Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface

In liquid columns (Prandtl number 8·9) with free cylindrical surface heated from above, strong thermocapillary convection (TC) has been observed. Stationary thermocapillary convection exists in the form of a single axially symmetric roll bound to the free surface. For aspect ratios l/a The influence of buoyant forces due to horizontal temperature gradients in the experiments was also studied. Buoyant forces become obvious for a contaminated free surface and in bulk regions far from the cylinder surface. The thermocapillary convection shows a transition to time-dependent oscillatory motion when a critical Marangoni number Ma c is exceeded. A unique Ma c = 7 × 10 3 has been found for zones with lengths l Ma c ) of the distortion has been found. The non-dimensional frequency of the temperature oscillations is independent of zone size if the aspect ratio is held constant. However, the non-dimensional frequency of temperature oscillations increases linearly with the aspect ratio of the zone. This result is interpreted as a dependence of the phase velocity of the running disturbance on the aspect ratio.

[1]  W. Wilcox,et al.  Thermocapillary convection in floating zone melting: Influence of zone geometry and prandtl number at zero gravity , 1979 .

[2]  C. Chun,et al.  A micro-gravity simulation of the Marangoni convection , 1978 .

[3]  M. Block,et al.  Surface Tension as the Cause of Bénard Cells and Surface Deformation in a Liquid Film , 1956, Nature.

[4]  R. M. Clever,et al.  Transition to time-dependent convection , 1974, Journal of Fluid Mechanics.

[5]  L. Scriven,et al.  On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity , 1964, Journal of Fluid Mechanics.

[6]  D. Schwabe,et al.  Some evidence for the existence and magnitude of a critical marangoni number for the onset of oscillatory flow in crystal growth melts , 1979 .

[7]  T. Bannister,et al.  Heat Flow and Convection Experiments aboard Apollo 17 , 1975, Science.

[8]  Donald A. Nield,et al.  Surface tension and buoyancy effects in cellular convection , 1964, Journal of Fluid Mechanics.

[9]  D. Schwabe,et al.  Verification of the oscillatory state of thermocapillary convection in a floating zone under low gravity , 1982 .

[10]  W. Wuest,et al.  Experiments on the transition from the steady to the oscillatory Marangoni-convection of a floating zone under reduced gravity effect , 1978 .

[11]  William R. Wilcox,et al.  Analysis of surface tension driven flow in floating zone melting , 1976 .

[12]  A. Scharmann,et al.  Experiments on surface tension driven flow in floating zone melting , 1978 .

[13]  W. Heywang,et al.  Zur Stabilität senkrechter Schmelzzonen , 1954 .

[14]  W. E. Langlois.  Conservative differencing procedures for rotationally symmetric flow with swirl , 1981 .

[15]  F. Busse.  The oscillatory instability of convection rolls in a low Prandtl number fluid , 1972, Journal of Fluid Mechanics.

[16]  J. Deardorff,et al.  The oscillatory motions of Rayleigh convection , 1970, Journal of Fluid Mechanics.

[17]  D. Schwabe,et al.  Marangoni convection in open boat and crucible , 1981 .

[18]  R. Birikh.  Thermocapillary convection in a horizontal layer of liquid , 1966 .

[19]  K. A. Smith.  On convective instability induced by surface-tension gradients , 1966, Journal of Fluid Mechanics.

[20]  W. E. Langlois.  Digital simulation of Czochralski bulk flow in microgravity , 1980 .

[21]  W. Wilcox,et al.  Influence of gravity on thermocapillary convection in floating zone melting of silicon , 1980 .

[22]  D. Schwabe,et al.  Studies of marangoni convection in floating zones , 1982 .

[23]  J. Pearson,et al.  On convection cells induced by surface tension , 1958, Journal of Fluid Mechanics.

[24]  D. Schwabe,et al.  Thermocapillary convection in crystal growth melts , 1980 .