Advertisement

Korean Journal of Chemical Engineering

, Volume 12, Issue 4, pp 421–427 | Cite as

Brownian motion of spherical particles near a deforming interface

  • Seung-Man Yang
Article

Abstract

In this paper Brownian diffusion of spherical particles near a deformable fluid interface was examined by considering interface deformations that were caused by impulsive motions of the Brownian particles. First, the velocity fields were constructed in terms of eigenfunctions on the bipolar coordinate system which facilitated the separation of variables. Then, the rate of interface deformation was determined to calculate the force acting on a Brownian sphere due to the interface relaxation back toward a flat configuration. In addition, the covariance function of velocity correlation was determined by solving the Langevin equation which included the effects of the interface relaxation. Finally, the diffusion coefficient of spherical particles was evaluated by utilizing the Einstein-Smoluchowski relation in conjunction with the particle mobility calculated in the presence of a deforming interface.

Key words

Brownian Motion Brownian Diffusivity Interface Deformation Velocity Autocorrelation Particle Mobility Bipolar Coordinates 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berdan, C. II and Leal, L. G., “Motion of a Sphere in the Presence of a Deformable Interface. I. Perturbation of the Interface from Flat: the Effects on Drag and Torque”,J. Colloid Interface Sci.,87, 62 (1982).CrossRefGoogle Scholar
  2. 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).CrossRefGoogle Scholar
  3. Buff, F. P., Lovett, R. A. and Stillingf, F. H., “Interfacial Density Profile for Fluids in the Critical Region”,Phys. Rev. Lett.,15, 621 (1965).CrossRefGoogle Scholar
  4. Fuentes, Y. O., Kim, S. and Jeffery, D. J., “Mobility Functions for Two Unequal Viscous Drops in Stokes Flow. I. Axisymmetric Motions”,Phys. Fluids,31, 2445 (1988).CrossRefGoogle Scholar
  5. Geller, A. S., Lee, S. H. and Leal, L. G., “The Creeping Motion of a Spherical Particle Normal to a Deformable Interface”,J. Fluid Meck,169, 27 (1986).CrossRefGoogle Scholar
  6. 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).CrossRefGoogle Scholar
  7. Happel, J. and Brenner, H., “Low Reynolds Number Hydrodynamics”, Martinus Nijhoff, Hague, Netherlands (1983).Google Scholar
  8. Hauge, E. H. and Martin-Löf, A., “Fluctuating Hydrodynamics and Brownian Motion”,J. Stat. Phys.,7, 259(1973).CrossRefGoogle Scholar
  9. Lee, S. H. and Leal, L. G., “The Motion of a Sphere in the Presence of a Deformable Interface. II. A Numerical Study of the Translation of a Sphere Normal to an Interface”,J. Colloid Interface Sci.,87, 81 (1982).CrossRefGoogle Scholar
  10. O’Neill, M. E. and Ranger, K. B., “The Approach of a Sphere to an Interface”,Phys. Fluids,26, 2035 (1983).CrossRefGoogle Scholar
  11. Russel, W. B., “Brownian Motion of Small Particles Suspended in Liquids”,Ann. Rev. Fluid Mech.,13, 425(1981).CrossRefGoogle Scholar
  12. Stoos, J. A. and Leal, L. G., “Particle Motion in Axisymmetric Stagnation Flow Toward an Interface”,AIChE J., 35(2), 196(1989).CrossRefGoogle Scholar
  13. Teletzke, G. F., Scriven, L. E. and Davis, H. T., “Gradient Theory of Wetting Transitions”,J. Colloid Interface Sci.,87, 550(1982).CrossRefGoogle Scholar
  14. 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).CrossRefGoogle Scholar
  15. Yang, S.-M., “Motions of a Sphere in a Time-Dependent Stokes Flow: A Generalization of Faxén’s Law”,Korean J. Chem. Eng.,4, 15(1987).CrossRefGoogle Scholar
  16. Yang, S.-M. and Leal, L. G., “Motions of a Fluid Drop near a Deformable Interface”,Int. J. Multiphase Flow,16, 597(1990).CrossRefGoogle Scholar
  17. Yang, S.-M., “Particle Motions Induced by Capillary Fluctuations of a Fluid-Fluid Interface”,Korean J. Chem. Eng.,12, 331 (1995).Google Scholar

Copyright information

© Korean Institute of Chemical Engineering 1995

Authors and Affiliations

  • Seung-Man Yang
    • 1
  1. 1.Department of Chemical EngineeringKorea Advanced Institute of Science and TechnologyTaejonKorea

Personalised recommendations