THE ROLE OF DYNAMIC SURFACE DEFORMATION IN OSCILLATORY MARANGONI CONVECTION IN LIQUID BRIDGE OF HIGH PRANDTL NUMBER FLUID

K. Nishino¹ and S. Yoda²

¹Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan
²National Space Development Agency of Japan, 2-1-1 Sengen, Tsukuba City, 305-8505, Japan

The onset of oscillation of surface tension driven convection (Marangoni convection) in liquid bridges simulating half floating zone models has been a target of extensive studies in thermal and fluid science from view points not only of the material processing in microgravity but of the fundamental instability mechanism in this unique convection. The uniqueness lies in the facts that (1) the convection is driven by the surface tension gradient along the liquid-gas interface, (2) there is a strong coupling between fluid motion and fluid temperature, and (3) the liquid surface may be deformed statically and dynamically. The last feature, particularly the dynamic surface deformation (DSD), has not been studied well so far while the surface deformation is known to impose a significant influence on the Benard-Marangoni instability of horizontal liquid layers. The present study aims at clarifying, in normal gravity experiments, the role of DSD in oscillatory Marangoni convection in a liquid bridge of high Pr fluid.

In the present study, a liquid bridge of silicone oil, n =5 cSt and Pr =69, is suspended between two coaxial disks, both 5 mm in diameter and 2.5 mm apart. The ratio of the liquid volume to the volume of the gap between the disks is varied from 0.6 to 1.1. Temperature difference between the disks is imposed to generate Marangoni convection, which becomes oscillatory when the temperature difference exceeds a critical value. The temperature distribution on the liquid surface is measured with an IR camera having a temporal resolution of 30 fps. Simultaneously, the DSD is measured with the microscopic imaging displacement meter (MIDM) developed in this project. The two signals are analyzed in detail to find out physical relations between DSD and surface temperature oscillation (STO).

The main findings gained in this study are that (1) in the supercritical condition, the surface of the liquid bridge oscillates at the same frequency of STO, (2) the amplitude of DSD is the order of 1 mm, varying with axial position of measurement (Fig.1), (3) the DSD is observed to grow from the region near the hot disk (Fig. 2), (4) there is definite phase relationships between DSD and STO (Fig.3), and (5) their phase difference is dependent on the volume ratio and axial position of measurement but is approximately out of phase near the hot disk for all the volume ratios studied (Fig.4). These findings strongly suggest important roles of DSD near the hot disk although further efforts are still needed to draw a complete picture that can explain the role of DSD in the onset of oscillation.

Figure. 1 Amplitude of DSD plotted vs. axial position for n =10 cSt, Ar =0.6, V/V₀ =0.62, DT =48.2-48.6^oC and DT_c =43.6^oC.


Figure. 2 Time delay in the onset of DSD, DT, as function of axial distance from the reference position, Dz: (a) V/V₀ =1.00 and (b) V/V₀ =0.62.

(a) V/V₀ =0.62
(b) V/V₀ =0.80
(c) V/V₀ =1.00
(d) V/V₀ =1.10
Figure. 3 Signals of DSD and STO obtained simultaneously at z =1250 mm for various volume ratios: (a) V/V₀ =0.62 and DT=30.7 ^oC, (b) V/V₀ =0.80 and DT=47.1 ^oC, (c) V/V₀ =1.00 and DT=37.9 ^oC, and (d) V/V₀ =1.10 and DT=34.5 ^oC.


Figure. 4 Phase differences between DSD and STO for various volume ratios plotted as function of z-position.