Marangoni Convection In Liquid Bridge Research Articles

Influence of Periodic Temperature Fluctuation on flow transition of Marangoni Convection in liquid bridge

Influence of Periodic Temperature Fluctuation on flow transition of Marangoni Convection in liquid bridge

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 −35mm/s (vertically downward) to +35mm/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.

Modeling of the experiments on the Marangoni convection in liquid bridges in weightlessness for a wide range of aspect ratios

Hydrodynamic stability of a two-dimensional steady thermocapillary flow under weightlessness in a high-Prandtl number liquid bridge is studied by means of three-dimensional numerical modeling for a wide range of aspect ratios. We suggest an explanation of the findings of a series of microgravity experiments on Marangoni convection in liquid bridges. Stability of the flow with heat transfer through the interface, modeled by the classical Fourier law, is compared with the stability of the same system under adiabatic conditions. Cooling the interface may significantly shift the threshold of hydrothermal instability as soon as the Biot number deviates from zero. It may also affect the structure of the basic Marangoni flow and the mode of the supercritical flow. We demonstrate that the heat loss has a destabilizing effect for the aspect ratios (ratio of radius to height) below 2.4 (with the exception of a region between 1.6 and 1.8), and for the longer liquid bridges the prevailing effect is stabilizing. The heat transfer coefficient as a function of the length of the liquid zone is theoretically calculated using a model of heat transport for laminar forced convection. Comparison of the results of the modeling with the experimental data shows that an incorrect assessment of the heat transfer may lead to wrong conclusions concerning both the critical parameters of the flow and its structure.

Instability and associated roll structure of Marangoni convection in high Prandtl number liquid bridge with large aspect ratio

This paper reports the experimental results on the instability and associated roll structures (RSs) of Marangoni convection in liquid bridges formed under the microgravity environment on the International Space Station. The geometry of interest is high aspect ratio (AR = height/diameter ≥ 1.0) liquid bridges of high Prandtl number fluids (Pr = 67 and 207) suspended between coaxial disks heated differentially. The unsteady flow field and associated RSs were revealed with the three-dimensional particle tracking velocimetry. It is found that the flow field after the onset of instability exhibits oscillations with azimuthal mode number m = 1 and associated RSs traveling in the axial direction. The RSs travel in the same direction as the surface flow (co-flow direction) for 1.00 ≤ AR ≤ 1.25 while they travel in the opposite direction (counter-flow direction) for AR ≥ 1.50, thus showing the change of traveling directions with AR. This traveling direction for AR ≥ 1.50 is reversed to the co-flow direction when the temperature difference between the disks is increased to the condition far beyond the critical one. This change of traveling directions is accompanied by the increase of the oscillation frequency. The characteristics of the RSs for AR ≥ 1.50, such as the azimuthal mode of oscillation, the dimensionless oscillation frequency, and the traveling direction, are in reasonable agreement with those of the previous sounding rocket experiment for AR = 2.50 and those of the linear stability analysis of an infinite liquid bridge.

Size Dependence on Transition to Oscillatory Marangoni Convection in Liquid Bridge

Size Dependence on Transition to Oscillatory Marangoni Convection in Liquid Bridge

Thermocapillary Convection in a Floating Half Zone

A numerical simulation has been conducted to investigate the effect of the external vibration referred to as g-jitter on the marangoni convection in liquid bridge of high Pr number fluid by taking both the dynamic free surface deformation and ambient air effects into consideration. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the free surface deformation is captured by introducing the mass conserving level set approach. The pressure distributions within the liquid bridge under external vibrations were investigated, and the results show that the pressure in liquid bridge presents periodic oscillation under external vibration. The closer to the hot disk, the greater the relative pressure value is. Moreover, the surface deformation and the surface amplitude under external vibration were investigated as well.

