ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Sennitskii V. L. On the structure of a viscous liquid flow under periodic influences which have no predominant direction in space. Izvestiya VUZ. Applied Nonlinear Dynamics, 2025, vol. 33, iss. 4, pp. 531-544. DOI: 10.18500/0869-6632-003163, EDN: OZISPR

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon and_2025-4_sennitskii_531-544.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Innovations in applied physics
Article type: 
Article
UDC: 
530.182, 532.516, 532.517, 517.928
DOI: 
10.18500/0869-6632-003163
EDN: 
OZISPR

On the structure of a viscous liquid flow under periodic influences which have no predominant direction in space

Autors: 
Sennitskii Vladimir Leonidovich,
Abstract: 

Purpose of the work is the revealing and the researching of peculiarities of the dynamics of a viscous liquid which is undergoing by periodic in time influences possessing no predominant direction in space underpossible simplest hydro-mechanical conditions (which are able to provide non-trivial behavior of the liquid).

Methods. The analytic investigational methods for boundary problems for Navier–Stokes and continuity equations are used that are the method of perturbations, the method of Fourier.

Results. A new problem on the flow of a viscous liquid is formulated and solved. The hydro-mechanical system consists of an incompressible viscous liquid and a moving absolutely solid wall which creates periodic influences to the liquid. A new peculiarity of the viscous liquid dynamics is revealed consisting in that in simplest hydro-mechanical conditions the liquid in the background of oscillatios (in average of time) performs a motion of a new type — a stationary fading with the distance from the wall motion which is characterized by the presence of a laminate structure. A physical interpretation of the formulation of the problem under consideration is given.

Conclusion. The obtained results can be used in particular in a scientific search of ways to control hydro-mechanical systems, under a developing methods of a creation of prescribed flows of liquid media.
 

