Dynamics and stability of an annular electrolyte film

Journal of Fluid Mechanics

Volumn 656, Issue , 2010, Pages 481-506

  Conroy, D T ^a   Craster, R V ^b   Matar, O K ^a   Papageorgiou, D T ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOLTZMANN EQUATION; ELECTRODYNAMICS; ELECTROHYDRODYNAMICS; ELECTROMAGNETIC FIELDS; ELECTROOSMOSIS; INITIAL VALUE PROBLEMS; INVERSE PROBLEMS; LINEAR STABILITY ANALYSIS; NONLINEAR ANALYSIS; NONLINEAR EQUATIONS; POISSON EQUATION;

CHARGE SEPARATIONS; ELECTROKINETIC EFFECT; ELECTROKINETIC FORCES; ELECTROSTATIC EFFECT; ELECTROSTATIC POTENTIALS; INTERFACIAL DYNAMICS; NONLINEAR EVOLUTION EQUATION; PERIODIC BOUNDARY CONDITIONS;

ELECTROLYTES;

CAPILLARY PRESSURE; ELECTRODYNAMICS; ELECTROKINESIS; ELECTROLYTE; FILM; FLUID DYNAMICS; NONLINEARITY; NUMERICAL MODEL;

EID: 77957103585     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010001254     Document Type: Article

References (49)

