Abstract.
The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the shear rate and the trap distance. Shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are linear in the shear rate, asymmetric in time, and occur for one particle as well as between both particles. Moreover, the shear rate enters as a quadratic correction to the well-known correlations of random displacements along parallel spatial directions. The correlation functions depend on the orientation of the connection vector between the potential minima with respect to the flow direction. As a consequence, the inter-particle cross-correlations between orthogonal fluctuations can have zero, one or two local extrema as a function of time. Possible experiments for detecting these predicted correlations are described.
Similar content being viewed by others
References
G. Taylor, Proc. R. Soc. London, Ser. A 219, 186 (1953)
J. Ottino, S. Wiggins, Philos. Trans. R. Soc. London, Ser. A 362, 923 (2004)
A. Groisman, V. Steinberg, Nature 410, 905 (2001)
J.K.G. Dhont, An Introduction to Dynamics of Colloids (Elsevier, Amsterdam, 1996)
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986)
J.C. Meiners, S.R. Quake, Phys. Rev. Lett. 82, 2211 (1999)
M. Reichert, H. Stark, Phys. Rev. E 69, 031407 (2004)
D. Smith, H. Babcock, S. Chu, Science 283, 1724 (1999)
P.G. deGennes, Science 276, 1999 (1997)
A. Groisman, V. Steinberg, Nature 405, 53 (2000)
T. Perkins, D. Smith, R. Larson, S. Chu, Science 268, 83 (1995)
F. Brochard-Wyart, Europhys. Lett. 23, 105 (1993)
R.G. Larson, T.T. Perkins, D.E. Smith, S. Chu, Phys. Rev. E 55, 1794 (1997)
R. Rzehak, D. Kienle, T. Kawakatsu, W. Zimmermann, Europhys. Lett. 46, 821 (1999)
R. Rzehak, W. Kromen, T. Kawakatsu, W. Zimmermann, Eur. Phys. J. E 2, 3 (2000)
D. Kienle, W. Zimmermann, Macromolecules 34, 9173 (2001)
R. Rzehak, W. Zimmermann, Phys. Rev. E 68, 021804 (2003)
P. Szymczak, M. Cieplak, J. Chem. Phys. 125, 164903 (2006)
D. Kienle, R. Rzehak, W. Zimmermann, submitted (2010)
P. Doyle, B. Ladoux, J. Viovy, Phys. Rev. Lett. 84, 4769 (2000)
M. Webster, J. Yeomans, J. Chem. Phys. 122, 164903 (2005)
R. Delgado-Buscalioni, Phys. Rev. Lett. 96, 088303 (2006)
C.A. Lueth, E.S.G. Shaqfeh, Macromolecules 42, 9170 (2009)
Y. Zhang et al., J. Chem. Phys. 130, 234902 (2009)
J. Hur, E. Shaqfeh, R. Larson, J. Rheol. 44, 713 (2000)
C. Schroeder, R. Teixeira, E. Shaqfeh, S. Chu, Phys. Rev. Lett. 95, 018301 (2005)
S. Gerashchenko, V. Steinberg, Phys. Rev. Lett. 96, 038304 (2006)
B. Eckhardt, R. Pandit, Eur. Phys. J. B 33, 373 (2003)
G. Khujadze, M. Oberlack, G. Chagelishvili, Phys. Rev. Lett. 97, 034501 (2006)
K. Miyazaki, D. Bedeaux, Physica A 217, 53 (1995)
G. Subramanian, J. Brady, Physica A 334, 343 (2004)
Y. Drossinos, M.W. Reeks, Phys. Rev. E 71, 031113 (2005)
L. Holzer, J. Bammert, R. Rzehak, W. Zimmermann, Phys. Rev. E 81, 041124 (2010)
A. Ziehl et al., Phys. Rev. Lett. 103, 230602 (2009)
R. Simmons, J. Finer, S. Chu, J. Spudich, Biophys. J. 70, 1813 (1996)
S. Henderson, S. Mitchell, P. Bartlett, Phys. Rev. Lett. 88, 088302 (2002)
E.R. Dufresne, T.M. Squires, M. Brenner, D.G. Grier, Phys. Rev. Lett. 85, 3317 (2000)
T. Franosch, S. Jeney, Phys. Rev. E 79, 031402 (2009)
J. Crocker et al., Phys. Rev. Lett. 85, 888 (2000)
P.T. Korda, M.B. Taylor, D.G. Grier, Phys. Rev. Lett. 89, 128301 (2002)
M.P. MacDonald, G.C. Spalding, K. Dholakia, Nature 426, 421 (2003)
J. Bammert, S. Schreiber, W. Zimmermann, Phys. Rev. E 77, 042102 (2008)
J. Bammert, W. Zimmermann, Eur. Phys. J. E 28, 331 (2009)
J. Crocker, D. Grier, J. Colloid Interface Sci. 179, 298 (1996)
B. Lukic et al., Phys. Rev. Lett. 95, 160601 (2005)
M. Atakhorrami, G.H. Koenderink, C.F. Schmidt, F.C. MacKintosh, Phys. Rev. Lett. 95, 208302 (2005)
S. Chu, Science 253, 861 (1991)
M. Polin, Y. Roichman, D.G. Grier, Phys. Rev. E 77, 051401 (2008)
G.G. Stokes, Trans. Cambridge Philos. Soc. IX, 8 (1850)
L.D. Landau, E.M. Lifschitz, Lehrbuch der Theoretischen Physik: Hydrodynamik, 2nd edition (Akademie Verlag, Berlin, 1987)
L. Holzer, Ph.D. Thesis, Universität Bayreuth (2009)
R. Rzehak, W. Zimmermam, Physica A 324, 495 (2003)
S. Martin, M. Reichert, H. Stark, T. Gisler, Phys. Rev. Lett. 97, 248301 (2006)
A. Ziehl, Ph.D. Thesis, Universität des Saarlandes (2010)
S. Schreiber, J. Bammert, P. Peyla, W. Zimmermann, in preparation (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bammert, J., Holzer, L. & Zimmermann, W. Dynamics of two trapped Brownian particles: Shear-induced cross-correlations. Eur. Phys. J. E 33, 313–325 (2010). https://doi.org/10.1140/epje/i2010-10675-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epje/i2010-10675-2