No Access Submitted: 23 March 1990 Accepted: 11 September 1990 Published Online: 04 June 1998
Physics of Fluids A: Fluid Dynamics 3, 267 (1991); https://doi.org/10.1063/1.858135
more...View Affiliations
  • I. Physikalisches Institut der Justus‐Liebig‐Universität, Heinrich‐Buff‐Ring 16, D‐6300 Giessen, Germany
Thermocapillary convection (TC) in cylindrical liquid bridges (floating zones) of liquids with Prandtl numbers Pr=1, 7, and 49 is investigated experimentally. The zones have been heated from above or from below to study the influence of buoyant forces. Fourier analyses of temperature signals from zones covering systematically wide ranges of aspect ratios A and Marangoni numbers Ma have shown the existence of various forms of periodic and nonperiodic TC. This paper reports on periodic TC existing under certain conditions between the onset of time‐dependent TC at the critical Marangoni number Mac and 7×Mac. From the measurements of the onset of periodic TC the dependence is reported for the threshold Mac and the period near the threshold τc on the aspect ratio. The development of periodic TC when further increasing Ma is shown by typical examples from measurements of the frequency and the amplitude of the oscillations. By correlation analyses from three temperature signals, different structures of periodic TC in the investigated A–Ma–Pr range were identified. Both the running waves with an azimuthal component (m≥1) and the axially running waves (m=0) were found and the findings of these and various other spatiotemporal structures of periodic TC were displayed in A–Ma/Mac state maps. These maps indicate as well the influence of the Prandtl number and of the buoyant forces on the preferred spatial structure of periodic TC, as discussed in the light of an already existing theory.
  1. 1. D. Schwabe, A. Seharmann, F. Preisser, and R. Oeder, J. Cryst. Growth 43, 305 (1978). Google ScholarCrossref
  2. 2. D. Schwabe and A. Scharmann, J. Cryst. Growth 46, 125 (1979). Google ScholarCrossref
  3. 3. C.-H. Chun and W. Wuest, Acta Astronaut. 5, 1073 (1979). Google ScholarCrossref
  4. 4. F. Preisser, D. Schwabe, and A. Scharmann, J. Fluid Mech. 126, 545 (1983). Google ScholarCrossref
  5. 5. Y. Kamotani, S. Ostrach, and M. Vargas, J. Cryst. Growth 66, 83 (1984). Google ScholarCrossref
  6. 6. D. Schwabe, F. Preisser, and A. Scharmann, Acta Astronaut. 9, 265 (1982). Google ScholarCrossref
  7. 7. C.-H. Chun, European Space Agency Report No. ESA SP-222,271, 1984. Google Scholar
  8. 8. M. K. Smith and S. H. Davis, J. Fluid Mech. 132, 119 (1983). Google ScholarCrossref
  9. 9. J.-J. Xu and S. H. Davis, Phys. Fluids 27, 1102 (1984). Google ScholarScitation
  10. 10. M. K. Smith, Phys. Fluids 29, 3182 (1986). Google ScholarScitation
  11. 11. S. H. Davis, Annu. Rev. Fluid Mech. 19, 403 (1987). Google ScholarCrossref
  12. 12. F. Preisser, thesis, Justus-Liebig-Universität Giessen, 1980. Google Scholar
  13. 13. C.-H. Chun, J. Cryst. Growth 48, 600 (1980). Google ScholarCrossref
  14. 14. D. Schwabe and A. Scharmann, European Space Agency Report No. ESA SP-222, 281, 1984. Google Scholar
  15. 15. R. Rupp, G. Müller, and G. Neumann, J. Cryst. Growth 97, 34 (1989). Google ScholarCrossref
  16. 16. T. J. McNeil, R. Cole and R. S. Subramanian, J. Colloid Interface Sci. 98, 210 (1984). Google ScholarCrossref
  17. 17. D. Schwabe and A. Scharmann, Z. Flugwiss. Weltraumforsch. 9, 21 (1985). Google Scholar
  18. 18. D. Schwabe and A. Scharmann, European Space Agency Report No. ESA SP-191, 213, 1983. Google Scholar
  19. 19. R. Monti, L. G. Napolitano, and G. Russo, European Space Agency Report No. ESA SP-191, 219, 1983. Google Scholar
  20. 20. A. Croll, W. Muller-Sebert, and R. Nitsche, BMFT-DFVLR Statusse-minar “Forschung unter Schwerelosigkeit,”edited by K. Kreutberg and P. Preu (DGLR, Bonn, 1988), p. 151ff. Google Scholar
  21. 21. H. Kölker, European Space Agency Report No. ESA SP-222, 169, 1984. Google Scholar
  22. 22. R. Velten, D. Schwabe, and A. Scharmann (in preparation). Google Scholar
  23. 23. C.-H. Chun, Acta Astronaut. 7, 479 (1980). Google ScholarCrossref
  24. 24. S. H. Davis (private communication). Google Scholar
  1. © 1991 American Institute of Physics.