Polymer scaling and dynamics in steady-state sedimentation at infinite Péclet number

V. Lehtola, O. Punkkinen, and T. Ala-Nissila
Phys. Rev. E 76, 051802 – Published 8 November 2007

Abstract

We consider the static and dynamical behavior of a flexible polymer chain under steady-state sedimentation using analytic arguments and computer simulations. The model system comprises a single coarse-grained polymer chain of N segments, which resides in a Newtonian fluid as described by the Navier-Stokes equations. The chain is driven into nonequilibrium steady state by gravity acting on each segment. The equations of motion for the segments and the Navier-Stokes equations are solved simultaneously using an immersed boundary method, where thermal fluctuations are neglected. To characterize the chain conformation, we consider its radius of gyration RG(N). We find that the presence of gravity explicitly breaks the spatial symmetry leading to anisotropic scaling of the components of RG with N along the direction of gravity RG, and perpendicular to it RG,, respectively. We numerically estimate the corresponding anisotropic scaling exponents ν0.79 and ν0.45, which differ significantly from the equilibrium scaling exponent νe=0.588 in three dimensions. This indicates that on the average, the chain becomes elongated along the sedimentation direction for large enough N. We present a generalization of the Flory scaling argument, which is in good agreement with the numerical results. It also reveals an explicit dependence of the scaling exponents on the Reynolds number. To study the dynamics of the chain, we compute its effective diffusion coefficient D(N), which does not contain Brownian motion. For the range of values of N used here, we find that both the parallel and perpendicular components of D increase with the chain length N, in contrast to the case of thermal diffusion in equilibrium. This is caused by the fluid-driven fluctuations in the internal configuration of the polymer that are magnified as polymer size becomes larger.

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  • Received 9 March 2007

DOI:https://doi.org/10.1103/PhysRevE.76.051802

©2007 American Physical Society

Authors & Affiliations

V. Lehtola1, O. Punkkinen1, and T. Ala-Nissila1,2,*

  • 1Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland
  • 2Department of Physics, Brown University, Providence, Rhode Island 02912-1843, USA

  • *Author to whom correspondence should be addressed.

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Vol. 76, Iss. 5 — November 2007

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