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Thermocapillary flow in drops under low gravity analysed by the use of liquid crystals

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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.

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a :

thermal diffusivity

Bo dyn :

dynamical Bond number, Eq. (4)

g :


g o :

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

n 21 :

refractive index ratio of medium 1 related to medium 2

P i :

point where P r is imaged

P k :

intersection point between light sheet beam and drop surface

p l :

point on the symmetry axis

P r :

point with real coordinates in the light-sheet plane

P s :

intersection point between observation beam and drop surface

Pr :

Prandtl number, Eq. (3)

R :

drop radius

Re M :

Reynolds number Eq. (1)

r i :

radial coordinate at the image

r r :

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 :


T w :

temperature at the warm stemple

T k :

temperature at the cold stemple

u r :

backflow velocity in the core region

U M :

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

X i :

imaged axial coordinate on the flow picture

x r :

real axial coordinate

y :

coordinate normal to x and z axis

y i :

imaged y-coordinate on the flow picture

y r :

real y-coordinate in the light-sheet plane

z :

coordinate in observation direction

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 :


σ :

surface tension


temperature dependence of the surface tension

gx :

angle in the light-sheet plane, Eq. (8)


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Author information

Correspondence to M. Treuner.

Additional information

This work was supported by the Deutsche Agentur für Raumfahrtangelegenheiten (DARA) under grant No. 50 QV 8717. The authors appreciate very much the high engagement of Dipl.-Ing. Ronald Mairose for the construction of the excellent electronic equipment and his support during the experiments and Prof. Dr. Dieter Langbein for several usefull inputs to the final manuscript.

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Treuner, M., Rath, H.J., Duda, U. et al. Thermocapillary flow in drops under low gravity analysed by the use of liquid crystals. Experiments in Fluids 19, 264–273 (1995). https://doi.org/10.1007/BF00196475

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  • Liquid Crystal
  • Temperature Field
  • Evaluation Method
  • Prandtl Number
  • Flow Behaviour