Preparation of JEREMI Experiment: Development of the Ground Based Prototype

This study has been performed in the frame of preparing the space experiment JEREMI (Japanese and European Research Experiment on Marangoni Instabilities). The use of forced coaxial gas flow is proposed as a way to stabilize the Marangoni convection in liquid bridges, which might have important technological applications in the floating zone technique. A new set-up is under development and all sub-systems have passed severe tests. Here we present the design of this set-up and preliminary results of experiments for shear-driven two-phase flows in a confined volume of liquid under conditions of normal gravity. The geometry corresponds to a cylindrical liquid bridge concentrically surrounded by an annular gas channel with external solid walls. Gas enters into the annular duct, flows between solid walls and upon reaching the liquid zone entrains initially quiescent liquid. The test liquids are ethanol, n-decane and 5 cSt silicone oil, which have different degrees of viscosity and of volatility. The gas flow along the interface strongly enhances the evaporation and, correspondingly, affects the interface shape. Silhouette measurements are used for optical determination of the interface shape. From the digital images the variation of the liquid volume as a function of flow rate is calculated.

3-D PTV measurement of Marangoni convection in liquid bridge in space experiment

Microgravity experiments have been conducted on the International Space Station in order to clarify the transition processes of the Marangoni convection in liquid bridges of high Prandtl number fluid. The use of microgravity allows us to generate large liquid bridges, 30 mm in diameter and up to 60 mm in length. Three-dimensional particle tracking velocimetry (3-D PTV) is used to reveal complex flow patterns that appear after the transition of the flow field to oscillatory states. It is found that a standing-wave oscillation having an azimuthal mode number equal to one appears in the long liquid bridges. For the liquid bridge 45 mm in length, the oscillation of the flow field is observed in a meridional plane of the liquid bridge, and the flow field exhibits the presence of multiple vortical structures traveling from the heated disk toward the cooled disk. Such flow behaviors are shown to be associated with the propagation of surface temperature fluctuations visualized with an IR camera. These results indicate that the oscillation of the flow and temperature field is due to the propagation of the hydrothermal waves. Their characteristics are discussed in comparison with some previous results with long liquid bridges. It is shown that the axial wavelength of the hydrothermal wave observed presently is comparable to the length of the liquid bridge and that this result disagrees with the previous linear stability analysis for an infinitely long liquid bridge.

Measurement of the dynamical free surface deformation in liquid bridges

We have designed and developed a new experimental procedure for investigating the dynamical free surface deformation due to Marangoni convection in liquid bridges on the basis of optical imaging. The images were formed by background illumination to give a silhouette effect, and recorded by a CCD camera with certain sampling rate. Global thresholding technique was used for processing the recorded digital images. The time-dependent behavior of the free surface was examined. Free surface displacements of sub-micron order were well determined by this method. The amplitudes and frequencies of the oscillations were measured for a wide range of applied temperature differences.

Onset of oscillatory thermocapillary convection in acetone liquid bridges: The effect of evaporation

Experiments have been carried out for half-zones of acetone ( Pr = 4.3) to investigate the effects of evaporative cooling on the flow structures and temperature fields during transition from steady to oscillatory convection. The unstable flow phenomena have been measured using a variety of diagnostic techniques to determine the effects of evaporative cooling on Marangoni convection in liquid bridges of intermediate Prandtl number. The results show that Marangoni convection in acetone liquid bridges with and without strong evaporation becomes unstable due to the same mechanism but the evaporation has a strong stabilizing effect on the onset of oscillatory Marangoni convection.

B233 液柱マランゴニ対流振動流遷移のモデル化

B233 液柱マランゴニ対流振動流遷移のモデル化

A234 液柱内マランゴニ対流における動的粒子集合 : 2. 数値シミュレーション

A234 液柱内マランゴニ対流における動的粒子集合 : 2. 数値シミュレーション

Transition and Modal Structure of Oscillatory Marangoni Convection in Liquid Bridge.

