Self-Organization in Viscous Liquids

V. I. Zasimchuk, O. E. Zasimchuk, O. S. Gatsenko

G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

Received: 14.08.2016; final version - 29.09.2017. Download: PDF

In this article, an amorphous solid is considered as a liquid with a very large coefficient of viscosity $\eta$. Its behaviour is studied by means of the continuity equation and Navier–Stokes equations. As revealed, the process of the relaxation of a liquid to a stress–strain loading can be unstable. An additional stationary state of a liquid, besides well-known one, is found. In this state, zones of the high and low densities are periodically alternate (by coordinate) that provides the plasticity of an amorphous solid.

Key words: amorphous solid, Navier–Stokes equations, equation of continuity, stability, stationary state, self-organization, periodical shear bands, hydrodynamic flow channels, plastic deformation.



PACS:, 61.43.Dq, 62.10.+s, 66.20.Cy, 83.10.Ff, 83.50.Ax, 83.60.-a

Citation: V. I. Zasimchuk, O. E. Zasimchuk, and O. S. Gatsenko, Self-Organization in Viscous Liquids, Metallofiz. Noveishie Tekhnol., 39, No. 10: 1435—1443 (2017) (in Russian)

  1. G. Nicolis and I. Prigogine, Samoorganizatsiya v Neravnovesnykh Sistemakh [Self-Organization in Nonequilibrium Systems] (Moscow: Mir: 1979) (Russian translation).
  2. P. Glansdorff and I. Prigogine, Termodinamicheskaya Teoriya Struktury, Ustoychivosti i Fluktuatsiy [Thermodynamic Theory of Structure, Stability and Fluctuations] (Moscow: Mir: 1973) (Russian translation).
  3. H. Haken, Sinergetika [Synergetics] (Moscow: Mir: 1980) (Russian translation).
  4. W. Ebeling, Obrazovanie Struktur pri Neobratimykh Protsessakh [Formation of Structures in Irreversible Processes] (Moscow: Mir: 1979) (Russian translation).
  5. J.-W. Qiao and Zh. Wang, Journal of Iron and Steel Research International, 23, No. 1: 7 (2016). Crossref
  6. A. L. Greer, Y. Q. Cheng, and E. Ma, Mater. Sci. Eng. R, 74: 71 (2013). Crossref
  7. L. D. Landau and E. M. Lifshitz, Teoreticheskaya Fizika. T. VI. Gidrodinamika [Theoretical Physics. Vol. VI. Hydrodynamics] (Moscow: Nauka: 1988) (in Russian).
  8. G. A. Korn and Th. M. Korn, Mathematical Handbook for Scientists and Engi-neers (New York: Mc Graw-Hill Book Company: 1968).
  9. O. Eh. Zasymchuk, V. I. Zasymchuk, and T. V. Turchak, Uspehi Fiziki Metallov, 14, No. 3: 275 (2013) (in Russian). Crossref