Key words: 
вязкая жидкость
периодические по времени воздействия
выделенное направление в пространстве
структура течения
Reference: 
  1. Chelomei VN. Paradoxes in mechanics caused by vibrations. Sov. Phys. Doklady. 1983;270(1): 6267 (in Russian).
  2. Sennitskii VL. Motion of a circular cylinder in a vibrating liquid. J. Appl. Mech. Tech. Phys. 1985;26(5):620623. DOI: 10.1007/BF00915307.
  3. Sennitskii VL. Motion of a gas bubble in a viscous vibrating liquid. J. Appl. Mech. Tech. Phys. 1988;29(6):865870. DOI: 10.1007/BF00858387.
  4. Sennitskii VL. The predominantly unidirectional motion of a gas bubble in a vibrating liquid. Sov. Phys. Doklady. 1991;319(1):117119 (in Russian).
  5. Sennitskii VL. On motion of inclusions in uniformly and non-uniformly vibrating liquid. In: Proceedings of the International workshop on G-jitter. Potsdam (USA): Clarkson University; 1993. P. 178186.
  6. Lyubimov DV. New approach in the vibrational convection theory. In: Proc. 14 IMACs Congress on Computational and Applied Mathematics. Atlanta, Georgia, USA. Atlanta: Georgia Institute of Technonogy; 1994. P. 5968.
  7. Sennitskii VL. The motion of inclusions in an oscillating liquid. Siberian Physical Journal. 1995;(4):1826 (in Russian).
  8. Ivanova AA, Kozlov VG, Evesque P. Dynamics of a cylindrical body in a liquid-filled sector of a cylindrical layer under rotational vibration. Fluid Dyn. 1998;33:488496. DOI: 10.1007/ BF02698213.
  9. Lyubimov DV, Lyubimova TP, Cherepanov AA. Dynamics of Interfaces in Vibrational Fields. M.: Fizmatlit; 2003. 216 p. (in Russian).
  10.  Ivanova AA, Kuzaev AF, Kozlov VG. Vibrational lift force acting on a body in a fluid near a solid surface. Doklady Physics. 2005;50(6):311314. DOI: 10.1134/1.1958123.
  11.  Sennitskii VL. Motion of an inclusion in uniformly and nonuniformly vibrating liquids. J. Appl. Mech. Tech. Phys. 2007;48:6570. DOI: 10.1007/s10808-007-0009-8.
  12.  Sennitskii VL. Pulsating motion of an inhomogeneous solid sphere in a vibrating liquid. J. Appl. Mech. Tech. Phys. 2009;50:936943. https://doi.org/10.1007/s10808-009-0127-6.
  13.  Ivanova , Kozlov VG, Shchipitsyn VD. A light cylinder under horizontal vibration in a cavity filled with a fluid. Fluid Dyn. 2010;45(6):889897. DOI: 10.1134/S0015462810060062.
  14.  Kozlov VG, Ivanova AA, Schipitsyn VD, Stambouli M. Lift force on the cylinder in viscous liquid under vibration. Acta Astronaut. 2012;79:4451. DOI: 10.1016/j.actaastro.2012.04.013.
  15.  Pyatigorskaya OS, Sennitskii VL. Example of motion of a cylindrical solid in a viscous liquid. J. Appl. Mech. Tech. Phys. 2013;54(2):237242. DOI: 10.1134/S0021894413020089.
  16.  Pyatigorskaya OS, Sennitskii VL. Motion of solid particles in an oscillating liquid. J. Appl. Mech. Tech. Phys. 2013;54(3):404407. DOI: 10.1134/S0021894413030085.
  17.  Ivanova AA, Kozlov VG, Shchipitsyn VD. Lift force acting on a cylindrical body in a fluid near the boundary of a cavity performing translational vibrations. J. Appl. Mech. Tech. Phys. 2014;55(5):773780. DOI: 10.1134/S002189441405006X.
  18.  Vlasova OA, Kozlov VG. The repulsion of flat body from the wall of vibrating container filled with liquid. Microgravity Sci. Technol. 2015;27:297303. DOI: 10.1007/s12217-015-9460-y.
  19.  Sennitskii VL. On the prescribed orientation of a solid inclusion in a viscous liquid. Siberian Journal of Industrial Mathematics. 2015;18(1):123128 (in Russian). DOI: 10.17377/SIBJIM. 2015.18.110.
  20.  Kozlov NV, Vlasova OA. Behaviour of a heavy cylinder in a horizontal cylindrical liquidfilled cavity at modulated rotation. Fluid Dyn. Res. 2016;48(5):055503. DOI: 10.1088/0169-5983/48/5/ 055503.
  21.  Sennitskii VL. Paradoxical motion of a liquid. International Journal of Applied and Fundamental Research. 2017;(8):2833 (in Russian). DOI: 10.17513/mjpfi.11753.
