Abstract
Laser interferometry was used to investigate diffusive and convective mass transfer in a multicomponent fluid mixture with a liquid–liquid or liquid–gas interface. For this purpose, an immobile gas bubble or insoluble fluid droplet, having the shape of a short cylinder with a free lateral surface, was inserted into a thin liquid layer. In the case of non-uniform distribution of the dissolved surfactant component, the Marangoni convection near the drop/bubble was initiated by the surface tension inhomogeneities, depending on the surfactant concentration. The applied experimental techniques allowed us to study the structure and evolution of the convective flows and concentration fields in a liquid layer, which due to its small thickness were nearly two-dimensional. Making use of both the vertical and horizontal orientation of the liquid layer, we investigated the mass transfer process at different levels of the interaction between gravity and capillary forces. During the experiments, we detected new solutocapillary phenomena, which were found to be caused by oscillatory regimes of solutal convection occurring around air bubbles and chlorobenzene drops in heterogeneous aqueous solutions of alcohol with a vertical surfactant concentration gradient. The role of the oscillatory instability in the processes of drop saturation by the surfactant from its water solution and an inverse process of surfactant extraction from the drop into the surrounding homogeneous fluid (water) was determined. A reasonable explanation for the driving mechanisms of the discovered effects has been proposed.
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Abbreviations
- d :
-
Bubble/drop diameter
- f :
-
Frequency of oscillations
- g :
-
Gravitational acceleration
- h :
-
Layer thickness
- n :
-
Refraction index
- r :
-
Radial position of concentration front
- t :
-
Time
- β C :
-
Volume concentration expansion coefficient
- σ :
-
Surface tension coefficient
- ρ:
-
Solution density
- η:
-
Solution dynamic viscosity
- τ:
-
Time unit \( = {\frac{{\rho h^{2} }}{\eta }} \)
- C :
-
Concentration
- C 0 :
-
Initial concentration of surfactant in surrounding solution
- C d :
-
Initial concentration of surfactant inside the drop
- ΔC :
-
Concentration difference
- D :
-
Surfactant diffusion coefficient
- N :
-
Isoline sequence number
- S :
-
Bubble/drop area
- T :
-
Period of oscillations
- Ma C :
-
Marangoni number, \( = {\frac{{h^{2} }}{\eta D}}\,{\frac{\partial \sigma }{\partial C}}\nabla C \)
- Gr C :
-
Grashof number, \( = {\frac{{\rho^{2} g\beta_{C} h^{4} }}{{\eta^{2} }}}\nabla C \)
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Acknowledgments
The work was supported by the joint project of SB, UB and F-EB of RAS No.116/09-C-1-1005 and also by the Russian Foundation for Basic Research (RFBR) Grants No. 09-01-00484 and No. 10-01-96028.
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Kostarev, K.G., Shmyrov, A.V., Zuev, A.L. et al. Convective and diffusive surfactant transfer in multiphase liquid systems. Exp Fluids 51, 457–470 (2011). https://doi.org/10.1007/s00348-011-1063-9
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DOI: https://doi.org/10.1007/s00348-011-1063-9