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Wave motion of low-tension interfaces with electrical double layers

Published online by Cambridge University Press:  29 March 2006

C. A. Miller
C. A. Miller
Affiliation:
Department of Chemical Engineering, Carnegie-Mellon University, Pittsburgh
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Abstract

An approximate solution is developed for the system of equations describing flow and ion transport in a diffuse electrical double layer slightly perturbed from equilibrium. The approximation is valid only when the potential difference across the diffuse layer is small, less than about 25 mV. When the approximate solution is used to study wave motion of low-tension interfaces, it is found chat ion transport in diffuse layers slows down interfacial motion in both stable and unstable situations. Although the slowing effect is relatively small (a few per cent or less) when the small potential approximation applies, the form of the solution suggests that the effect could be significant for potential differences in the 50–100 mV range, which exist in many systems of interest. There are also indications that the slowing effect can significantly influence wave motion of thin liquid films with diffuse layers, e.g. soap films, although a detailed analysis of the thin-film situation is not carried out.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 4 , 24 October 1972 , pp. 641 - 657
Copyright
© 1972 Cambridge University Press

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References

Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. Wiley.
Buck, R. P. 1969 Diffuse layer charge relaxation at the ideally polarized electrode. J. Electroanal. Chem. 23, 219–240.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Mann, J. A. & Hansen, R. S. 1963 Propagation characteristics of capillary ripples. III. Capillary ripple velocity and attenuation dispersion on clean water surfaces and on various monolayers. J. Colloid Sci. 18, 805–819.Google Scholar
Melcher, J. R. 1963 Field-Coupled Surface Waves. M.I.T. Press.
Melcher, J. R. & Smith, C. V. 1969 Electrohydrodynamic charge relaxation and interfacial perpendicular-field instability. Phys. Fluids, 12, 778–790.Google Scholar
Miller, C. A. & Scriven, L. E. 1968 The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417–435.Google Scholar
Miller, C. A. & Scriven, L. E. 1970a Interfacial instability due to electrical forces in double layers. I. General considerations. J. Colloid Interface Sci. 33, 360–370.Google Scholar
Miller, C. A. & Scriven, L. E. 1970b Interfacial instability due to electrical forces in double layers. II. Stability of interfaces with diffuse layers. J. Colloid Interface Sci. 33, 371–383.Google Scholar
Penfield, P. & Haus, H. A. 1967 Electrodynamics of Moving Media. M.I.T. Press.
Sanfeld, A. 1968 Introduction to the Thermodynamics of Charged and Polarized Layers. Interscience.
Saville, D. A. 1971 Electrohydrodynamic stability: effects of charge relaxation at the interface of a liquid jet. J. Fluid Mech. 48, 815–827.Google Scholar
Taylor, G. I. & McEwan, A. D. 1965 The stability of a horizontal interface in a vertical electric field. J. Fluid Mech. 22, 1–15.Google Scholar
Verwey, E. J. W. & Overbeek, J. T. G. 1948 Theory of the Stability of Lyophobic Colloids. Elsevier.
Vrij, A., Hesselink, F. T., Lucassen, J. & van den Tempel, M. 1970 Waves in thin liquid films. II. Symmetrical modes in very thin films and film rupture. Proc. K. Ned. Akad. Wet. B73, 124–135.Google Scholar
Zadoff, L. N. & Begun, M. 1968 Resistive instabilities of a viscous fluid with horizontal boundary. Phys. Fluids, 11, 1238–1244.Google Scholar