najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1032Research ArticlePHYSICSФИЗИКАBenchmark solutions for nanoflowsPopovA. I.

Kronverkskiy 49, 197101, St. Petersburg

popov239@gmail.comLobanovI. S.

Kronverkskiy 49, 197101, St. Petersburg

PopovI. Yu.

Kronverkskiy 49, 197101, St. Petersburg

GeryaT. V.

5 Sonnegstrasse, CH-8092 Zurich

taras.gerya@erdw.ethz.chITMO UniversityRussian FederationInstitute of Geophysics, Department of Earth Sciences, Swiss Federal Institute of Technology Zurich (ETH)Switzerland20141508202553391399Copyright © Popov A.I., Lobanov I.S., Popov I.Y., Gerya T.V., 20252025Popov A.I., Lobanov I.S., Popov I.Y., Gerya T.V.Popov A.I., Lobanov I.S., Popov I.Y., Gerya T.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1032

Essential viscosity variation creates additional difficulties for numerical investigation of flows through nanotubes and nanochannels. Benchmark solutions of the Stokes and continuity equations with variable viscosity are suggested. This is useful for testing of numerical algorithms applied to this problem.

nanotubeStokes flowbenchmark solutionThis work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by the Ministry of Science and Education of the Russian Federation (GOSZADANIE 2014/190, Project 14.Z50.31.0031), by grants of the President of Russia (state contracts 14.124.13.2045-MK and 14.124.13.1493-MK).ReferencesLi, D. (Ed.) Encyclopedia of Microfluidics and Nanofluidics. Springer, New York (2008).Li, D. (Ed.) Encyclopedia of Microfluidics and Nanofluidics. Springer, New York (2008).Popov I.Yu. Statistical derivation of modified hydrodynamic equations for nanotube flows, Phys. Scripta., 83, P. 045601/1-3 (2011).Popov I.Yu. Statistical derivation of modified hydrodynamic equations for nanotube flows, Phys. Scripta., 83, P. 045601/1-3 (2011).I.Yu. Popov, S.A. Chivilikhin, V.V. Gusarov. Flows in nanostructures: hybrid classical-quantum models. Nanosystems: Phys., Chem., Math., 3(1), P. 7–26 (2012).I.Yu. Popov, S.A. Chivilikhin, V.V. Gusarov. Flows in nanostructures: hybrid classical-quantum models. Nanosystems: Phys., Chem., Math., 3(1), P. 7–26 (2012).Frenkel Ya. I. New development of the theory of liquid state. Appl. Uspekhi Fiz. Nauk., 25. P. 1-18 (1941).Frenkel Ya. I. New development of the theory of liquid state. Appl. Uspekhi Fiz. Nauk., 25. P. 1-18 (1941).Antognozzi M., Humphris A. D. L., Miles M. J. Observation of molecular layering in a confined water film and study of the layers viscoelastic properties. Appl. Phys. Lett., 78, P. 300-302 (2001).Antognozzi M., Humphris A. D. L., Miles M. J. Observation of molecular layering in a confined water film and study of the layers viscoelastic properties. Appl. Phys. Lett., 78, P. 300-302 (2001).Li T.-D., Gao J., Szoszkeiwicz R., Landmann U., Riedo E. Structured and viscous water in subnanometer gaps. Phys. Rev. B., 75, P. 115415-1115415-6 (2007).Li T.-D., Gao J., Szoszkeiwicz R., Landmann U., Riedo E. Structured and viscous water in subnanometer gaps. Phys. Rev. B., 75, P. 115415-1115415-6 (2007).Kolesnikov A.I., Zanotti J.-M., Loong Ch.-K., and Thiyagarajan P.Anomalously Soft Dynamics of Water in a Nanotube: A Revelation of Nanoscale Confinement. Phys. Lett., 93, P. 035503-1035503-4 (2004).Kolesnikov A.I., Zanotti J.-M., Loong Ch.-K., and Thiyagarajan P.Anomalously Soft Dynamics of Water in a Nanotube: A Revelation of Nanoscale Confinement. Phys. Lett., 93, P. 035503-1035503-4 (2004).Kolesnikova A.I., C.-K. Loonga C.K., de Souzaa N.R., Burnhamb C.J. Moravskyc A.P. Anomalously soft dynamics of water in carbon nanotubes. Physica B, 385386, P. 272–274 (2006).Kolesnikova A.I., C.-K. Loonga C.K., de Souzaa N.R., Burnhamb C.J. Moravskyc A.P. Anomalously soft dynamics of water in carbon nanotubes. Physica B, 385386, P. 272–274 (2006).Deryagin B. V., Ovcharenko F. D., Churaev V. N. (Eds.) Water in Disperse Systems. Moskow, Nauka (1989).Deryagin B. V., Ovcharenko F. D., Churaev V. N. (Eds.) Water in Disperse Systems. Moskow, Nauka (1989).Gerya T. Introduction to Numerical Geodynamic Modelling, Cambridge University Press, Cambridge (2010).Gerya T. Introduction to Numerical Geodynamic Modelling, Cambridge University Press, Cambridge (2010).Gerya T.V., May D.A., Duretz T. An adaptive staggered grid finite difference method for modeling geodynamic Stokes flows with strongly variable viscosity. Geochem., Geophys., Geosyst. 14, DOI: 10.1002/ggge.20078 (2013).Gerya T.V., May D.A., Duretz T. An adaptive staggered grid finite difference method for modeling geodynamic Stokes flows with strongly variable viscosity. Geochem., Geophys., Geosyst. 14, DOI: 10.1002/ggge.20078 (2013).Blankenbach B., Busse F., Christensen U. et al, A benchmark comparison for mantle convection codes. Geophysical Journal International 98, P. 23–38 (1989).Blankenbach B., Busse F., Christensen U. et al, A benchmark comparison for mantle convection codes. Geophysical Journal International 98, P. 23–38 (1989).Gerya T.V., Yuen D.A., Characteristic-based marker-in-cell method with conservative finite-difference schemes for modeling geological flows with strongly variable transport properties. Phys. Earth Planetary Interiors, 140, P. 293–318 (2003).Gerya T.V., Yuen D.A., Characteristic-based marker-in-cell method with conservative finite-difference schemes for modeling geological flows with strongly variable transport properties. Phys. Earth Planetary Interiors, 140, P. 293–318 (2003).Gerya T.V., Yuen D.A. Robust characteristics method for modeling multiphase visco-elasto-plastic thermo-mechanical problems. Phys. Earth Planetary Interiors, 163, P. 83–105 (2007).Gerya T.V., Yuen D.A. Robust characteristics method for modeling multiphase visco-elasto-plastic thermo-mechanical problems. Phys. Earth Planetary Interiors, 163, P. 83–105 (2007).

The authors declare that there are no conflicts of interest present.