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Experimental study of Marangoni bubble migration in normal gravity

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Abstract

Marangoni convection, whether thermal or solutal, is known to have a profound impact on many technological processes involving gas inclusions in a liquid phase. Evidently, similar phenomena may arise both in thermocapillary and solutocapillary situations, due to similarity of the motion driving mechanisms. However, the fact that the characteristic times of heat and surfactant diffusion generally differ by several orders of magnitude lends singularity to the behavior of Marangoni convection in inhomogeneous mixtures. Moreover, in the solutocapillary case one can meet the action of some additional effects associated with dissolution of the surfactant in a liquid, its adsorption at the interface and evaporation into a gas phase. This paper presents a comparative analysis of the results of ground experiments studying the behavior of air bubbles in a liquid under the action of thermocapillary and solutocapillary forces. The use of original experimental techniques makes it possible to eliminate the influence of gravity effects. A new Marangoni phenomenon—solutocapillary bubble migration—was detected and investigated. The results of studying thermal and concentration convective flows and bubble motion, in relation to bubble size, time, liquid layer thickness and fluids properties, are presented and discussed.

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Abbreviations

T :

Temperature

∇ T:

Thermal gradient, =∂T/∂x

C :

Concentration

∇ C:

Concentration gradient, =∂C/∂x

σ :

Surface tension

σ′T:

Temperature coefficient of surface tension, =∂σ/∂T

σ′C:

Concentration coefficient of surface tension, =∂σ/∂C

ν :

Kinematic viscosity

η :

Dynamic viscosity

ρ :

Density

n :

Refraction index

χ :

Thermal diffusivity

D :

Surfactant diffusion coefficient

β :

Volume thermal expansion coefficient

g :

Gravitational acceleration

d :

Bubble diameter

R :

Bubble radius

h :

Layer thickness

x :

Horizontal coordinate

u :

Bubble migration velocity

U 0 :

Bubble migration velocity scale, =(R/η)(∂σ/∂x)

U :

Dimensionless bubble migration velocity, =u/U0

Ma T :

Thermal Marangoni number, =(R2/ηχ)(∂σ/∂x)=(R2/ηχ)σ′ T ∇T

Ma C :

Concentrational Marangoni number, =(R2/ηD)(∂σ/∂x)=(R2/ηD)σ′ C ∇C

Re :

Reynolds number, =U0 R/ν

Pe :

Péclet number, =U0  R/χ=(R2/ηχ)(∂σ/∂x)=MaT

Ra :

Rayleigh number, =(ρ  g β  h4/ηχ)∇ T

Pr :

Prandtl number, =ν/χ

TC:

Thermocapillary

SC:

Solutocapillary

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Acknowledgements

This work was partially supported by Russian Foundation for Basic Research (RFBR) project No. 03-01-00579 and INTAS-ESA project No. 99-01505. Special thanks to Prof. A.F. Pshenichnikov for useful discussions.

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Authors and Affiliations

  1. Perm State University, 15 Bukireva Street, 614600, Perm, Russia

    Yu. K. Bratukhin

  2. Institute of Continuous Media Mechanics, 1 Acad. Korolev Street, 614013, Perm, Russia

    K. G. Kostarev & A. L. Zuev

  3. Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Università di Napoli, via Roma 29, 81031, Aversa, Italy

    A. Viviani

Authors
  1. Yu. K. Bratukhin
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  2. K. G. Kostarev
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  3. A. Viviani
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  4. A. L. Zuev
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Correspondence to A. Viviani.

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Bratukhin, Y.K., Kostarev, K.G., Viviani, A. et al. Experimental study of Marangoni bubble migration in normal gravity. Exp Fluids 38, 594–605 (2005). https://doi.org/10.1007/s00348-005-0930-7

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  • DOI: https://doi.org/10.1007/s00348-005-0930-7

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