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Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse transverse to the axis

Published online by Cambridge University Press:  13 April 2010

B. U. FELDERHOF
B. U. FELDERHOF*
Affiliation:
Institut für Theoretische Physik A, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
*
†Email address for correspondence: ufelder@physik.rwth-aachen.de
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Abstract

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis and directed transverse to the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. The flow behaviour differs qualitatively from that for a point impulse in the direction of the axis in that there is no coupling to a diffusive sound mode. As a consequence, the transverse velocity autocorrelation function of a suspended Brownian particle decays at long times faster than t−3/2.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 649 , 25 April 2010 , pp. 329 - 340
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Felderhof, B. U. 2005 Effect of the wall on the velocity autocorrelation function and long-time tail of Brownian motion in a viscous compressible fluid. J. Chem. Phys. 123, 184903.CrossRefGoogle Scholar
Felderhof, B. U. 2006 Diffusion and velocity relaxation of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls. J. Chem. Phys. 124, 054111.CrossRefGoogle Scholar
Felderhof, B. U. 2009 Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse. J. Fluid Mech. 603, 285.CrossRefGoogle Scholar
Frydel, D. & Rice, S. A. 2006 Lattice Boltzmann study of the transition from quasi-two-dimensional to three-dimensional one particle hydrodynamics. Mol. Phys. 104, 1283.CrossRefGoogle Scholar
Frydel, D. & Rice, S. A. 2007 Hydrodynamic description of the long-time tails of the linear and rotational velocity autocorrelation functions of a particle in a confined geometry. Phys. Rev. E 76, 061404.CrossRefGoogle Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Table of Integrals, Series and Products. Academic Press.Google Scholar
Hagen, M. H. J., Pagonabarraga, I., Lowe, C. P. & Frenkel, D. 1997 Algebraic decay of velocity fluctuations in a confined fluid. Phys. Rev. Lett. 78, 3785.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff.Google Scholar
Hasimoto, H. 1976 Slow motion of a small sphere in a cylindrical domain. J. Phys. Soc. Japan 41, 2143.CrossRefGoogle Scholar
Ishii, K. & Hasimoto, H. 1980 Lateral migration of a spherical particle in flows in a circular tube. J. Phys. Soc. Japan 48, 2144.CrossRefGoogle Scholar
Jones, R. B. 1981 Hydrodynamic fluctuation forces. Physica A 105, 395.CrossRefGoogle Scholar
Liron, N. & Shahar, R. 1978 Stokes flow due to a Stokeslet in a pipe. J. Fluid Mech. 78, 727.CrossRefGoogle Scholar
Lorentz, H. A. 1907 Ein allgemeiner Satz, die Bewegung einer reibenden Flüssigkeit betreffend, nebst einigen Anwendungen desselben. In Abhandlungen über theoretische Physik, p. 23. Teubner.Google Scholar
Pagonabarraga, I., Hagen, M. H. J., Lowe, C. P. & Frenkel, D. 1999 Short-time dynamics of colloidal suspensions in confined geometries. Phys. Rev. E 59, 4458.CrossRefGoogle Scholar