Nature of Self-Diffusion in Fluids
Keywords:self-diffusion coefficient, shear viscosity, molecular liquids
The nature of the self-diffusion in low-molecular fluids is discussed. The particular attention is paid to atomic fluids (such as argon), liquid metals, and associated fluids (such as water). The self-diffusion coefficient in the fluids of all indicated types is considered to be the sum of two components: one of them is associated with the transfer of molecules by hydrodynamic vortex modes, and the other is generated by the circulatory motion of local molecular groups. The both components have a collective nature, they are genetically related to each other and differ only by their scales: the former is mesoscopic, the latter is nanoscopic. Manifestations of the collective vortical transport of molecules as specific features in the time dependence of the root-mean-square displacement of molecules are discussed. Sound arguments are proposed concerning the inadequacy of the activation mechanism of thermal molecular motion in low-molecular liquids. The immanent contradiction of exponential temperature dependences for the viscosity and self-diffusion coefficients is proved. In all cases, the preference is given to qualitative arguments.
E.I. Kharkov, V.I. Lysov, V.E. Fedorov. Physics of Liquid Metals (Vyshcha Shkola, Kyiv, 1979) (in Russian).
L.A. Bulavin, T.V. Lokotosh, N.P. Malomuzh. Role of the collective self-diffusion in water and other liquids. J. Mol. Liq. 137, 1 (2008). https://doi.org/10.1016/j.molliq.2007.05.003
I.Z. Fisher. Hydrodynamic asymptotics of autocorrelation function of molecular velocity in classical fluid. Zh. ` Eksp. Teor. Fiz. 61, 1647 (1971) (in Russian).
N.P. Malomuzh, I.Z. Fisher. On the collective nature of thermal motion in fluids. Fiz. Zhidk. Sost. 1, 33 (1973) (in Russian).
L.A. Bulavin, A.A. Vasilkevich, A.K. Dorosh, V.T. Krotenko, V.I. Slisenko. Self-diffusion of water in aqueous solutions of singly charged electrolytes. Ukr. Fiz. Zh. 31, 1703 (1986) (in Russian).
L.A. Bulavin, P.G. Ivanitskii, V.T. Krotenko, V.N. Lyaskovskaya. Neutron studies of water self-diffusion in aqueous electrolyte solutions. Zh. Fiz. Khim. 61, 3270 (1987) (in Russian).
N.P. Malomuzh, K.S. Shakun. Maxwell relaxation time for argon. Physica (to be published).
T.V. Lokotosh, N.P. Malomuzh, K.N. Pankratov. Thermal motion in water-electrolyte solutions according to quasi- elastic incoherent neutron scattering data. J. Chem. Eng. Data 55, 2021 (2010). https://doi.org/10.1021/je9009706
A. Einstein. Eine neue Bestimmung der Molekuldimensionen. Ann. Phys. 19, 289 (1906). https://doi.org/10.1002/andp.19063240204
E.M. Lifshitz, Fluid Mechanics (Pergamon Press, 1993).
J. Frenkel. Kinetic Theory of Liquids (Dover, 1955).
E.N. da C. Andrade. The viscosity of liquids. Proc. Phys. Soc. 52, 748 (1940). https://doi.org/10.1088/0959-5309/52/6/302
H. Eyring. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4, 283 (1936). https://doi.org/10.1063/1.1749836
CRS Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data. Edited by R.C. West, (CRS Press, 1996).
NIST Chemistry WebBook, NIST Standard Reference Database Number 69. Edited by P.J. Linstrom, W.G. Mallar [http://webbook.nist.gov].
V.P. Slusar, N.S. Rudenko, V.M. Tretyakov. Experimental study of the viscosity of simple substances on the saturation line and under pressure. II Argon, krypton, xenon. Ukr. Fiz. Zh. 17, 1257 (1972) (in Russian).
V.N. Makhlaichuk. Kinematic shear viscosity of liquid alkaline metals. Ukr. J. Phys. 62, 672, (2017). https://doi.org/10.15407/ujpe62.08.0672
O.Ya. Samoilov, Structure of Aqueous Electrolyte Solutions and the Hydration of Ions (Consultants Bureau, 1965).
T. Iida, N. Tripathi, M. Isac, R.I.L. Guthrie. Models and equations for atomic transport coefficients of liquid metals: Viscosity and self-diffusivity. Mater. Sci. Forum 539–543, 2509 (2007). https://doi.org/10.4028/www.scientific.net/MSF.539-543.2509
T.V. Lokotosh, M.P. Malomuzh, K.M. Pankratov, K.S. Shakun. New results in the theory of collective self-diffusion in liquids. Ukr. Fiz. Zh. 60, 697 (2015) (in Ukrainian).
P.V. Makhlaichuk, M.P. Malomuzh, I.V. Zhyganiuk. Nature of hydrogen bond in water. Ukr. J. Phys. 57, 113 (2012).
D. Eisenberg, V. Kauzmann. The Structure and Properties of Water (Oxford Univ. Press, 1969). C.A. Croxton. Liquid State Physics – A Statistical Mechanical Introduction (Cambridge Univ. Press, 1974).
