Marangoni effects caused by contaminants adsorbed on bubble surfaces

Journal of Fluid Mechanics

Volumn 647, Issue , 2010, Pages 143-161

  Lakshmanan, Peter ^a   Ehrhard, Peter ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONTAMINATION; SHEAR STRESS; STRESS ANALYSIS;

CONTAMINANT TRANSPORT; DEFORMABLE BUBBLES; LEVEL SET METHOD; MARANGONI EFFECTS; MARANGONI STRESS; SOLID PARTICLES; STRESS PROFILE; TENSION VARIATION;

NUMERICAL METHODS;

ADSORPTION; BUBBLE; COMPUTER SIMULATION; POLLUTANT TRANSPORT; SHEAR STRESS; SURFACE AREA; SURFACE TENSION;

EID: 77952325530     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009993077     Document Type: Article

References (27)

1. Anderson, D. M. & McFadden, G. B. 1998 Diffusive-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30, 139-168.
2. Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
3. Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modelling surface tension. J. Comput. Phys. 100, 335-354.
4. Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles. Academic Press.
5. Cuenot, B., Magnaudet, J. & Spennato, B. 1997 The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339, 25-53.
6. Drumright-Clark, M. A. & Renardy, Y. 2004 The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia. Phys. Fluids 16, 14-21.
7. Enright, D., Fedkiw, R., Ferizger, J. & Mitchel, I. 2002 A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183, 83-116.
8. Frumkin, A. & Levich, V. G. 1947 On surfactants and interfacial motion. Zhurnal Fizicheskoi Khimii 21, 1183-1208.
9. Harper, J. F. 1974 On spherical bubbles rising steadily in dilute surfactant solutions. Q. J. Mech. Appl. Math. 17, 87-100.
10. Hirt, C. W & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201-225.
11. James, A. J. & Lowengrub, J. 2004 A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. J. Comput. Phys. 201, 685-722.
12. Li, J. 2006 The effect of an insoluble surfactant on the skin friction of a bubble. Eur. J. Mech. B/Fluids 25, 59-73.
13. McLaughlin, J. B. 1996 Numerical simulation of bubble motion in water. J. Colloid Interface Sci. 184, 614-625.
14. Mei, R., Klausner, J. F. & Lawrence, C. J. 1994 A note on the history force on a spherical bubble at finite Reynolds number. Phys. Fluids 6, 418-420.
15. Olsson, E. & Kreiss, G. 2005 A conservative level set method for two phase flow. J. Comput. Phys. 210, 225-246.
16. Palaparthi, R., Papageorgiou, D. T. & Maldarelli, C. 2006 Theory and experiments on the stagnant cap regime in the motion of spherical surfactant-laden bubbles. J. Fluid Mech. 559, 1-44.
17. Peskin, C. S. 2002 The immersed boundary method. Acta Numer. 11, 479-517.
18. Renardy, Y. Y., Renardy, M. & Cristini, V. 2002 A new volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at low viscosity ratio. Eur. J. Mech. B/Fluids 21, 49-59.
19. Sadhal, S. S. & Johnson, R. E. 1983 Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film-exact solution. J. Fluid Mech. 129, 237.
20. Savic, P. 1953 Circulation and distortion of liquid drops falling through a viscous medium. Natl Res. Counc. Can. Div. Mech. Engng Rep. MT-22, 1-35.
21. Schiller, L. & Naumann, A. Z. 1933 Uber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. Zeitung VDI 77, 318-320.
22. Stone, H. A. 1990 A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface. Phys. Fluids A 2, 111-112.
23. Sussman, M. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 149-159.
24. Sussman, M. & Puckett, E. G. 2000 A coupled level set and volume of fluid method for computing 3D and axissymmetric incompressible two-phase flows. J. Comput. Phys. 162, 301-337.
25. Tomiyama, A., Kataoka, I., Zun, I. & Sakaguchi, T. 1998 Drag coefficients of single bubbles under normal and micro gravity conditions. Japan Soc. Mech. Engnng Intl J. Ser. B 41, 472-479.
26. Wang, Y., Papageorgiou, D. T. & Maldarelli, C. 1999 Increased mobility of a surfactant-retarded bubble at high bulk concentrations. J. Fluid Mech. 390, 251-270.
27. Xu, J.-J., Li, Z., Lowengrub, J. & Zhao, H. 2006 A level-set method for interfacial flows with surfactant. J. Comput. Phys. 212, 590-616.