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Marangoni-convection in a rotating liquid container

Marangoni-Konvektion in einer in einem Behälter rotierenden Flüssigkeit

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Abstract

In a partially filled and constantly spinning container in zerogravity condition there arises under the action of an axial temperature gradient a thermo-capillary convection. This so-called Marangoni convection has been treated analytically for a directly imposed temperature gradient upon the free liquid surface and also for a constant but different temperature at the upper and lower disc wall. The streamfunction and circulation have been obtained, from which the velocity distribution could be determined.

Zusammenfassung

Durch das Vorhandensein eines axialen Temperaturgradienten ergibt sich in einem mit konstanter Geschwindigkeit rotierenden teilweise mit Flüssigkeit gefüllten Behälter eine thermalkapillare Korrelation. Diese sogenannte Marangoni-Konvektion wird analytisch behandelt für eine lineare axiale und eine beliebige axiale Temperaturverteilung auf der Flüssigkeitsoberfläche. Stromfunktion und Zirkulation werden analytisch bestimmt. Daraus ergeben sich die Geschwindigkeitsverteilungen in radialer, zirkumferentialer und axialer Richtung.

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Abbreviations

a :

radius of cylindrical container

b :

radius to free liquid surface

h :

height of container

I m, Km :

Modified Besselfunktions of first and second kind and orderm

k λj :

roots of bi-cubic equation (24 b)

k=b/a :

diameter ratio of location of free liquid surface and container wall

r, ϕ, z :

polar cylindrical coordinates

T(r, z):

temperature distribution of liquid

u, v, w :

radial-, circumferential-, and axial velocity of the liquid, resp.

β :

thermal expansion coefficient

η :

dynamic viscosity of liquid

ν=η/ϱ :

kinematic viscosity

ϱ :

density of liquid

σ:

surface tension of liquid

τ rϕ ,τ rz :

shear stresses

φ(r, z):

circulation

Ψ(r, z):

stream function

Ω 0 :

speed of spin of container about axis of symmetry

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  1. Institut für Raumfahrttechnik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, W-8014, Neubiberg, FRG

    H. F. Bauer

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Bauer, H.F. Marangoni-convection in a rotating liquid container. Warme - und Stoffubertragung 28, 131–138 (1993). https://doi.org/10.1007/BF01541109

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  • DOI: https://doi.org/10.1007/BF01541109

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