Skip to main content
    • Aa
    • Aa

Brownian motion in thin sheets of viscous fluid

  • P. G. Saffman (a1)

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.

Hide All
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, 21810.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 61 *
Loading metrics...

Abstract views

Total abstract views: 323 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.