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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2012, 3 (1), P. 7–26

FLOWS IN NANOSTRUCTURES: HYBRID CLASSICAL-QUANTUM MODELS

S.A. Chivilikhin – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia, associate professor, sergey.chivilikhin@gmail.com
V.V. Gusarov – Saint Petersburg State Institute of Technology (Technical University), Saint Petersburg, Russia, Ioffe Physical Technical Institute, Saint Petersburg, Russia, Head of Department of Physical Chemistry, Corresponding member of RAS, victor.v.gusarov@gmail.com
I.Yu. Popov – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia, Professor, Doctor of Science, Head of Department of Higher Mathematics, popov@mail.ifmo.ru

Flow through nanotube has many interesting peculiarities.To describe these unusual properties we suggest a model of the flow based on crystallite liquid theory. Slip boundary condition is used instead of conventional no-slip condition. The condition is derived by consideration of interaction of flow particles with the nanotube wall potential in the
framework of quantum mechanics. For nanotube with elastic walls another mechanism of flow plays an important role. Namely, a model of flow caused by elastic soliton wave in its wall is suggested. As for general consideration, a modification of the Navier-Stokes equations for the nanotube flow is derived from many-particle Hamiltonian in the framework of quantum statistical physics. Particularly, for a model confinement the effective viscosity of
the nanotube flow is got. The obtained dependence of the viscosity on the nanotube diameter is in good correlation with the corresponding experimental results.

Keywords: nanotube, flow, crystallite, soliton, quantum statistics.

UDC 539.3

PACS 68.90.+g, 05.60.-k

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