Effect of ambient gas flow on the instability of Marangoni convection in liquid bridges of various volume ratios

Instability of Marangoni convection in liquid bridges (LBs) of high Prandtl number (Pr) fluids has been studied by focusing on the effect of ambient gas flow on the LBs of various volume ratios. The working fluids are 2 cSt (Pr = 28) and 5 cSt (Pr = 67) silicone oils. The LB is suspended in a gap between the upper heating rod and the lower cooling rod and it is surrounded by a coaxial cylindrical wall to form an annular passage between the LB and the inner wall surface. The ambient gas motion is given to this annular passage in the range from −35 mm/s (vertically downward) to +35 mm/s (vertically upward). The ratio of the LB volume to the gap volume is varied from 0.80 (slender LB) to 1.10 (slightly fat LB). The critical temperature differences for the onset of instability are measured and corresponding critical Marangoni numbers are determined. Numerical computations are carried out to understand the flow and temperature fields both in the LB and in the ambient gas at each measured critical temperature difference. The computation results are used to evaluate the convective and the radiative heat transfers from the LB. The effect of the ambient gas motion on the relationship between the critical Marangoni number and the volume ratio is revealed. The effect is discussed in terms of the Biot number defined using the heat transfer and the critical temperature difference. It is shown that the Biot number increases with the ambient gas velocity for slender LBs while it is nearly constant for slightly fat LBs. It is found that the critical Marangoni numbers plotted as a function of the Biot number for various volume ratios and ambient gas velocities fall on a single profile corresponding to each Pr. Such a behavior is shown to be in accord with the previous data taken under various ambient gas temperatures and cooling rod temperatures.