Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T12:21:06.857Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow of a viscous incompressible fluid after a sudden point impulse near a wall

Published online by Cambridge University Press:  15 June 2009

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]
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow of a viscous incompressible fluid generated by a sudden impulse near a wall with no-slip boundary condition is studied on the basis of the linearized Navier–Stokes equations. It turns out that the flow differs significantly from that for the perfect slip boundary condition, except far from the wall and at short times. At short time the flow is irrotational and can be described by a potential which varies with the square root of time. Correspondingly the pressure disturbance is quite large at short times. It shows an oscillation at later times if the impulse is directed parallel to the wall and decays monotonically for impulse perpendicular to the wall.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 629 , 25 June 2009 , pp. 425 - 443
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Acheson, D. J. 1990 Elementary Fluid Dynamics. Clarendon.CrossRefGoogle Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids. Clarendon.Google Scholar
Cichocki, B. & Felderhof, B. U. 2000 Long-time tails in the solid-body motion of a sphere immersed in a suspension. Phys. Rev. E 62, 5383.Google Scholar
Felderhof, B. U. 2005 a Effect of the wall on the velocity autocorrelation function and long-time tail of Brownian motion. J. Phys. Chem. 109, 21406.CrossRefGoogle ScholarPubMed
Felderhof, B. U. 2005 b. Effect of the wall on the velocity autocorrelation function and long-time tail of Brownian motion: erratum J. Phys. Chem. 110, 13304.CrossRefGoogle Scholar
Felderhof, B. U. 2005 c 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. Diffusion and velocity relaxation of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls 124, 054111.Google Scholar
Felderhof, B. U. 2009 Diffusion and convection after escape from a potential well. Physica A 388, 1388.CrossRefGoogle Scholar
Frydel, D. & Rice, S. A. 2006 Lattice-Boltzmann study of the transition from quasi-two-dimensional to three-dimensional one particle hydrodynamics. Lattice-Boltzmann study of the transition from quasi-two-dimensional to three-dimensional one particle hydrodynamics 104, 1283.Google 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.Google Scholar
Hagen, M. H. J., Pagonabarraga, I., Lowe, C. P. & Frenkel, D. 1997 Algebraic decay of velocity fluctuations in a confined fluid. Algebraic decay of velocity fluctuations in a confined fluid 78, 3785.Google Scholar
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff.Google Scholar
Jeney, S., Lukić, B., Kraus, J. A., Franosch, T. & Forró, L. 2008 Anisotropic memory effects in confined colloidal diffusion. Phys. Rev. Lett. 100, 240604.CrossRefGoogle ScholarPubMed
Jones, R. B. 1981 Hydrodynamic fluctuation forces. Physica A 105, 395.CrossRefGoogle Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.Google Scholar
Kraus, J. A. 2007 Hydrodynamics at micro- and nanoscales. Diploma thesis, University of Munich.Google Scholar
Lighthill, J. 1986 An Informal Introduction to Theoretical Fluid Mechanics. Clarendon.Google Scholar
Oseen, C. W. 1927 Hydrodynamik. Akademische Verlagsgesellschaft.Google Scholar
Pagonabarraga, I., Hagen, M. H. J., Lowe, C. P. & Frenkel, D. 1998 Algebraic decay of velocity fluctuations near a wall. Phys. Rev. E 58, 7288.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
Pozrikidis, C. 1989 A singularity method for unsteady linearized flow. Phys. Fluids A 1, 1508.CrossRefGoogle Scholar
Schlichting, H. 1987 Boundary Layer Theory. McGraw-Hill.Google Scholar
Sommerfeld, A. 1909 Über die Ausbreitung der Wellen in der drahtlosen Telegraphie. Über die Ausbreitung der Wellen in der drahtlosen Telegraphie 28, 665.Google Scholar
Sommerfeld, A. & Renner, F. 1942 Strahlungsenergie und Erdabsorption bei Dipolantennen. Strahlungsenergie und Erdabsorption bei Dipolantennen 41, 1.Google Scholar