河村 洋,小野 嘉久,上野 一郎 Transition and Modal Structure of Oscillatory Marangoni Convection in Liquid Bridge Hiroshi KAWAMURA, Yoshihisa ONO and Ichiro UENO Dept. Mech. Eng., Fac. Sci. & Tech., Science University of Tokyo, 2641 Yamazaki, Noda-shi, Chiba 278-8510, Japan A large number of terrestrial experiments have been conducted on Marangoni convection in a liquid bridge to date. The limitation in the terrestrial experiments lies in the maximum size of the bridge and thus in the maximum attainable Marangoni number in normal gravity. In the present study, a series of experiments was performed in a low temperature environment in order to suppress the evaporation of fluid while realizing a large temperature difference between the both ends of the bridge to attain a high Marangoni number in spite of a small size of the bridge. The test fluid was silicone oil of 1, 2 and 5 cSt. The temperature difference ∆T was increased gradually and a critical point of transition from steady to oscillatory flow was obtained. With increase of ∆T, a pulsative oscillatory mode and then a rotational one became discernable. In this series of experiments a wide range of aspect ratio of the bridge was concerned and thus flow structures with mode number m = 1, 4, 5 and 6 were realized. The product of the mode number and the aspect ratio was found to be approximately unity as often pointed out.

Evaluation of the onset of oscillatory thermocapillary convection in liquid bridge with empirical correlations in terms of a modified Marangoni number

For the onset of oscillatory Marangoni convection in liquid bridge, the present paper proposes an empirical correlation in terms of the modified Marangoni number that was proposed in order to take into account the effect of the free-surface axial curvature by the present authors [Yamamoto, Torii, J. Crystal Growth 182 (1997) 485]. The proposed equation can correlate the available experimental data within 22% error for Ma R<3×10 4 and within 24% error for Ma R>3×10 4. It is found that the critical Marangoni number for the onset of oscillatory convection in liquid bridge can be well correlated in terms of three parameters of the aspect ratio, the Prandtl number and the curvature parameter ( C-parameter).

Theoretical examination for the onset of oscillatory Marangoni convection in liquid bridge

It has been considered that the onset of oscillatory Marangoni convection in liquid bridge is difficult to predict by Marangoni number alone. Based on an idea that this phenomenon is to be driven by a thermocapillary action on its free surface, the present paper theoretically examines the balance of force there and proposes a new Marangoni number containing parameters for the curvature deformation of liquid bridge ( C-parameter) and the effect of representative length. Since this C-parameter reflects the thermocapillary force changing with the curvature deformation of liquid bridge, the new Marangoni number is proven to be universally applicable to various shapes of liquid bridge, differing from a conventional Marangoni number.

Oscillatory Thermocapillary Flows in Simulated Floating-zones with Time-dependent Temperature Boundary Conditions

This study deals with numerical simulations of the Maxus sounding rocket experiment on oscillatory Marangoni convection in liquid bridges. The problem is investigated through direct numerical solution of the non-linear, time-dependent, three-dimensional Navier–Stokes equations. In particular, a liquid bridge of silicon oil 2[cs] with a length L=20 [mm] and a diameter D=20 (mm) is considered. A temperature difference ΔT=30 [K] is imposed between the supporting disks, by heating the top disk and cooling the bottom one with different rates of ramping. The results show that the oscillatory flow starts as an ‘axially running wave', but after a transient time the instability is described by the dynamic model of a ‘standing wave', with an azimuthal spatial distribution corresponding to m=1 (where m is the critical wave number). After the transition, the disturbances become larger and the azimuthal velocity plays a more important role and the oscillatory field is characterized by a travelling wave. The characteristic times for the onset of the different flow regimes are computed for different rates of ramping.

Marangoni Convection in a Liquid Bridge under Microgravity Conditions During Parabolic Flight.

Marangoni convection in a silicone oil liquid bridge under microgravity conditions during parabolic flight was observed. The developing process of axis-symmetric laminar Marangoni convection was studied experimentally and numerically. To reach a steady state of the temperature field, much more time was needed than to reach a steady state of the velocity field.The effects of initial temperature conditions inside a liquid bridge, heat transfer across the free surface, and temperature dependence of viscosity on both velocity and temperature field were studied numerically.