By Isaac Newton
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Extra info for Mathematic Principals Of Natural Philosophy
M. Lifshitz. "Hydrodynamics," Nauka, Moscow (1986). I. Universite Paris-Sud BP 133 91403 Orsay Cedex, France ABSTRACT Convective instabilities generated in liquid cells, under earth's gravity, for a destabilizing thermal gradient, can be removed by centrifugation. Experiments on molten tin show a reversible transition from an unstable to a stable regime, at a well defined value of the rotation rate. These observations can be understood by considering that the axial buoyancy force depends on both the density gradient and the acceleration generated along the axis of a fluid cell installed on a centrifuge.
6). 1 g. --.. 3 .......... 2 ao u 0; ~ -2 ~ -3 os -4 L-~ o __L-J-~~~~~~~UL~~WU~~~ 50 150 200 100 Ti me (minutes) 250 300 Figure 5. Radial temperature gradient measured inside destabilizing tin melt, height 80 mm and diameter 27 mm. Change of rotation speed occurs at vertical dashed lines, with the values between representing the resultant acceleration in g. a o - 1 ....... u ..... , ~ . ;:; -4 -< o o -5 CI o L -____~_ _L-~__~JL~~~_ _~_L~_ _~ o 50 100 150 200 Time (mi nutes) 250 300 Figure 6. Axial temperature gradient measured inside destabilizing tin melt, height 70 mm and diameter 17 mm.
A. Arnold, NASA GSRP (1992). 12. R. Bird. W. Stewart and E. Lightfoot. , New York: 45 and 98 (1960). 34 CONVECTIVE FLOWS DURING CRYSTAL GROWTH IN A CENTRIFUGE Vadim A. F. Ioffe Institute of Physics and Technology 194201 St. Petersburg, Russia ABSTRACT Convective phenomena in the melt strongly influence crystal growth in a centrifuge. Large scale convective flows are induced, because hydrostatic equilibrium cannot be established in the melt, if the temperature gradient is not parallel to the "total" (gravitational plus centrifugal) acceleration.
Mathematic Principals Of Natural Philosophy by Isaac Newton