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Brownian motion in thin sheets of viscous fluid

Published online by Cambridge University Press:  29 March 2006

P. G. Saffman
Applied Mathematics, California Institute of Technology, Pasadena


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.

Research Article
© 1976 Cambridge University Press

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