N.P. Malomuzh, V.P. Oleynik. Nature of the kinematic shear viscosity of water. J. Struct. Chem. 49, 1055 (2008). https://doi.org/10.1007/s10947-008-0178-1
L.A. Bulavin, A.I. Fisenko, N.P. Malomuz. Surprisin properties of the kinematic shear viscosity of water. Chem. Phys. Lett. 453, 183 (2008). https://doi.org/10.1016/j.cplett.2008.01.028
K. Okada, M. Yao, Y. Hiejima, H. Kohno, Y. Kojihara. Dielectric relaxation of water and heavy water in the whole fluid phase. J. Chem. Phys. 110, 3026 (1999). https://doi.org/10.1063/1.477897
H.R. Pruppacher. Self-diffusion coefficient of supercooled water. J. Chem. Phys. 56, 101 (1972). https://doi.org/10.1063/1.1676831
K. Simpson, M. Karr. Diffusion and nuclear spin relaxation in water. Phys. Rev. 111, 1201 (1958) https://doi.org/10.1103/PhysRev.111.1201
L.A. Bulavin, N.P. Malomuzh, K.N. Pankratov. The character of the thermal motion of water molecules according to the data of quasi-elastic incoherent slow neutron scattering. Zh. Strukt. Khim. 47, 54 (2006) (in Russian).
L.A. Bulavin, N.P. Malomuzh, K.N. Pankratov. Specific features of self-diffusion in water.Zh. Strukt. Khim. 47, S54 (2006) (in Russian).
L.A. Bulavin, N.P. Malomuzh. Upper temperature limit for the existence of living matter. J. Mol. Liq. 124, 136 (2006). https://doi.org/10.1016/j.molliq.2005.11.027
T.V. Lokotosh, S. Magazu, G. Maisano, N.P. Malomuzh. Nature of self-diffusion and viscosity in supercooled liquid water. Phys. Rev. E 62, 3572 (2000). https://doi.org/10.1103/PhysRevE.62.3572
P.V. Makhlaichuk, V.N. Makhlaichuk, N.P. Malomuzh. Nature of the kinematic shear viscosity of low-molecular liquids with averaged potential of Lennard-Jones type. J. Mol. Liq. 225, 577 (2017). https://doi.org/10.1016/j.molliq.2016.11.101
N.P. Malomuzh, K.S. Shakun, A.A. Kuznetsova. New possibilities provided by the analysis of the molecular velocity autocorrelation function in liquids. Ukr. Fiz. Zh. 63, 317 (2018) (in Ukrainian). https://doi.org/10.15407/ujpe63.4.317
V.M. Makhlaichuk. Qualitative properties of shear viscosity in liquids. Ukr. Fiz. Zh. (to be published) (in Ukrainian). https://doi.org/10.15407/ujpe63.11.986
P. Resibois, M. De Leener. Classical Kinetic Theory of Fluids (Wiley, 1978).
V.S. Oskotskii. To the theory of quasi-elastic scattering of cold neutrons in liquids. Fiz. Tverd. Tela 5, 1082 (1962) (in Russian).
S.A. Mikhailenko, V.V. Yakuba, A.E. Butko. Self-diffusion and nuclear magnetic relaxation in methane-argon liquid mixtures. Fiz. Nizk. Temp. 4, 562 (1978) (in Russian).
S.A. Mikhailenko, V.V. Yakuba. Self-diffusion and nuclear magnetic relaxation in liquid propylene and its mixtures with krypton. Ukr. Fiz. Zh. 27, 712 (1982) (in Russian).
T.V. Lokotosh, N.P. Malomuzh. Lagrange theory of thermal hydrodynamic fluctuations and collective diffusion in liquids. Physica A 286, 474 (2000). https://doi.org/10.1016/S0378-4371(00)00107-2
T.V. Lokotosh, N.P. Malomuzh. Manifestation of the collective effects in the rotational motion of molecules in liquids. J. Mol. Liq. 93, 95 (2001). https://doi.org/10.1016/S0167-7322(01)00214-8
T.V. Lokotosh, N.P. Malomuzh, K.S. Shakun. Nature of oscillations for the autocorrelation functions for transversal and angular velocities of a molecule. J. Mol. Liq. 96–97, 245 (2002). https://doi.org/10.1016/S0167-7322(01)00351-8
V.P. Voloshin, G.G. Malenkov, Yu.I. Naberukhin. The study of collective motions in computer models of water. Large-scale and long-term correlations. Zh. Strukt. Khim. 54 S2, 239 (2013) (in Russian).
G.G. Malenkov, Y.I. Naberukhin, V.P. Voloshin. Collective effects in molecular motions in liquids. Russ. J. Phys. Chem. A 86, 1378 (2012). https://doi.org/10.1134/S003602441209004X
A.V. Anikeenko, G.G. Malenkov, Yu.I. Naberukhin. Vizualization of the collective vortex-like motions in liquid argon and water: Molecular dynamic simulation. J. Chem. Phys. 148, 094508 (2018). https://doi.org/10.1063/1.5018140
N.P. Malomuzh, V.N. Makhlaichuk. Theory of self-diffusion in liquid metals. Rasplavy 5, 561 (2018) (in Russian).
N.P. Malomuzh, V.N. Makhlaychuk. Peculiarities of self-diffusion and shear viscosity in transition and post-transition metals. Rasplavy 5, 578 (2018) (in Russian).
V.M. Makhlaichuk. Shear viscosity of aqueous electrolyte solutions. Ukr. Fiz. Zh. (to be published) (in Ukrainian).
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.