10.1007/s13204-019-01207-x

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