Skip to main content
SpringerLink
Log in

Thermocapillary Instability of a Cylindrical Layer in the Presence of a Radial Temperature Gradient

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

Within a linear formulation, the thermocapillary instability of equilibrium of a cylindrical layer of heat-conducting viscous fluid in the presence of a radial temperature gradient is investigated with respect to arbitrary disturbances. It is shown that the Rayleigh instability mechanism results in the appearance of monotonous disturbances of a new type. For steady disturbances, the neutral curve is split into two separate segments, each corresponding to its own type of disturbances. For a deformable free boundary, new oscillating disturbances in the form of surface waves develop. It is found that, in the case of axial symmetry, the behavior of these disturbances completely coincides with the oscillating disturbance behavior in a plane layer.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. J. R. A. Pearson, “On convective cells induced by surface tension,” J. Fluid Mech.. 4,Pt. 5, 489 (1958).

    Google Scholar 

  2. L. E. Scriven and C. V. Sternling, “On cellular convection driven by surface-tension gradients,” J. Fluid Mech., 19,Pt.3, 321 (1964).

    Google Scholar 

  3. A. Vidal and A. Acrivos, “Nature of the neutral state in surface-tension driven convection,” Phys. Fluids, 9, No. 3, 615 (1966).

    Google Scholar 

  4. E. A. Ryabitskii, “Thermocapillary instability of the equilibrium of a plane layer in the presence of a vertical temperature gradient,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 19 (1992).

  5. M. Ya. Antimirov and V. R. Liepinya, “Onset of thermocapillary convection in a cylindrical liquid layer in weightlessness,” Izv. AN Latv. SSR, Ser. Fiz. Tekhn. Nauk, No. 3, 90 (1978).

  6. E. A. Ryabitskii, “Onset of thermocapillary convection in a cylindrical layer for various ways of heating,” Prikl. Mekh. Tekh. Fiz., No. 1, 28 (1991).

  7. S. Chandrasekar, Hydrodynamic and Hydromagnetic Stability, Oxford Univ. Press, Oxford (1961).

    Google Scholar 

  8. V. K. Andreev and E. A. Ryabitskii, “Numerical investigation of thermocapillary instability of Marangoni convection in cylindrical layer,” Microgravity Sci. Technol., 7, No. 1, 36 (1994).

    Google Scholar 

Download references

Authors
  1. E. A. Ryabitskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ryabitskii, E.A. Thermocapillary Instability of a Cylindrical Layer in the Presence of a Radial Temperature Gradient. Fluid Dynamics 36, 341–348 (2001). https://doi.org/10.1023/A:1019232614312

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019232614312

Keywords

Search

Navigation