Thermocapillary flow in drops under low gravity analysed by the use of liquid crystals
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Abstract
Thermocapillary flow within large sized drops of diameters up to 15 mm was studied experimentally during KC-135 parabolic flights. For the simultaneous observation of the flow and the temperature fields inside the drops, visualisation by means of liquid crystal tracers was applied. Due to the curved surfaces of the drops, a special evaluation method has to be taken into account. The experimental set up and the test procedure as well as a qualitative description of the observed flow behaviour in high Prandtl number liquids are described.
Keywords
Liquid Crystal Temperature Field Evaluation Method Prandtl Number Flow BehaviourList of symbols
- a
thermal diffusivity
- Bodyn
dynamical Bond number, Eq. (4)
- g
acceleration
- go
acceleration due to gravity on earth
- Gr
Grashof number, Eq. (5)
- H
distance between the stemples
- Ma
Marangoni number, Eq. (2)
- m
order of reflected wavelength
- n
refractive index
- n21
refractive index ratio of medium 1 related to medium 2
- Pi
point where P r is imaged
- Pk
intersection point between light sheet beam and drop surface
- pl
point on the symmetry axis
- Pr
point with real coordinates in the light-sheet plane
- Ps
intersection point between observation beam and drop surface
- Pr
Prandtl number, Eq. (3)
- R
drop radius
- ReM
Reynolds number Eq. (1)
- ri
radial coordinate at the image
- rr
real radial coordinate in the light-sheet plane
- S(x)
function of the drop shape
- S′(x)
derivative dS/dx
- ΔT
maximum temperature difference applied to the drop
- T
temperature
- Tw
temperature at the warm stemple
- Tk
temperature at the cold stemple
- ur
backflow velocity in the core region
- UM
characteristic Marangoni velocity
- \(\overrightarrow V _L \)
light sheet beam in the drop
- \(\overrightarrow V _B \)
reflected beam in the drop
- x
axial coordinate of the drop
- Xi
imaged axial coordinate on the flow picture
- xr
real axial coordinate
- y
coordinate normal to x and z axis
- yi
imaged y-coordinate on the flow picture
- yr
real y-coordinate in the light-sheet plane
- z
coordinate in observation direction
Greek letters
- α
reflection angle in fluid 2
- β
reflection angle in fluid 1, thermal expansion coefficient
- ɛ
inclination angle between observation axis and light-sheet plane
- η
dynamic viscosity
- λ
heat conductivity
- ϕ
reflection angle on the crystal's surface
- v
kinematic viscosity
- ϱ
density
- σ
surface tension
- ∂σ/∂T
temperature dependence of the surface tension
- gx
angle in the light-sheet plane, Eq. (8)
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References
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