  22.  Sennitskii VL. Predominantly unidirectional rotation of a solid body and a viscous liquid. J. Appl. Ind. Math. 2017;11:284288. DOI: 10.1134/S1990478917020144.
  23.  Vlasova , Kozlov VG, Kozlov NV. Lift force acting on a heavy solid in a rotating liquidfilled cavity with a time-varying rotation rate. J. Appl. Mech. Tech. Phys. 2018;59:219228. DOI: 10.1134/S0021894418020050.
  24.  Konovalov VV, Lyubimova TP. Numerical study of the influence of vibrations on the interaction in an ensemble of gas bubbles and solid particles in a liquid. Fluid Dyn. 2019;12(1):4856 (in Russian). DOI: 10.7242/1999-6691/2019.12.1.5.
  25.  Sennitskii VL. On the motion of a viscous liquid in the absence of a predominant direction in space. International Journal of Applied and Fundamental Research. 2021;(2):6771 (in Russian). DOI: 10.17513/mjpfi.13181.
  26.  Sennitskii VL. Predominantly unidirectional flow of a viscous fluid. J. Appl. Ind. Math. 2021;15: 326330. DOI: 10.1134/S1990478921020149.
  27.  Sennitskii VL. On the flow of a viscous liquid in a gravity field. Thermophys. Aeromech. 2021;28:347351. DOI: 10.1134/S0869864321030057.
  28.  Konovalov VV, Lyubimova TP. Influence of acoustic vibrations on the interaction of a gas bubble and a solid particle in a liquid. In: Lyubimova TP, editor. Perm hydrodynamical scientific readings. Digest of articles by the materials of VIII all-Russian conference dedicated for the memory of professors G. Z. Gershuny, E. M. Juhovitskii and D. V. Lyubimov. Perm: Perm state national research university; 2022. P. 254261 (in Russian).
  29.  Sennitskii VL. On peculiarities of a liquid flow in a gravity field // Siberian Electronic Mathematical Reports. 2022;19(1):241247 (in Russian). DOI: 10.33048/semi.2022.19.018.
  30.  Sennitskii VL. Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences. Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(2):197208 (in Russian). DOI: 10.18500/0869-6632-003091.
  31.  Sennitskii VL. Motion of a sphere in fluid caused by vibrations of another sphere. J. Appl. Mech. Tech. Phys. 1986;27:501505. DOI: 10.1007/BF00910190.
  32.  Lugovtsov BA, Sennitskii VL. Motion of a body in a vibrating liquid. Sov. Phys. Doklady. 1986;289(2):314317 (in Russian).
  33.  Lyubimov DV, Lyubimova TP, Cherepanov AA. On the motion of a solid body in a vibrating fluid. In: Convective Flows. Perm: Perm. Ped. Institute Publishing; 1987. P. 6171 (in Russian).
  34.  Chelomei VN. Selected Works. M.: Mashinostroenie; 1989. 336 p. (in Russian).
  35.  Sennitskii VL. On the motion of a gas bubble in a viscous vibrating liquid. In: Gagarins Scientific Readings on Cosmonautics and Aviation 1988. M.: Nauka; 1989. P. 267 (in Russian).
  36.  Sennitskii VL. Predominantly unidirectional motion of a compressible solid body in a vibrating liquid. J. Appl. Mech. Tech. Phys. 1993;34:9697. DOI: 10.1007/BF00851812.
  37.  Lyubimov DV. Thermovibrational flows in nonuniform systems. Microgravity Quarterly. 1994;4(1): 221225.
  38.  Kozlov VG. Solid body dynamics in cavity with liquid under high-frequency rotational vibration. Europhysics Letters. 1996;36(9):651656. DOI: 10.1209/epl/i1996-00282-0.
  39.  Sennitskii VL. Behavior of a gas bubble in a viscous oscillating liquid in the presence of gravity. J. Appl. Mech. Tech. Phys. 1997;38:718723. DOI: 10.1007/BF02467883.
  40.  Lyubimov DV, Lyubimova TP, Meradji S, Roux B. Vibrational control of crystal growth from liquid phase. J. Crystal Growth. 1997;180(34):648659. DOI: 10.1016/S0022-0248(97)00294-7.
  41.  Luybimov DV, Perminov AV, Cherepanov AA. Generation of averaged flows in a vibrational field close to the interface of mediums. In: Vibration Effects in Hydrodynamics. Perm: Perm University Publishing; 1998. P. 204221 (in Russian).
  42.  Sennitskii VL. Motion of a sphere in a vibrating liquid in the presence of a wall. J. Appl. Mech. Tech. Phys. 1999;40:662668. DOI: 10.1007/BF02468441.
