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Last update 4th Apr. 2008

Experimental Benchmark : Onset of instability in liquid bridge

Experiments in liquid bridges are very sensitive to the experimental conditions such as environment, geometry of the particular set-up, increasing speed of temperature difference and physical properties of a test liquid. Further, assumptions often made in the numerical simulations, such as perfectly conducting rigid walls and, especially, boundary conditions at the free surface, can be accurately defined in numerical works, but are not always realized in experiments. The comparison of numerical results with a single experiment can lead to a large discrepancy due to specific experimental conditions. Cumulative experimental results promise to be reliable and useful for the validation of advanced numerical models and forthcoming experiments.

1. Choice of liquid
A wide spectrum of silicone oils is often used in terrestrial and microgravity experiments. The reasons for using silicone oils are the reproducibility of the surface tension and its well-defined dependency upon temperature. To minimize the evaporation of liquid from interface 5 cSt silicone oil (Pr=68) is chosen as a primary test liquid. The silicone oil of 2 cSt is also included as additional test fluid to examine the effect of viscosity. The physical properties are listed in a Table (according handbook). 5cSt silicone oil is a mixture of the polymers, so it is strongly recommended to use the same provider, i.e. Daw Corning. As a limit, Valentina Shevtsova can send you a small sample by request ( )

  ν(m2/s) β(1/K) σ(N/m) α(m2/s) σT=dσ/dT
5cSt 5• 10-6 1.09• 10-3 1.97• 10-2 7.31• 10-8 -6.37• 10-5 912
2cSt 2• 10-6 1.24• 10-3 1.83• 10-2 7.12• 10-8 -7.15• 10-5 873

2. Geometry of the system
This is the most peculiar point, as different experimental group have different set-up and the benchmark study can not demand to use the same radius of the rod. For example, MRC, ULB (Brussels) has rods with a diameter D=2R0=6.0mm and TUS (Tokyo), D=2R0=5.0mm. It is rather difficult to re-design the set-up in a short time. The participants are requested to use the following specific aspect ratios on the basis of available rods. Heating is normally from the top end surface. If not, please specify. (Γ is the aspect ratio (height/radius) and m is the expected azimuthal mode number for a straight cylinder)

Case I: Γ= 0.64 (m=3), Case II: Γ= 1.0 (m=2), Case III: Γ= 1.2 (m= 2)

3. Liquid volume
The dimensionless volume of the liquid is defined with respect to the straight cylinder, V= Vol/V0 where V0= πR02H , H is the height of cylinder.

Please carry out experiments for
Case a: V= 1.0, Case b: V= 0.9, Case c: V= 0.8

4. Environmental conditions:
It is difficult to demand some special conditions, as it is strongly related to the location and arrangement of the existing set-up's. However, it is strongly recommended to perform experiments at room temperature in the range T=22°C ± 2°C. Please, foresee measurement of the air temperature in the vicinity of liquid bridge (5-7 cm away from the free surface, not more). Continuous recording is the best.
In addition, the critical point is highly dependent on the heat loss from the liquid bridge.

5. Measurements:
The goal is to determine the onset of oscillatory regime: critical temperature difference ΔT and the frequency f at the critical point. If one can determine the azimuthal mode number m at the critical point, report of m is recommended. The mode number could be a mixture of several modes. It is expected to measure the temperature oscillation of the liquid using thermocouples. However, any other methods are welcome. Please mention the measurement position and method of the temperature.

6. Temperature ramping:
Temperature ramp may be implemented by different ways:
(a) Keep the temperature cold rod constant and heat from above
(b) Keep the mean temperature constant, i.e. reduce Tcold and increase Thot.
As second choice may introduce additional constrains, both methods are acceptable. However choosing one of the cases, please, try to satisfy following conditions
(a) Tcold ≈ Troom
(b) Tmean ≈ 0.5(Tcold +Thot) ≈ Troom
Please, specify your choice of ramping way in your report.

At the beginning of the experiments the rate of ΔT increase can have arbitrary value. Approaching to the critical point, it is recommended to keep the ΔT rate to 0.05-0.1K/min.

7. Determination of the critical point
The critical point is defined as the condition at which oscillation of temperature or orbit of tracer particles can be sustained during 2 thermal times, which is defined as τth=H2/α [s] ≈ 100s. Report the ΔTcr at the critical point.

8. Publishing
According to the results of the benchmark it is planed to publish a paper in a high level scientific standard journal. Definitely, one person from each team will be included in the list of authors. Other team members will also be listed in the article, although maximum number might be limited.

9. Other items to be reported
(1) The last column (A) is the amplitude of the temperature oscillation when system is 5% above the critical point.
(2) Attach a sketch or a photograph of the test configuration including liquid bridge and its surroundings to roughly guess the heat loss.
(3) Describe the approximate elapsed time [min] until the critical condition has reached, because it affects the critical condition significantly. The elapsed time must be an order of the τth=H2/α [s]. This data need not be given for each run, but description of a rough average value is requested.

Viscosity [cSt]:                         Average Elapsed time [min]
  Case I: Γ=0.64
Volume ratio R0 Tamb ΔTcr fcr m A( at ΔTcr×1. 05)
a)      1.0            
b)      0.9            
c)      0.8            

  Case II: Γ=1.0
Volume ratio R0 Tamb ΔTcr fcr m A( at ΔTcr×1. 05)
a)      1.0            
b)      0.9            
c)      0.8            

  Case III: Γ=1.2
Volume ratio R0 Tamb ΔTcr fcr m A( at ΔTcr×1. 05)
a)      1.0            
b)      0.9            
c)      0.8            

10. Numerical results
Numerical results on the onset of oscillation are also encouraged to be presented for comparison. In this case, please report

(1) Pr number, (2) Marangoni number at the onset of oscillation, (3) Thermal boundary condition at the free surface, (4) Number of mesh in r , z and θ directions.

(Only three dimensional calculations (no two dimensional one) will be accepted for comparison.)


Conf. Chair: Professor Hiroshi KAWAMURA
Head of Local Executive Committee: Dr, Ichiro UENO
Dept. Mech. Eng., Fac. Sci. & Tech., Tokyo University of Scinence
2641 Yamazaki,Noda,Chiba 278-8510,JAPAN
IMA4: 21st-23rd Oct. 2008 at Tokyo University of Science
Research Center for Holistic Computational Science
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