Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T02:48:06.096Z Has data issue: false hasContentIssue false
  • English
  • Français

Shape oscillations of drops in the presence of surfactants

Published online by Cambridge University Press:  26 April 2006

Hui-Lan Lu  and
Robert E. Apfel
Hui-Lan Lu
Affiliation:
Department of Mechanical Engineering, Yale University, New Haven, CT 06520, USA
Robert E. Apfel
Affiliation:
Department of Mechanical Engineering, Yale University, New Haven, CT 06520, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The shape oscillations of drops in another fluid with or without surfactants has been analysed by normal mode expansions. The effects of surfactants are accommodated by considering the Gibbs elasticity, associated with the redistribution of surfactants, and a Boussinesq surface fluid with two surface viscosities. A general transcendental equation for the complex frequency of the free oscillations is derived. Explicit dispersion relations are given for fluids of small bulk viscosities and an interface of small, moderate, and large interfacial properties by a perturbation method. We have found that the oscillation always damps out faster for an interface exhibiting interfacial properties other than the interfacial tension, and the Gibbs elasticity is the most important parameter that alters the free-oscillation frequency and the damping constant. Moreover, the energy dissipation for an extensible interface can be much higher than that of an inextensible interface owing to the strong vorticity generated in the boundary layers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 351 - 368
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adamson, A. W.: 1982 Physical Chemistry of Surfaces, 4th edn, pp. 484–485, 56–58, 10–39. 112–114, 120–121, 117, 84. Wiley.
Boussinesq, J.: 1913 Velocity of the fall of a spherical drop into a viscous fluid of less specific gravity. Ann. Chim. Phys. (8) 29, 364.Google Scholar
Bupara, S. S.: 1964 Spontaneous movements of small round bodies in viscous fluids. Ph.D. dissertation, Department of Chemical Engineering, University of Minnesota.
Chandrasekhar, S.: 1961 Hydrodynamics and Hydromagnetic Stability. Dover.
Cohen, S. & Swiatecki, W. J., 1962 The deformation energy of a charged drop. IV: Evidence for a discontinuity in the conventional family of saddle point shapes. Ann. Phys. 19, 67.Google Scholar
Hsu, C. & Apfel, R. E., 1987 Model for the quadrupole oscillations of drops for determining interfacial tension. J. Acoust. Soc. Am. 82, 2135.Google Scholar
Lamb, H.: 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M., 1959 Fluid Mechanics, pp. 53, 91. Pergamon.
Levich, V. G.: 1962 Physicochemical Hydrodynamics. Prentice-Hall.
Lu, H.: 1988 Study of interfacial dynamics of drops in the presence of surfactants or contaminants. Ph.D. thesis, Department of Mechanical Engineering, Yale University.
Lu, H. & Apfel, R. E., 1990 Quadrupole oscillations of drops for studying interfacial properties. J. Colloid Interface Sci. 134, 245.Google Scholar
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.Google Scholar
Maeston, P. L.: 1980 Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses—Theory. J. Acoust. Soc. Am. 67, 15.Google Scholar
Miller, C. A. & Scriven, L. E., 1968 The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417.Google Scholar
Nix, J. R.: 1972 Calculation of fission barriers for heavy and superheavy nuclei. Ann. Rev. Nucl. Sci. 22, 65.Google Scholar
Prosperetti, A.: 1977 Viscous effects on perturbed spherical flows. Q. Appl. Maths 35, 339.Google Scholar
Prosperetti, A.: 1980 Free oscillations of drops and bubbles: the initial-value problem. J. Fluid Mech. 100, 333.Google Scholar
Rayleigh, Loed 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 71.Google Scholar
Rayleigh, Loed 1882 On the equilibrium of liquid conducting masses charged with electricity. Phil. Mag. 14, 184.Google Scholar
Rayleigh, Loed 1902 On the pressure of vibrations. Phil. Mag. 3, 338.Google Scholar
Reichl, L. E.: 1980 A Modern Course in Statistical Physics, pp. 42–44, 66–68. University of Texas Press.
Reid, W. H.: 1960 The oscillations of a viscous liquid drop. Q. Appl. Maths 18, 86.Google Scholar
Scriven, L. E.: 1960 Dynamics of a fluid interface. Chem. Engng Sci. 12, 98.Google Scholar
Tempel, M. & Riet, R. P., 1965 Damping of waves by surface active materials. J. Chem. Phys. 42, 2769.Google Scholar
Ting, L., Wasan, D. T. & Miyano, K., 1985 Longitudinal surface waves for the study of dynamic properties of surfactant systems. III. Liquid-liquid interface. J. Colloid Interface Sci. 107, 345.Google Scholar