Abstract
Temperature and velocity fields near an air-bubble in silicon-oil under a heated horizontal wall were investigated. The studies were made with silicon oils of different viscosities so that a wide range of Marangoni numbers was encountered. Schlieren interferograms were taken to analyse the temperature field. For the axisymmetric problem the Abel integral equation was solved numerically by using a coefficient procedure. From the recorded temperature distributions isotherms, radial temperature lines and the temperature along the bubble surface were determined graphically. At low Prandtl- and high Marangoni-numbers an oscillatory instability was observed. The flow field was investigated with neutral-buoyant light scattering glass spheres by observation of the meridian plane of the bubble with a thin light-sheet. The convective mechanism of the flow was recorded photographically by taking pictures with various exposure times. Thus a qualitative and quantitative description of the flow was possible.
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Abbreviations
- a :
-
thermal diffusivity
- c :
-
chemical concentration
- f :
-
focal length
- f 0 :
-
frequency of flow oscillation
- h b :
-
bubble height
- k (x) :
-
function of interference fringe distribution
- Mg :
-
Maragoni number,Mg = ur b /a
- n :
-
normal coordinate
- n :
-
refractive index
- Pr :
-
Prandtl number,Pr = v/a
- p :
-
pressure
- \(\dot q\) :
-
heat flow
- R :
-
radial boundary of axisymmetric phase object
- R A ,R B :
-
radii of curvature
- Re :
-
Reynolds number,Re — ur b /v
- r :
-
radial coordinate
- r â :
-
radial coordinate at the boundary (Fig. 7)
- r> b :
-
bubble radius
- r * :
-
dimensionless radial coordinate,r * = r/r a
- S j, i :
-
solution coefficients
- T :
-
temperature
- T a :
-
temperature at the axial boundary
- T u :
-
temperature of the upper copper wall
- ΔT :
-
temperature difference,ΔT = T u —T a
- T * :
-
dimensionless temperature,\(T^ * = \frac{{T - T_a }}{{\Delta T}}\)
- t :
-
tangential coordinate along interface
- u :
-
reference velocity,\(u = \frac{{r_b }}{\mu } \cdot \left| {\frac{{d\sigma }}{{dT}}} \right| \cdot \left| {\frac{{dT}}{{dt}}} \right|\)
- x :
-
coordinate normal to the optical axis
- y :
-
coordinate in direction of the optical axis
- z :
-
axial coordinate normal to the wall
- z a :
-
axial coordinate at the boundary (Fig. 7)
- z * :
-
dimensionless axial coordinate,z * =z/z a
- ɛ:
-
separation angle of the Wollaston prism
- χ(x):
-
weight function of interference fringe distribution
- λ:
-
wave length
- μ:
-
dynamic viscosity
- v :
-
kinematic viscosity
- ρ:
-
density
- ρ e :
-
electrical charge density
- σ:
-
surface tension
- τ:
-
exposure times
References
Chun, Ch. H. 1986: Thermocapillary flow in surroundings of a bubble under a heated wall. In: Proc. 15th Int. Symp. Space Technology and Science (ISTS), Tokyo 1986, 2127–2136
Kao, Y. S.; Kenning, D. B. R. 1972: Thermocapillary flow near a hemisperical bubble on a heated wall. J. Fluid Mech. 53, 715–735
Kean, L. 1961: Coefficients for axisymmetric schlieren evaluations. Aeronautical Systems Division (SD), Technical note 61-56, United States Air Force, May 1961
Merzkirch, W. 1974: Flow visualization. London: Academic Press
Ostrach, S. 1982: Low-gravity fluid flows. Ann. Rev. Fluid Mech. 14, 313–345
Raake, D. 1986: Experimentelle Untersuchung von Thermokapillar-Konvektionen in der Umgebung einer Luftblase unter einer beheizten horizontalen Wand. Thesis, Universität Essen, FB 12 Mechanik
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Dedicated to Prof. Dr.-Ing. J. Zierep on the occasion of his 60th birthday
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Raake, D., Siekmann, J. & Chun, C.H. Temperature and velocity fields due to surface tension driven flow. Experiments in Fluids 7, 164–172 (1988). https://doi.org/10.1007/BF02332981
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DOI: https://doi.org/10.1007/BF02332981