Thermocapillary Liquid Bridges and Marangoni Convection under Microgravity—Results and Lessons Learned
Tóm tắt
We describe the first measurements of the critical Marangoni number of thermocapillary flow in liquid bridges under microgravity. The experiments were conducted during the ballistic flight of rockets with small liquid bridges established by melting the equivalent cylindrical rod of solid sodium nitrate under microgravity. Fine thermocouples in the melt indicated the onset of flow oscillations by the increase of temperature oscillations. The critical Marangoni number M
a
c
was measured to be approximately 1·104 for Prandtl number P
r = 9. This type of experiment was especially simple, effective and suitable for execution during the short microgravity–time available during sounding rockets flights. The lessons learned from these experiments have been collected. In a second part of this paper we review five more sophisticated microgravity experiments in sounding rockets in which the surface tension driven flow was visualized by tracers and suitable illumination. Two experiments are devoted to the very first demonstration of the classical cellular Bénard-Marangoni instability of thin liquid layers with free surface, heated from below. We could demonstrate in another experiment chaotic thermocapillary flow in a cubic cuvette filled with oil up to a flat free surface. Two experiments dealt with liquid bridges (LBs); in one the LB was nearly as long as possible at all. Here we could observe the helical nature of the hydrothermal wave in the geometry of the LB and measured a much smaller critical Marangoni number than in the short liquid bridges on ground. In the other experiment we investigated particle accumulation structures (PAS) and could show that PAS develops independently from gravity forces though it was indicated that gravity has an influence on PAS–formation by changing the flow field.
Tài liệu tham khảo
Bénard, H.: Les tourbillons cellulaires dans une nappe liquide. Rev. Gén. Sci. Pure Appl. 11, 1261–1271 (1900)
Chang, Ch.E., Wilcox, W.R.: Inhomogeneities due to thermocapillary flow in float zone melting. J. Crystal Growth 28, 8–12 (1975)
Chun, Ch.-H.: Berechnung des Ein usses elektromagnetischer Krfte auf Strmungsvorgnge in Schmelzen. Vortrag Nr. 10, Statusseminar Spacelab-Nutzung Werkstoff-Forschung und Verfahrenstechnik 06.-08. 1976, Bad Kissingen, ISBN 3-88135-038-1 (1976)
Croell, A., Müller-Seibert, K., Benz, K.W., Nitsche, R.: Natural and thermocapillary convection in partially confined silicon melt zones. Microgravity Sci. Technol. 3, 204–215 (1991)
Eyer, A., Leiste, H., Nitsche, R.: Floating zone growth of silicon and microgravity in a sounding rocket. J. Crystal Growth 71, 173–182 (1985)
Frank, S., Schwabe, D.: Temporal and spatial elements of thermocapillary convection in floating zones. Exp. Fluids 23, 234–251 (1997)
Grodzka, P.G., Bannister, T.C.: Heat flow and convection demonstration Experiments Aboard Apollo 14. Science 176, 506–508 (1972)
Grodzka, P.G., Bannister, T.C.: Heat flow and convection demonstration Experiments Aboard Apollo 17. Science 187, 165–167 (1975)
Hofmann, E., Kuhlmann, H.C.: Particle accumulation on periodic orbits by repeated free surface collisions. Phys. Fluids 23, 072106 (2011)
Koschmieder, E.L.: Private communication (1990)
Lubimov, D.V., Lubimova, T.P., Straube, A.V.: Understanding the role inertia of the particls in PAS-formation. Microgravity Sci. Technol. 14, 210 (2005)
Melnikov, D.E., Pushkin, D., Shevtsova, V.: Synchronization of finite-size particles by a traveling wave in a cylindrical flow. Phys. Fluids 25, 092108 (2013)
Metzger, J., Schwabe, D., Cramer, A., Scharmann, A.: Marangoni convection in a rectangular open cavity in microgravity. ESA SP 1132 4, 60–70 (1994)
