Skip to main content

Particle motions induced by capillary fluctuations of a fluid-fluid interface

Korean Journal of Chemical Engineering volume 12, pages 331–339 (1995)Cite this article

Abstract

The motion of a Brownian particle in the presence of a deformable interface is studied by considering the random distortions of interface shape due to spontaneous thermal impulses from the surrounding fluid. The fluctuation-dissipation theorem is derived for the spontaneous fluctuations of interface shape using the method of normal modes in conjunction with a Langevin type equation of motion for a Brownian particle, in which the fluctuating force arises from the continuum motions induced near the particle by the fluctuation of interface shape. The analysis results in the prediction of autocorrelation functions for the location of the dividing surface, for the random force acting on the particle, and for the particle velocity. The particle velocity correlation, in turn, yields the effective diffusion coefficient due to random fluctuations of the interface shape.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  • Batchelor, G. K., “Developments in Microhydrodynamics”, In Theoretical and Applied Mechanics”, ed. W. Koiter, Amsterdam, Netherlands (1976).

  • Brenner, H. and Leal, L. G., “A Model of Surface Diffusion on Solids”,J Colloid Interface Sci.,62, 238 (1977).

    Article  CAS  Google Scholar 

  • Brenner, H. and Leal, L. G., “Conservation and Constitutive Equations for Adsorbed Species Undergoing Surface Diffusion and Convection at a Fluid-Fluid Interface”,J. Colloid Interface Sci.,88, 136 (1982).

    Article  CAS  Google Scholar 

  • Buff, F. P., Lovett, R. A. and Stillinger, F. H., “Interfacial Density Profile for Fluids in the Critical Region”,Phys. Rev Lett,15, 621 (1965).

    Article  Google Scholar 

  • Chaplin, J. R., “Nonlinear Forces on a Horizontal Cylinder beneath Waves”,J Fluid Mech.,147, 449 (1984).

    Article  Google Scholar 

  • Evans, R., “The Role of Capillary Wave Fluctuations in Determining the Liquid-Vapor Interface”,Mol. Phys.,42, 1169 (1981).

    Article  CAS  Google Scholar 

  • Gotoh, T. and Kaneda, Y., “Effect of an Infinite Plane Wall on the Motion of a Spherical Brownian Particle”,J. Chem. Phys.,76, 3193 (1982).

    Article  CAS  Google Scholar 

  • Hauge, E. H. and Martin-Löf, A., “Fluctuating Hydrodynamics and Brownian Motion”,J Stat. Phys.,7, 259 (1973).

    Article  Google Scholar 

  • Hinch, E. J., “Application of the Langevin Equation to Fluid Suspensions”,J. Fluid Mech.,72, 499 (1975).

    Article  Google Scholar 

  • Jhon, M. S., Desai, R. C. and Dahler, J. S., “The Origin of Surface Wave”,J. Chem. Phys.,68, 5615 (1978).

    Article  CAS  Google Scholar 

  • Kreuzer, H. J., “Nonequilibrium Thermodynamics and its Statistical Foundations”, Oxford University Press, Oxford (1984).

    Google Scholar 

  • Lamb, H., “Hydrodynamics”, Dover, New York, N.Y. (1932).

    Google Scholar 

  • Landau, L. D. and Lifshitz, E. M., “Fluid Mechanics”, Pergamon Press, New York, N.Y. (1959).

    Google Scholar 

  • Landau, L. D. and Lifshitz, E. M., “Statistical Physics. Part I”, Pergamon Press, New York, N.Y. (1980).

    Google Scholar 

  • Lee, S. H., Chadwick, R. S. and Leal, L. G., “Motion of a Sphere in the Presence of a Plane Interface. Part 1. An Approximation Solution by Generalization of the Method of Lorentz”,J Fluid Mech.,93, 705(1979).

    Article  Google Scholar 

  • Lee, S. H. and Leal, L. G., “Motion of a Sphere in the Presence of a Plane Interface. Part 2. An Exact Solution in Bipolar Coordinates”,J. Fluid Mech.,98, 193 (1980).

    Article  Google Scholar 

  • Squire, H. B., “On the Stability for Three-Dimensional Disturbances of Viscous Fluid Flow between Parallel Walls”,Proc. Roy. Soc. London,A142, 621 (1933).

    Article  Google Scholar 

  • Teletzke, G. F., Scriven, L. E. and Davis, H. T., “Gradient Theory of Wetting Transitions”,J. Colloid Interface Sci.,87, 550 (1982).

    Article  CAS  Google Scholar 

  • Whitham, G. B., “Linear and Nonlinear Waves”, Wiley-Interscience, New York, N.Y. (1974).

    Google Scholar 

  • Yang, S.-M. and Leal, L. G., “Particle Motion in Stokes Flow near a Plane Fluid-Fluid Interface. Part 1. Slender Body in a Quiescent Fluid”,J.Fluid Mech.,136, 393 (1983).

    Article  CAS  Google Scholar 

  • Yang, S.-M. and Leal, L. G., “Particle Motion in Stokes Flow near a Plane Fluid-Fluid Interface. Part 2. Linear Shear and Axisymmetric Straining Flows”,J Fluid Mech.,149, 275 (1984).

    Article  CAS  Google Scholar 

  • Yang, S.-M., “Motions of a Sphere in a Time-Dependent Stokes Flow: A Generalization of Faxén’s Law”,KJChE,4(1), 15 (1987).

    CAS  Google Scholar 

  • Yang, S.-M. and Hong, W.-H., “Brownian Diffusion near a Plane Fluid Interface”,KJChE,4, 187(1987).

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusung-dong, Yusung-ku, 305-701, Taejon

    Seung-Man Yang

Authors
  1. Seung-Man Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yang, SM. Particle motions induced by capillary fluctuations of a fluid-fluid interface. Korean J. Chem. Eng. 12, 331–339 (1995). https://doi.org/10.1007/BF02705765

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02705765

Key words

  • Brownian Particle and Diffusion
  • Interface Fluctuations
  • Capillary Wave
  • Velocity Autocorrelation
  • Langevin Equation
  • Normal Mode Decomposition