  43.  Lavrenteva OM. On the motion of particles in non-uniformly vibrating liquid. Europ. J. Appl. Math. 1999;10(3):251263. DOI: 10.1017/S0956792599003745.
  44.  Sennitskii VL. The motion of a pulsating rigid body in an oscillating viscous liquid. J. Appl. Mech. Tech. Phys. 2001;42(1):7276. DOI: 10.1023/A:1018808628235.
  45.  Pyatigorskaya OS, Sennitskii VL. Motion of a sphere in a liquid caused by vibrations of another sphere. J. Appl. Mech. Tech. Phys. 2004;45:542545. DOI:10.1023/B:JAMT.0000030331.35411.2e.
  46.  Lyubimov D, Lyubimova T, Vorobev A, Moitabi A, Zappoli B. Thermal vibrational convection in near-critical fluids. Part I: Non-uniform heating. Journal of Fluid Mechanics. 2006;564:159183. DOI: ff10.1017/S0022112006001418.
  47.  Hassan S, Lyubimova TP, Lyubimov DV, Kawaji M. Motion of a sphere suspended in a vibrating liquid-filled container. J. Appl. Mech. 2006;73(1):7278. DOI: 10.1115/1.1992516.
  48.  Lyubimov DV, Lyubimova TP, Shklyaev SV. Behavior of a drop on an oscillating solid plate. Physics of Fluids. 2006;18:012101. DOI: 10.1063/1.2137358.
  49.  Shevtsova V, Melnikov D, Legros JC, Yan Y, Saghir Z, Lyubimova T, Sedelnikov G, Roux B. Influence of vibrations on thermodiffusion in binary mixture: A benchmark of numerical solutions. Physics of Fluids. 2007;19:017111. DOI: 10.1063/1.2409622.
  50.  Ivanova , Kozlov VG, Kuzaev F. Vibrational hydrodynamic interaction between a sphere and the boundaries of a cavity. Fluid Dyn. 2008;43:194202. DOI: 10.1134/S001546280802004X.
  51.  Lyubimov DV, Baydin AY, Lyubimova TP. Particle dynamics in a fluid under high frequency vibrations of linear polarization // Microgravity Science Technology. 2013. Vol. 25. P. 121126. DOI: 10.1007/s12217-012-9336-3.
  52.  Sennitskii VL. On the levitation of a liquid. International Journal of Applied and Fundamental Research. 2021;(6):8790 (in Russian). DOI: 10.17513/mjpfi.13236.
  53.  Sennitskii VL. Effects of a paradoxical motion of a viscous liquid in a gravity field. In: Aerocosmic Technique, High Technologies and Innovations - 2021. Materials of All-Russian ScientificTechnical Conference, 1820 November, 2021, Perm, Russia. Perm: PNIPU; 2021. Vol. 1. P. 138142 (in Russian).
  54.  Sennitskii VL. The motion of an inclusion in a vibrating liquid. In: Aero-cosmic Technique, High Technologies and Innovations - 2022. Materials of All-Russian Scientific-Technical Conference, 1618 November, 2022, Perm, Russia. Perm: PNIPU; 2022. P. 207209 (in Russian).
  55.  Sennitskii VL. Forced rotatory oscillations of a hydro-mechanical system. In: The Collection of Articles of International Scientific-Technical Conference Minsk Scientific Readings - 2022 (Minsk, 0709 December 2022). Minsk: BGTU; 2022. Vol. 3. P. 181186 (in Russian).
  56.  Sennitskii VL. On the diagnostics of a hydro-mechanical system. In: Aero-Cosmic Technique, High Technologies and Innovations-2023. Materials of All-Russia Scientific-Technical Conference (Perm, 1517 November, 2023). Perm: PNIPU; 2023. P. 205207 (in Russian).
  57.  Sennitskii VL. On the motion of an inclusion in a liquid medium. In: Hydro-Processes in Catalysis. V Scientific-Technology Symposium, 36 October 2024, Sochi, Russia. Novosibirsk: Institute of Catalysis SB RAS; 2024. P. 180182 (in Russian).
  58.  Kapitsa PL. Pendulum with a vibrating suspension. Sov. Phys. Usp. 1951;44(1):720 (in Russian). DOI: 10.3367/UFNr.0044.195105b.0007.
  59.  Krilov NM, Bogolyubov NN. Introduction in Non-Linear Mechanics. Moscow-Ijevsk: NITs RKhD; 2004. 352 p. (in Russian).
  60.  Bogolyubov NN, Mitropolskii YuA. Asimptotic Methods in the Theory of Non-Linear Oscillations. M.: GIF-ML; 1958. 408 p. (in Russian).
  61.  Sennitskii VL. Force interaction of a sphere and a viscous liquid in the presence of a wall. J. Appl. Mech. Tech. Phys. 2000;41:5054. DOI: 10.1007/BF02465236.
Received: 
27.09.2024
Accepted: 
30.01.2025
Available online: 
03.02.2025
Published: 
31.07.2025
  • 1039 reads