Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-06-09T04:46:08.668Z Has data issue: false hasContentIssue false
  • English
  • Français

Rotatory Brownian motion of a rigid dumbbell

Published online by Cambridge University Press:  29 March 2006

Shousun C. Szu  and
J. J. Hermans
Shousun C. Szu
Affiliation:
Department of Chemistry, University of North Carolina, Chapel Hill
J. J. Hermans
Affiliation:
Department of Chemistry, University of North Carolina, Chapel Hill
Get access Rights & Permissions [Opens in a new window]

Abstract

The frictional torque on a dumbbell rotating with time-dependent angular velocity is calculated from the hydrodynamic interaction between the two ends of the dumbbell. This leads to the correlation function for the random torque in rotatory Brownian motion. Although the motion of each dumbbell end has the characteristics of a translational motion, the correlation function at large times decays like t−5/2, as in the case of a solid sphere. The correlation function may be calculated for the limiting case of very small angular displacements. The results for displacements of arbitrary magnitude are the same provided that terms quadratic in the angular velocity are negligible.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 66 , Issue 2 , 6 November 1974 , pp. 385 - 390
Copyright
© 1974 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

Berne, B. J. 1972 Hydrodynamic theory of the angular velocity autocorrelation function J. Chem. Phys. 56, 2164–2168.Google Scholar
Burgers, J. M. 1938 On the motion of small particles of elongated form in a viscous liquid. 2nd Rep. on Viscosity & Plasticity, N.H. Uitgev. Mij, Amsterdam.Google Scholar
Case, K. M. 1971 Velocity fluctuations of a body in a fluid Phys. Fluids, 14, 2091–2095.Google Scholar
Chow, T. S. 1973 Simultaneous translational and rotational Brownian movement of particles of arbitrary shape Phys. Fluids, 16, 31–34.Google Scholar
Chow, T. S. & Hermans, J. J. 1972a Effect of inertia on the Brownian motion of rigid particles in a viscous fluid J. Chem. Phys. 56, 3150–3154.Google Scholar
Chow, T. S. & Hermans, J. J. 1972b On the hydrodynamic interaction of two Brownian particles in a viscous, inert fluid Kolloid-Z. u. Z. Polymere, 250, 404–409.Google Scholar
Kirkwood, J. G. 1956 Non-Newtonian viscoelastic properties of rod-like macromolecules in solution J. Chem. Phys. 24, 665–669.Google Scholar
Kowalewski, G. 1930 Integralgleichungen. Berlin: Walter de Gruyter.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Addison-Wesley.
Oseen, C. W. 1927 Hydrodynamik. Leipzig: Akademische Verlagsgesellschaft.
Szu, S. C. & Hermans, J. J. 1973 J. Polymer Phys. 11, 1941–1948.