Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Theory of thermal instability of the flow of a viscoelastic fluid

  • 16 Accesses

  • 1 Citations


The problem of the stability of the flow of viscoelastic fluids has fundamental importance for the technology of the production of polymer products and viscosimetry. This problem is not reduced only to classical inertial turbulence. A number of other mechanisms leading to flow instability are known [1, 2]. A thermal mechanism based on the allowance for dissipative heating and elastic properties within the framework of a linear model of a viscoelastic fluid was drawn upon to explain this phenomenon in [1]. The possibility of a self-oscillatory mode of flow was demonstrated on the basis of a qualitative analysis of the theological equation and the equation of heat balance in application to simple shear flow and uniform stretching. A theoretical analysis of the self-heating of flowing systems possessing viscoelastic properties is carried out in the present report. The main laws of the thermal instability of viscoelastic fluids discovered in [1] are described.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    A. M. Stolin and S. I. Khudyaev, “Nonisothermal instability of the flow of viscoelastic media,” Dokl. Akad. Nauk SSSR,207, No. 1 (1972).

  2. 2.

    A. Ya. Malkin and A. I. Leonov, “Unstable polymer flow,” in: Progress in Polymer Rheology [in Russian], Khimiya, Moscow (1970).

  3. 3.

    A. I. Vol'pert and S. I. Khudyaev, Analysis in Classes of Discontinuous Functions and the Equations of Mathematical Physics [in Russian], Nauka, Moscow (1975).

  4. 4.

    A. N. Tikhonov, “Systems of differential equations containing small parameters in the derivatives,” Mat. Sb.,131, No. 3 (1952).

  5. 5.

    A. G. Merzhanov and A. M. Stolin, “On the thermal theory of flow of a viscous fluid,” Dokl. Akad. Nauk SSSR,198, No. 6 (1971).

  6. 6.

    L. M. Buchatskii, A. M. Stolin, and S. I. Khudyaev, “Self-heating of a viscous fluid during cyclic deformation,” Zh. Prikl. Mat. Tekh. Fiz., No. 1 (1979).

  7. 7.

    A. S. Kechek'yan, G. P. Andrianova, and V. A. Kargin, “Periodic oscillations during the stretching of polyethylene terephthalate,” Vysokomol. Soedin.,A12, No. 11 (1970).

  8. 8.

    G. I. Barenblatt, “Self-oscillatory extension of a neck in polymers,” Izv, Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5 (1970).

  9. 9.

    D. T. Griggs and D. W. Baker, “The origin of deep-focus earthquakes,” in: Properties of Matter under Unusual Conditions, New York (1969).

  10. 10.

    A. Ya. Malkin and A. I. Leonov, “On the criteria of instability of modes of shear deformations of viscoelastic polymer systems,” Dokl. Akad. Nauk SSSR,151, No. 2 (1963).

Download references

Author information

Additional information

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 115–122, May–June, 1979.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Buchatskii, L.M., Stolin, A.M. & Khudyaev, S.I. Theory of thermal instability of the flow of a viscoelastic fluid. J Appl Mech Tech Phys 20, 350–355 (1979).

Download citation


  • Linear Model
  • Elastic Property
  • Industrial Mathematic
  • Shear Flow
  • Present Report