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Atomic scale design and three-dimensional simulation of ionic diffusive nanofluidic channels

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Abstract

Recent advance in nanotechnology has led to rapid advances in nanofluidics, which has been established as a reliable means for a wide variety of applications, including molecular separation, detection, crystallization and biosynthesis. Although atomic and molecular level consideration is a key ingredient in experimental design and fabrication of nanofluidic systems, atomic and molecular modeling of nanofluidics is rare and most simulations at nanoscale are restricted to one or two dimensions in the literature, to our best knowledge. The present work introduces atomic scale design and three-dimensional (3D) simulation of ionic diffusive nanofluidic systems. We propose a variational multiscale framework to represent the nanochannel in discrete atomic and/or molecular detail while describing the ionic solute by continuum. Apart from the major electrostatic and entropic effects, the non-electrostatic interactions between the channel and solution, and among solvent molecules are accounted in our modeling. We derive generalized Poisson–Nernst–Planck equations for nanofluidic systems. Mathematical algorithms, such as Dirichlet-to-Neumann mapping and the matched interface and boundary methods, are developed to rigorously solve the aforementioned equations to the second-order accuracy in 3D realistic settings. Three ionic diffusive nanofluidic systems, including a negatively charged nanochannel, a bipolar nanochannel and a double-well nanochannel, are designed to investigate the impact of atomic charges to channel current, density distribution and electrostatic potential. Numerical findings, such as gating, ion depletion and inversion, are in good agreements with those from experimental measurements and numerical simulations in the literature.

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Acknowledgments

This work was supported in part by NSF Grants IIS-1302285 and DMS-1160352, and NIH Grant R01GM-090208. The authors thank an anonymous reviewer for useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Jin Kyoung Park, Kelin Xia & Guo-Wei Wei

  2. Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Guo-Wei Wei

  3. Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI, 48824, USA

    Guo-Wei Wei

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  1. Jin Kyoung Park
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  2. Kelin Xia
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Correspondence to Guo-Wei Wei.

Appendix

Appendix

See Tables 5 and 6.

Table 5 Positions and charges of all atomic charges in the negatively charged channel
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Table 6 Positions and charges of all atomic charges in the bipolar channel
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Park, J.K., Xia, K. & Wei, GW. Atomic scale design and three-dimensional simulation of ionic diffusive nanofluidic channels. Microfluid Nanofluid 19, 665–692 (2015). https://doi.org/10.1007/s10404-015-1593-1

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