The influence of changes in the cross-sections of nanochannels on their electrohydrodynamic characteristics
DOI:
https://doi.org/10.7242/1999-6691/2023.16.3.30Keywords:
nanochannel, Debye layer, Nernst–Planck, Poisson, Navier–Stokes system, electroosmosis, surface charge, finite difference schemes, Runge–Kutta methodAbstract
The description of electrolyte solution flows in nanochannels with variable cross-section is one of the open problems in microelectrohydrodynamics. This problem has become especially important because of the possibility of fabricating narrow channels – as thin as 10 nm – and their practical significance. In addition to an external electric field that appears due to a potential difference between the inlet and outlet of the channel, the field generated by the surface charge on the channel walls is also essential. The assumption of smallness of the Debye layer thickness, which is commonly used to simplify the problem, is often invalid for nanochannels. Besides, there are difficulties connected with the validity of a continuity hypothesis and no-slip wall conditions. This paper presents a simplified approach that relies on the smallness of surface charge density along the channel rather than on the smallness of the Debye layer thickness. The flow parameters are assumed to vary much slower in the wall-tangential direction than in the wall-normal direction. In the Nernst–Planck, Poisson, Navier–Stokes system describing the flow, this makes it possible to implement the normal coordinate averaging, which is similar to the Kármán–Pohlhausen averaging, and to eventually reduce the system to a nonlinear differential equation with respect to a one-dimensional function. For the resulting equation, the sequences of ignoring the boundary no-slip conditions and those of anisotropy of diffusivity and viscosity coefficients are qualitatively analyzed. Stationary flows in simple diffuser/nozzle-shaped channels are modelled numerically in order to understand the behavior of more complex systems. The model proposed can be extended to describe electrolytes with an arbitrary number of charged species (specifically, to a ternary electrolyte), thus enabling to predict more sophisticated effects like local concentration of charged particles.
Downloads
References
Levich V.G. Physicochemical hydrodynamics. New York, Prentice Hall, 1962. 700 p.
Probstein R.F. Physicochemical hydrodynamics: An introduction. John Wiley and Sons Inc., 1994. 416 p. https://doi.org/10.1002/0471725137
Sand H.J.S. On the concentration at the electrodes in a solution, with special reference to the liberation of hydrogen by electrolysis of a mixture of copper sulphate and sulphuric acid. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1901, vol. 1, no. 1, pp. 45-79. https://doi.org/10.1080/14786440109462590
Stoynov Z.B., Grafov B.M., Savvova-Stoynova B.S., Elkin V.V. Elektrokhimicheskiy impedans [Electrochemical impedance]. Moscow, Nauka, 1991. 336 p.
Siraev R., Ilyushin P., Bratsun D. Mixing control in a continuous-flow microreactor using electro-osmotic flow. Math. Model. Nat. Phenom., 2021, vol. 16, 49. https://doi.org/10.1051/mmnp/2021043
Siraev R.R., Bratsun D.A. Numerical simulation of electrohydrodynamic convection induced by fast oscillating field emission. Vychisl. mekh. splosh. sred – Computational Continuum Mechanics, 2022, vol. 15, no. 2, pp. 193-208. https://doi.org/10.7242/1999-6691/2022.15.2.15
Chang H.-C., Yeo L.Y. Electrokinetically-driven microfluidics and nanofluidics. Cambridge University Press, 2010. 526 p.
Nichka V.S., Mareev S.A., Porozhnyy M.V., Shkirskaya S.A., Safronova E.Yu., Pismenskaya N.D., Nikonenko V.V. Modified microheterogeneous model for describing electrical conductivity of membranes in dilute electrolyte solutions. Membr. Membr. Technol., 2019, vol. 1, pp. 190-199. https://doi.org/10.1134/S2517751619030028
Frants E.A., Artyukhov D.A., Kireeva T.S., Ganchenko G.S., Demekhin E.A. Vortex formation and separation from the surface of a charged dielectric microparticle in a strong electric field. Fluid Dyn., 2021, vol. 56, pp. 134-141. https://doi.org/10.1134/S0015462821010043
Schnitzer O., Yariv E. Nonlinear electrophoresis at arbitrary field strengths: small-Dukhin-number analysis. Phys. Fluids, 2014, vol. 26, 122002. https://doi.org/10.1063/1.4902331
Wang Y.-C., Stevens A.L., Han J. Million-fold preconcentration of proteins and peptides by nanofluidic filter. Anal. Chem., 2005, vol. 77, pp. 4293-4299. https://doi.org/10.1021/ac050321z
Wang S.-C., Wei H.-H., Chen H.-P., Tsai M.-H., Yu C.-C., Chang H.-C. Dynamic superconcentration at critical-point double-layer gates of conducting nanoporous granules due to asymmetric tangential fluxes. Biomicrofluidics, 2008, vol. 2, 014102. https://doi.org/10.1063/1.2904640
Nekrasov O.O., Smorodin B.L. Electroconvection of a weakly conducting liquid subjected to unipolar injection and heated from above. Vychisl. mekh. splosh. sred – Computational Continuum Mechanics, 2022, vol. 15, no. 3, pp. 316-332. https://doi.org/10.7242/1999-6691/2022.15.3.24
Bruus H. Theoretical microfluidics. Oxford University Press, 2007. 288 p.
