MATHEMATICAL MODEL OF ROTATIONAL OSCILLATIONS OF A POROUS SPHERICAL SHELL WITH A GAS CAVITY IN VISCOUS FLUID

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

A mathematical model of viscous fluid flow induced by the rotational-oscillatory motion of a submerged porous spherical shell with a spherical gas cavity is considered. In the Stokes approximation, analytical solutions are obtained for the time-dependent Brinkman equation that describes viscous fluid flow in the porous medium and the Navier–Stokes equation that describes viscous fluid flow outside the porous medium. An analysis of the obtained mathematical model is given. The case of uniform rotation about a fixed axis of the porous spherical shell with a spherical gas cavity inside it in a viscous fluid is considered.

About the authors

O. A Bazarkina

Evsev’ev Mordovian State Pedagogical University

Email: o.a.bazarkina@mail.ru
Saransk, Russia

N. G Taktarov

Evsev’ev Mordovian State Pedagogical University

Email: n.g.taktarov@mail.ru
Saransk, Russia

References

  1. Landau L.D., Lifshitz E.M. Theoretical Physics. V. 6. Fluid Mechanics. New York: Pergamon Pres, 2013.
  2. Batchelor G.K. An Introduction to Fluid Dynamics. Cambridge at the University Press. 1970.
  3. Grosan T., Postelnicu A., Pop I. Brinkman flow of a viscous fluid through a spherical porous medium embedded in another porous medium // Transport in Porous Media. 2010. V. 81. P. 89–103.
  4. Rajvanshi S.C., Wasu S. Slow extensional flow past a non-homogeneous porous spherical shell // Int. J. of Applied Mechanics and Engineering. 2013. V. 18. No. 2. P. 491–502.
  5. Jones I.P. Low Reynolds number flow past a porous spherical shell // Math. Proc. Camb. Phis. Soc. 1973. V. 73. No. 1. P. 231–238.
  6. Deo S., Yadav P.K., Tiwari A. Slow viscous flow through a membrane built up from porous cylindrical particles with an impermeable core // Appl. Math. Modelling. 2010. V. 34. No. 5. P. 1329–1343.
  7. Bazarkina O.A., Taktarov N.G. Rotational oscillations of a porous spherical shell in viscous fluid // Fluid Dynamics. 2020. V. 55. № 6. P. 817–824.
  8. Bazarkina O.A., Taktarov N.G. Translational oscillatory motions of a porous spherical shell with a solid impermeable core in a viscous fluid // Theoretical Foundations of Chemical Engineering. 2021. V. 55. No. 5. P. 962–970.
  9. Базаркина О.А., Тактаров Н.Г. Вращательные колебания пористой сферической оболочки с непроницаемым ядром в вязкой жидкости // Изв. высших учебных заведений. Поволжский регион. Физикоматематические науки. 2020. № 1 (53). С. 73–87.
  10. Brinkman H.C. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles // Appl. Sci. Res. 1947. V. A1. No. 1. P. 27–34.
  11. Ochoa-Tapia J.A., Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid. – I. Theoretical development // Int. J. Heat and Mass Transfer. 1995. V. 38. No. 14. P. 2635–2646.
  12. Taktarov N.G. Viscous fluid flow induced by rotationaloscillatory motion of a porous sphere // Fluid Dynamics. 2016. V. 51. No. 5. Р. 703–708.
  13. Тактаров Н.Г. Течения вязкой жидкости при колебательных движениях погруженного пористого шара // Сб. тр. в 4 Т. XII Всероссийского съезда по фундаментальным проблемам теоретической и прикладной механики. Т. 2. Механика жидкости и газа. РИЦ БашГУ. Уфа. 2019. С. 889–891.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2025 Russian Academy of Sciences