1. Aul, R. W. & Olbricht, W. L. 1990 Stability of a thin annular film pressure-driven, low-Reynoldsnumber flow through a capillary. J. Fluid Mech. 215, 585-599.
2. Campana, D., Di Paolo, J. & Saita, F. 2004 A two-dimensional model of Rayleigh instability incapillary tubes: surfactant effects. Intl J. Multiphase Flow 30, 431-454.
3. Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
4. Chang, H.-C. & Demekhin, E. A. 1999 Mechanism for drop formation on a coated vertical fibre.J. Fluid Mech. 380, 233-255.
5. Chang, H.-C. & Yeo, L. Y. 2010 Electrokinetically Driven Microfluidics and Nanofluidics. CambridgeUniversity Press.
6. Chang, H.-C. & Yossifon, G. 2009 Understanding electrokinetics at the nanoscale: a perspective.Biomicrofluidics 3, 012001.
7. Craster, R. V. & Matar, O. K. 2006 On viscous beads flowing down a vertical fibre. J. Fluid Mech.553, 85-106.
8. Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys.81, 1131-1198.
9. Everett, D. H. & Haynes, J. M. 1972 Model studies of capillary condensation. 1. Cylindrical poremodel with zero contact angle. J. Colloid Interface Sci. 38, 125-137.
10. Frenke, A. L., Babchin, A. J., Levich, B. G., Shlang, T. & Sivashinsky, G. I. 1987 Annular flowcan keep unstable flow from breakup: nonlinear saturation of capillary instability. J. ColloidInterface Sci. 115, 225-233.
11. Gauglitz, P. A. & Radke, C. J. 1988 An extended evolution equation for liquid-film break up incylindrical capillaries. Chem. Engng Sci. 43, 1457-1465.
12. Georgiou, E., Papageorgiou, D. T., Maldarelli, C. & Rumschitzki, D. S. 1991 The doublelayer-capillary stability of an annular electrolyte film surrounding a dielectric-fluid core in atube. J. Fluid Mech. 226, 149-174.
13. Gitlin, I., Stroock, A. D., Whitesides, G. M. & Ajdari, A. 2003 Pumping based on transverseelectrokinetic effects. Appl. Phys. Lett. 83, 1486-1488.
14. Glasner, K. B. & Witelski, T. P. 2003 Coarsening dynamics of dewetting films. Phys. Rev. E 67,016302.
15. Goren, S. L. 1962 The instability of an annular thread of fluid. J. Fluid Mech. 12, 309-319.
16. Grotberg, J. B. & Jensen, O. E. 2004 Biofluid mechanics in flexible tubes. Annu. Rev. Fluid Mech.36, 121-147.
17. Hagerdon, J. G., Martyn, N. S. & Douglas, J. F. 2004 Breakup of a fluid thread in a confinedgeometry: droplet-plug transition, perturbation sensitivity, and kinetic stabilization withconfinement. Phys. Rev. E 69, 056312.
18. Halpern, D. & Grotberg, J. B. 2003 Nonlinear saturation of the Rayleigh instability due tooscillatory flow in a liquid-lined tube. J. Fluid Mech. 492, 251-270.
19. Hammond, P. S. 1983 Nonlinear adjustment of a thin annular film of viscous fluid surrounding athread of another within a circular cylindrical pipe. J. Fluid Mech. 137, 363-384.
20. Hosoi, A. E. & Mahadevan, L. 1999 Axial instability of a free-surface front in a partially filledhorizontal rotating cylinder. Phys. Fluids 11, 97-106.
21. Jensen, O. E. 1997 The thin liquid lining of a weakly curved cylindrical tube. J. Fluid Mech. 331,373-403.
22. Johnson, M., Kamm, R. D., Ho, L. W., Shapiro, A. & Pedley, T. J. 1991 The nonlinear growth ofsurface-tension-driven instabilities of a thin annular film. J. Fluid Mech. 233, 141-156.
23. Jones, A. F. & Wilson, S. D. R. 1978 The film drainage problem in droplet coalescence. J. FluidMech. 87, 263-288.
24. Joseph, D. D., Bai, R., Chen, K. P. & Renardy, Y. Y. 1997 Core-annular flows. Annu. Rev. FluidMech. 29, 65-90.
25. Kalliadasis, S. & Chang, H.-C. 1994 Drop formation during the coating of vertical fibres. J. FluidMech. 261, 135-168.
26. Kas-Danouche, S., Papageorgiou, D. T. & Siegel, M. 2009 Nonlinear dynamics of core-annularflows in the presence of surfactant. J. Fluid Mech. 626, 415-448.
27. Keast, P. & Muir, K. H. 1991 Algorithm 688 EPDCOL: a more efficient PDECOL code. ACMTrans. Math. Software 17, 153-166.
28. Kerchman, V. 1995 Strongly nonlinear interfacial dynamics in core-annular flows. J. Fluid Mech.290, 131-166.
29. Kliakhandler, I. L., Davis, S. H. & Bankoff, S. G. 2001 Viscous beads on vertical fibre. J. FluidMech. 429, 381-390.
30. Lister, J. R., Rallison, J. M., King, A. A., Cummings, L. J. & Jensen, O. E. 2006 Capillarydrainage of an annular film: the dynamics of collars and lobes. J. Fluid Mech. 552, 311-343.
31. Maitland, G. C. 2000 Oil and gas production. Curr. Opinion Colloid Interface Sci. 5, 301-311.
32. Moffatt, H. K. 1977 Behaviour of a viscous film on the outer surface of a rotating cylinder.J. Mec. 16, 651-673.
33. Newhouse, L. A. & Pozrikidis, C. 1992 The Rayleigh-Taylor instability of a viscous-liquid layerresting on a plane wall. J. Fluid Mech. 217, 615-638.
34. Olbricht, W. L. 1996 Pore-scale prototypes of multiphase flow in porous media. Annu. Rev. FluidMech. 28, 187-213.
35. Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod.Phys. 69, 931-980.
36. Papageorgiou, D. T., Maldarelli, C. & Rumschitzki, D. S. 1990 Nonlinear interfacial stability ofcore-annular film flow. Phys. Fluids A 2, 340-352.
37. Quéré, D. 1990 Thin-films flowing on vertical fibers. Europhys. Lett. 13, 721-726.
38. Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31, 347-384.
39. Ruyer-Quil, C., Treveleyan, P., Giorgiutti-Dauphiné, F., Duprat, C. & Kalliadasis, S. 2008 Modelling film flows down a fibre. J. Fluid Mech. 603, 431-462.
40. Saville, D. A. 1997 Electrohydrodynamics: the Taylor-Melcher leaky-dielectric model. Annu. Rev.Fluid Mech. 29, 27-64.
41. Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217-252.
42. Squires, T. M. & Quake, S. R. 2005 Micro-fluidics: fluid physics at the nanoliter scale. Rev. Mod.Phys. 77, 977-1024.
43. Thorodsen, S. T. & Mahadevan, L. 1997 Experimental study of coating flows in a partially-filledhorizontally rotating cylinder. Exp. Fluids 23, 1-13.
44. Tsvelodub, O. Y. & Trifonov, Y. Y. 1992 Nonlinear waves on the surface of a falling liquid film.Part 2. Bifurcations of the first-family waves and other types of nonlinear waves. J. FluidMech. 244, 149-169.
45. Vaynblat, D., Lister, J. R. & Witelski, T. P. 2001 Rupture of thin viscous films by Van Der Waalsforces: evolution and self-similarity. Phys. Fluids A 13, 1130-1140.
46. Wang, Q. 2009 Nonlinear evolution of annular layers and liquid threads in electric fields. PhDthesis, New Jersey Institute of Technology, Newark, New Jersey.
47. Wei, H.-H. & Rumschitzki, D. 2002 The linear stability of a core-annular flow in an asymptoticallycorrugated tube. J. Fluid Mech. 466, 113-147.
48. Weidner, D. E., Schwartz, L. W. & Eres, M. H. 1997 Simulation of coating layer evolution anddrop formation on horizontal cylinders. J. Colloid Interface Sci. 187, 243-258.
49. Z h an g, W. W. & Lister, J. R. 1999 Similarity solutions for Van Der Waals rupture of a thin filmon a solid substrate. Phys. Fluids 11, 2454-2462.