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Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

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Summary

The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (Ω>2Ω 0) and hyperbolic frequency range (Ω>2Ω 0). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequencyΩ/2Ω 0. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.

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Abbreviations

a :

radius of liquid bridge

h :

length of liquid bridge

I 0,I 1 :

modified Besselfunctions

J 0,J 1 :

Besselfunctions

p :

liquid pressure

r, ϕ,z :

cylindrical polar coordinates

t :

time

u, v, w :

velocity distribution in rotating liquid

\(We \equiv \frac{{\varrho a^3 \Omega _0 ^2 }}{\sigma }\) :

Weber number

z0 :

axial excitation amplitude

\(\alpha ^2 = 1 - \frac{{4\Omega _0 ^2 }}{{\Omega ^2 }} > 0\) :

elliptic case (Ω>2Ω 0)

\(\beta ^2 = \frac{{4\Omega _0 ^2 }}{{\Omega ^2 }} - 1 > 0\) :

hyperbolic case (Ω>2Ω 0)

ϱ:

liquid density

σ:

surface tension

ζ:

liquid surface displacement

Φ:

acceleration potential

Ω 0 :

rotational speed

Ω:

axial forcing frequency

ω:

natural frequency of rotating system

ω0n :

natural frequency of harmonic axial response

References

  1. Scriven, L. E., Sternling, L. V.: Marangoni effects. Nature187, 186–188 (1960).

    Google Scholar 

  2. Chun, C. H., Wuest, W.: Suppression of temperature oscillations of thermal Marangoni convection in a floating zone by superimposing of rotating flows. Acta Astron.9, 225–230 (1982).

    Google Scholar 

  3. Bauer, H. F.: Marangoni convection in rotating liquid systems. Microgravity Sci. Technol. II/3, 142–157 (1989).

    Google Scholar 

  4. Bauer, H. F.: Minimization of Marangoni convection. CSME Mechan. Engin. Forum 1990, pp. 65–70. Univ. of Toronto, June 3–9, 1990.

  5. Tomotika, S.: On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. Roy. Soc. A150, 322–337 (1935).

    Google Scholar 

  6. Hocking, L. M., Michael, D. H.: The stability of a column of rotating liquid. Mathematika6, 25–32 (1959).

    Google Scholar 

  7. Hocking, L. M.: The stability of a rotating column of liquid. Mathematika7, 1–9 (1960).

    Google Scholar 

  8. Gillis, J.: Stability of a column of rotating viscous liquid. Proc. Cambridge Phil. Soc.57, 152–159 (1961).

    Google Scholar 

  9. Gillis, J., Shuh, K. S.: Stability of a rotating liquid column. Phys. Fluids5, 1149–1155 (1962).

    Google Scholar 

  10. Gillis, J., Kaufmann, B.: The stability of a rotating viscous jet. Quart. Appl. Math.19, 301–308 (1962).

    Google Scholar 

  11. Bauer, H. F.: Coupled oscillations of a solidly rotating liquid bridge. Acta Astron.9, 547–563 (1982).

    Google Scholar 

  12. Bauer, H. F.: Response of a spinning liquid column to axial excitation. Acta Mech.77, 153–170 (1989).

    Google Scholar 

  13. Bauer, H. F.: Response of differently axially excited spinning liquid columns. Acta Mech.84, 155–173 (1990).

    Google Scholar 

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Author notes

  1. H. F. Bauer

    Present address: Institut für Raumfahrttechnik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, D-W-8014, Neubiberg, Federal Republic of Germany

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    1. H. F. Bauer
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    Bauer, H.F. Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension. Acta Mechanica 90, 21–35 (1991). https://doi.org/10.1007/BF01177396

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    • DOI: https://doi.org/10.1007/BF01177396

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