Liu C., Li Z. On the validity of the Navier-Stokes equations for nanoscale liquid flows: The role of channel size. AIP Advances, 2011, vol. 1, 032108. https://doi.org/10.1063/1.3621858
Rudyak V., Belkin A. Molecular dynamics simulation of fluid viscosity in nanochannels. Nanosystems: Physics, Chemistry, Mathematics, 2018, vol. 9, no. 3, pp. 349-355. https://doi.org/10.17586/2220-8054-2018-9-3-349-355
Andryushchenko V.A., Rudyak V.Ya. Self-diffusion of fluid molecules in nanochannels. Vestn. Tomsk. gos. un-ta. Matem. i mekh. – Tomsk State University Journal of Mathematics and Mechanics, 2012, no. 2(18), pp. 63-66.
Nguyen N.-T., Wereley S.T. Fundamentals and applications of microfluidics. Artech House Publishers, 2002. 471 p.
Malkin A.Ya., Patlazhan S.A., Kulichikhin V.G. Physicochemical phenomena leading to slip of a fluid along a solid surface. Russ. Chem. Rev., 2019, vol. 88, pp. 319-349. https://doi.org/10.1070/RCR4849
Bazant M. The electric double layer in concentrated electrolytes and ionic liquids. The 14th International Symposium on Electrokinetics. ELKIN, Tel-Aviv, Israel, July 4-6, 2022. P. 87. https://web2.eng.tau.ac.il/wtest/elkin2022/wp-content/uploads/2022/07/program-abstracts-new.pdf
Mani A., Zangle T.A., Santiago J.G. On the propagation of concentration polarization from microchannel-nanochannel interfaces. Part I: Analytical model and characteristic analysis. Langmuir, 2009, vol. 25, pp. 3898-3908. https://doi.org/10.1021/la803317p
Zangle T.A., Mani A., Santiago J.G. On the propagation of concentration polarization from microchannel-nanochannel interfaces. Part II: Numerical and experimental study. Langmuir, 2009, vol. 25, pp. 3909-3916. https://doi.org/10.1021/la803318e
Mani A., Bazant M.Z. Deionization shocks in microstructures. Phys. Rev. E, 2011, vol. 84, 061504. https://doi.org/10.1103/PhysRevE.84.061504
Yaroshchuk A. Over-limiting currents and deionization “shocks” in current-induced polarization: Local-equilibrium analysis. Adv. Colloid Interface Sci., 2012, vol. 183-184, pp. 68-81. https://doi.org/10.1016/j.cis.2012.08.004
Schlichting H., Gersten K. Boundary layer theory. Springer, 2017. 805 pp. https://doi.org/10.1007/978-3-662-52919-5
Nikitin N.V. Third-order-accurate semi-implicit Runge-Kutta scheme for incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids, 2006, vol. 51, pp. 221-233. https://doi.org/10.1002/fld.1122
Frantz E.A., Schiffbauer J., Demekhin E.A. Eksperimental’noye issledovaniye vypryamleniya elektricheskogo toka v zhidkostnykh mikrodiodakh na osnove elektrokineticheskoy neustoychivosti [Experimental study of electric current rectification in liquid microdiodes on the basis of electrokinetic instability]. Ekologicheskiy vestnik NTs ChES – Ecological bulletin of research centers of the Black Sea economic cooperation, 2014, vol. 11, no. 3, pp. 69-74.
Chang H.-C., Yossifon G., Demekhin E.A. Nanoscale electrokinetics and microvortices: How microhydrodynamics affects nanofluidic ion flux. Annu. Rev. Fluid Mech., 2012, vol. 44, pp. 401-426. https://doi.org/10.1146/ANNUREV-FLUID-120710-101046
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.