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Probability distribution of a trapped Brownian particle in plane shear flows
Phys. Rev. E 82, 052102 – Published 4 November, 2010
DOI: https://doi.org/10.1103/PhysRevE.82.052102
Abstract
We investigate the statistical properties of an overdamped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is determined via the corresponding Smoluchowski equation, which is solved analytically for a linear shear flow. In the case of a plane Poiseuille flow, analytical approximations for the distribution are obtained by a perturbation analysis and are substantiated by numerical results. There is good agreement between the two approaches for a wide range of parameters.
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References (24)
- J. K. G. Dhont, An Introduction to Dynamics of Colloids (Elsevier, Amsterdam, 1996).
- H. Berg, Random Motions in Biology (Princeton University Press, Princeton, 1993).
- R. T. Foister and T. G. M. van de Ven, J. Fluid Mech. 96, 105 (1980).
- Y. Drossinos and M. W. Reeks, Phys. Rev. E 71, 031113 (2005).
- D. C. Swailes, Y. Ammar, M. W. Reeks, and Y. Drossinos, Phys. Rev. E 79, 036305 (2009).
- M. H. Vainstein and J. M. Rubi, Phys. Rev. E 75, 031106 (2007).
- K. Miyazaki and D. Bedeaux, Physica A 217, 53 (1995).
- G. Subramanian and J. F. Brady, Physica A 334, 343 (2004).
- A. Ziehl, J. Bammert, L. Holzer, C. Wagner, and W. Zimmermann, Phys. Rev. Lett. 103, 230602 (2009).
- L. Holzer, J. Bammert, R. Rzehak, and W. Zimmermann, Phys. Rev. E 81, 041124 (2010).
- J. Bammert, L. Holzer, and W. Zimmermann, Eur. Phys. J. E (in print), e-print arXiv:1006.1560.
- H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer-Verlag, Berlin, 1989).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, England, 1992).
- R. Skalak and P. I. Branemar, Science 164, 717 (1969).
- H. Noguchi and G. Gompper, Proc. Natl. Acad. Sci. U.S.A. 102, 14159 (2005).
- G. Danker, P. M. Vlahovska, and C. Misbah, Phys. Rev. Lett. 102, 148102 (2009).
- B. Kaoui, G. Biros, and C. Misbah, Phys. Rev. Lett. 103, 188101 (2009).
- J. C. Meiners and S. R. Quake, Phys. Rev. Lett. 84, 5014 (2000).
- T. Perkins, D. Smith, R. Larson, and S. Chu, Science 268, 83 (1995).
- F. Brochard-Wyart, EPL 23, 105 (1993).
- R. Rzehak, D. Kienle, T. Kawakatsu, and W. Zimmermann, EPL 46, 821 (1999).
- R. Rzehak, W. Kromen, T. Kawakatsu, and W. Zimmermann, Eur. Phys. J. E 2, 3 (2000).
- P. S. Doyle, B. Ladoux, and J. L. Viovy, Phys. Rev. Lett. 84, 4769 (2000).
- L. Holzer and W. Zimmermann, Phys. Rev. E 73, 060801(R) (2006).