DOI: 10.1017/s0022112076001511. Brownian motion in thin sheets of viscous fluid

Brownian motion in thin sheets of viscous fluid

10.1017/s0022112076001511

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

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.

Bibliography

Saffman, P. G. (1976). Brownian motion in thin sheets of viscous fluid. Journal of Fluid Mechanics, 73(4), 593â602.

Authors 1

P. G. Saffman (first)

References 14 Referenced 308

WAX, N. (ed.) 1954 Selected Papers on Noise and Stochastic Processes. Dover.
Hu, C. & Zwanzig, R. 1974 J. Chem. Phys. 60,4354. (10.1063/1.1680910)
Edidin, M. 1974 Ann. Rev. Biophys. Bioengng,3,179. (10.1146/annurev.bb.03.060174.001143)
Bauer, D. R. , Brauman, J. I. & Pecora, R. 1974 J. Am. Chem. Soc. 96,6840. (10.1021/ja00829a004)
Einstein, A. 1956 Theory of Brownian Motion. Dover.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Zwanzig, R. & Bixon, M. 1975 J. Fluid Mech. 69,21–810.
Tranter, C. J. 1966 Integral Transforms. Methuen.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics Pergamon.
Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Titchmarsh, E. C. 1948 Theory of Fourier Integrals. Oxford University Press.
Kubo, R. 1957 J. Phys. Soc. Japan,12,570. (10.1143/JPSJ.12.570)
Saffman, P. G. & DELBRÜCK, M. 1975 Proc. Nat. Acad. Sci. 72,3111.
Richardson, S. 1973 J. Fluid Mech. 59,707. (10.1017/S0022112073001801)

Dates

Type	When
Created	19 years, 5 months ago (March 29, 2006, 4:18 a.m.)
Deposited	6 years, 4 months ago (April 4, 2019, 12:56 p.m.)
Indexed	1 week ago (Aug. 22, 2025, 12:47 a.m.)
Issued	49 years, 6 months ago (Feb. 24, 1976)
Published	49 years, 6 months ago (Feb. 24, 1976)
Published Online	19 years, 5 months ago (March 29, 2006)
Published Print	49 years, 6 months ago (Feb. 24, 1976)

Funders 0

None

BibTeX

@article{Saffman_1976, title={Brownian motion in thin sheets of viscous fluid}, volume={73}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112076001511}, DOI={10.1017/s0022112076001511}, number={4}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Saffman, P. G.}, year={1976}, month=feb, pages={593–602} }

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