Pearson, J.R.: On convection cells induced by surface tension. J. Fluid Mech 4, 489–500 (1958)
Preisser, F., Schwabe, D., Scharmann, A.: Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface. J. Fluid Mech. 126, 545–567 (1983)
Pushkin, D., Melnikov, D.E., Shevtsova, V.M.: Ordering of small particles in one-dimensional coherent structures by time-periodic flows. Phys. Rev. Lett. 23, 234501 (2011)
Rosenblat, S., Homsy, G.M., Davis, S.H.: Non-linear Marangoni convection in bounded layers. Part 1. Circular cylindrical containers. J. Fluid Mech. 120, 91–122 (1982)
Schwabe, D.: The Bénard-Marangoni-Instability in small circular containers under microgravity: experimental results. Adv. Space Res. 24, 1347–1356 (1999)
Schwabe, D.: Unpublished experiments (2000)
Schwabe, D.: Hydrothermal waves in a liquid bridge with aspect ratio near the Rayleigh-limit under microgravity. Phys. Fluids 17, 112104–1 to -8 (2005)
Schwabe, D.: Marangoni convection in small circular containers under microgravity. Exp. Fluids 40, 942–950 (2006)
Schwabe, D., Scharmann, A.: Some evidence for the existence and magnitude of a critical Marangoni number for the onset of oscillatory flow in crystal growth melts. J. Crystal Growth 46, 125–131 (1979)
Schwabe, D., Scharmann, A.: Messung der kritischen Marangonizahl für den übergang von stationärer zu oszillatorischer thermokapillarer konvektion unter Mikrogravitation: Ergebnisse der Experimente in den ballistischen Raketen TEXUS 5 und TEXUS 8. Z. Flugwiss. Weltraumtechnik 9, 21–28 (1985)
Schwabe, D., Frank, S.: Experiments on the transition to chaotic thermocapillary flow in floating zones under microgravity. Adv. Space Res. 24, 1391–1396 (1999)
Schwabe, D., Scharmann, A., Preisser, F., Oeder, R.: Experiments on surface tension driven flow in floating zone melting. J. Crystal Growth 43, 305–312 (1978)
Schwabe, D., Preisser, F., Scharmann, A.: Instabile Marangonikonvektion unter Mikrogravitation. Z. Flugwiss Weltraumtechnik 9, 309–315 (1982a)
Schwabe, D., Scharmann, A., Preisser, F.: Studies of Marangoni convection in floating zones. Acta Astronautica 9, 183–186 (1982b)
Schwabe, D., Velten, R., Scharmann, A.: The instability of surface tension driven flows in models for floating zones under normal and reduced gravity. J. Crystal Growth 99, 1258–1264 (1990)
Schwabe, D., Hintz, P., Frank, S.: New features of thermocapillary convection in floating zones revealed by particle accumulation structures (PAS). Microgravity Sci. Technol. 9, 163–168 (1996)
Schwabe, D., Tanaka, S., Mizev, A., Kawamura, H.: Particle accumulation structures in time-dependent thermocapillary flow in a liquid bridge under Microgravity. Microgravity Sci. Technol. 18, 117–127 (2006)
Schwabe, D., Mizev, A.I., Udhayasankar, M., Tanaka, S.: Formation of dynamic particle accumulation structures in oscillatory thermocapillary flow in liquid bridges. Phys. Fluids 19, 072102 (2007)
Velten, R., Schwabe, D., Scharmann, A.: The periodic instability of thermocapillary flow in cylindrical liquid bridges. Phys. Fluids A3, 267–279 (1991)
Xu, J.J., Davis, S.H.: Convective thermocapillary instabilities in liquid bridges. Phys. Fluids 27, 1102–1107 (1984)
Yano, T., Ueno, I., Kawamura, H., Nishino, K., Matsumoto, S., Onishi, M., Sakurai, M.: Space experiment on the instability of Marangoni convection in large liquid bridge-MEIS-4: effect of Prandtl number. J. Phys. Conf. Ser. 327, 012029 (2011)
Yano, T., Ueno, I., Kawamura, H., Nishino, K., Matsumoto, S., Onishi, M., Sakurai, M.: Space experiments on the instability of Marangoni convection in liquid bridge-MEIS-3: effect of volume ratio and observation of PAS. Space Utilization Research 28, 1–2 (2012). (Proc. 28th Symp. Space Utilization Research (Jan. 23rd – 24th, 2012, Tokyo))