Bubble Behavior in Molten Glass in a Temperature Gradient
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Guy E. Rindone, editor
BUBBLE BEHAVIOR IN MOLTEN GLASS IN A TEMPERATURE GRADIENT
M. MEYYAPPAN, R. S. SUBRAMANIAN AND W. R. WILCOX Department of Chemical Engineering, Clarkson College of Technology, York 13676, USA
Potsdam, New
and H. SMITH Westinghouse R & D Center, Pittsburgh, Pennsylvania,
USA
ABSTRACT Gas bubble motion in a temperature gradient was observed in a sodium borate melt in a reduced gravity rocket experiment under the NASA SPAR program. Large bubbles tended to move faster than smaller ones, as predicted by theory. When the bubbles contacted a heated platinum strip, motion virtually ceased because the melt only imperfectly wets platinum. In some cases bubble diameter increased noticeably with time.
INTRODUCTION In the absence of surfactants, a gas bubble in a liquid is predicted in response to a temperature gradient, VT, because of the dependence of tension o on temperature T. If we assume that the bubble is spherical, neglect convective momentum and energy transport, the bubble velocity V absence of gravity is predicted to be
to move surface and in the
VT
a
()
where 'a' is the bubble radius and n is the liquid viscosity [1]. The assumption of negligible convective transport is valid only in the limit of small 2 values of the Marangoni number Ma where VT 1 1 21 oa a
M3Vj -T and a is the thermal diffusivity of the liquid. For small, but non-zero, values of the Marangoni number, a result obtained by the method of matched asymptotic expansions [2] gives V 11
I
oT
VT
1
L2
14,400
Ma2 + O(Ma 4
J
(2)
Theoretical treatments also have been developed in the quasi-static limit for bubble migration normal to.a surface and pairs of bubbles aligned along a temperature gradient [3,4]. In order to observe thermocapillary bubble motion in melted glass without the complicating effects of gravity, a SPAR experiment lasting approximately six minutes was performed on dried sodium borax. As described in detail elsewhere in these proceedings [5], a thin layer of melt was held between a silica cover glass and a tapered platinum heating strip. This produced a temperature gradient inclined to the heating strip, causing bubble motion both along the platinum and toward it. We report here on quantitative measurements made on the 35 mm SPAR flight film, taken at 1 frame per second.
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314 RESULTS The motion of eight bubbles was monitored via frame-by-frame measurements A crack in the cover glass provided a using a Vanguard Motion Analyzer [4]. fiducial mark so that bubble positions could be followed from one frame to the next. Measurements were taken from frames after melt down and stabilization had occurred. In the following, time zero represents the frame on which measurements were first taken (different for each bubble), rather than the first frame of t
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