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Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse

Published online by Cambridge University Press:  11 February 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: [email protected]
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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 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. Owing to the finite velocity of sound the flow behaviour differs qualitatively from that of an incompressible fluid. The flow velocity and the pressure disturbance at any fixed point different from the source point vanish at short time and decay at long times with a t−3/2 power law.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 644 , 10 February 2010 , pp. 97 - 106
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Bedeaux, D. & Mazur, P. 1974 A generalization of Faxen's theorem to nonsteady motion of a sphere through a compressible fluid in arbitrary flow. Physica A 78, 505.Google Scholar
Blake, J. R. 1979 On the generation of viscous toroidal eddies in a cylinder. J. Fluid Mech. 95, 209.CrossRefGoogle Scholar
Faxén, H. 1959 About T. Bohlin's paper: on the drag on rigid spheres, moving in a viscous liquid inside cylindrical tubes. Kolloid. Z. 167, 146.CrossRefGoogle Scholar
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. 2009 Transient flow of a viscous incompressible fluid in a circular tube after a sudden point impulse. J. Fluid Mech. 603, 285.CrossRefGoogle 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
Hasimoto, H. 1976 Slow motion of a small sphere in a cylindrical domain. J. Phys. Soc. Jpn 41, 2143.CrossRefGoogle Scholar
Jones, R. B. 1981 Hydrodynamic fluctuation forces. Physica A 105, 395.CrossRefGoogle Scholar
Kubo, R., Toda, M. & Hashitsume, N. 1991 Statistical Physics II. Springer.CrossRefGoogle Scholar
Liron, N. & Shahar, R. 1978 Stokes flow due to a Stokeslet in a pipe. J. Fluid Mech. 78, 727.CrossRefGoogle 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