Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-19T00:33:49.044Z Has data issue: false hasContentIssue false
  • English
  • Français

Brownian motion in thin sheets of viscous fluid

Published online by Cambridge University Press:  29 March 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena
Get access Rights & Permissions [Opens in a new window]

Abstract

The drag on a cylindrical particle moving in a thin sheet of viscous fluid is calculated. It is supposed that the sheet is embedded in fluid of much lower viscosity. A finite steady drag is obtained, which depends logarithmically on the ratio of the viscosities. The Einstein relation is used to determine the diffusion coefficient for Brownian motion of the particle, with application to the movement of molecules in biological membranes. In addition, the Brownian motion is calculated using the Langevin equation, and a logarithmically time-dependent diffusivity is obtained for the case when the embedding fluid has zero viscosity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 4 , 24 February 1976 , pp. 593 - 602
Copyright
© 1976 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

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Bauer, D. R., Brauman, J. I. & Pecora, R. 1974 J. Am. Chem. Soc. 96, 6840.
Edidin, M. 1974 Ann. Rev. Biophys. Bioengng, 3, 179.
Einstein, A. 1956 Theory of Brownian Motion. Dover.
Hu, C. & Zwanzig, R. 1974 J. Chem. Phys. 60, 4354.
Kubo, R. 1957 J. Phys. Soc. Japan, 12, 570.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics Pergamon.
Richardson, S. 1973 J. Fluid Mech. 59, 707.
Saffman, P. G. & DELBRÜCK, M. 1975 Proc. Nat. Acad. Sci. 72, 3111.
Titchmarsh, E. C. 1948 Theory of Fourier Integrals. Oxford University Press.
Tranter, C. J. 1966 Integral Transforms. Methuen.
WAX, N. (ed.) 1954 Selected Papers on Noise and Stochastic Processes. Dover.
Zwanzig, R. & Bixon, M. 1975 J. Fluid Mech. 69, 21–810.