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Ewald sum of the Rotne–Prager tensor

J. Chem. Phys. 85, 1581 (1986); doi:10.1063/1.451199

Issue Date: 1 August 1986

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C. W. J. Beenakker
Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands
The lattice sum of the Rotne–Prager hydrodynamic mobility tensor is cast into a rapidly converging form by an Ewald summation technique. The result has a direct application to the problem of how to deal with the long range of hydrodynamic interactions in computer simulations of macromolecular solutions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
History: Received 2 April 1986; accepted 17 April 1986
Permalink: http://link.aip.org/link/?JCPSA6/85/1581/1
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KEYWORDS and PACS

Keywords
PACS
  • 61.25.Hq
    Structure of liquids and solids; crystallography Studies of specific liquid structures Macromolecular and polymer solutions (solubility, swelling, etc.); polymer melts
  • 61.20.Ja
    Structure of liquids and solids; crystallography Classical, semiclassical, and quantum theories of liquid structure Computer simulation of static and dynamic behavior
  • 47.90.+a
    Fluid dynamics Other topics in fluid dynamics
  • YEAR: 1986

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (14)

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  1. S. G. Brush, H. L. Sahlin, and E. Teller, J. Chem. Phys. 45, 2102 (1966);
  2. R. O. Watts and I. J. McGee, Liquid State Chemical Physics (Wiley, New York, 1976).
  3. P. P. Ewald, Ann. Phys. 64, 253 (1921).
  4. W. van Megen, I. Snook, and P. N. Pusey, J. Chem. Phys. 78, 931 (1983).
  5. J. Bacon, E. Dickinson, and R. Parker, Faraday Discuss. Chem. Soc. 76, 165 (1983).
  6. I. Snook, W. van Megen, and R. J. A. Tough, J. Chem. Phys. 78, 5825 (1983).
  7. The point is that the screened mobility results from Darcy's equation for flow through a bed of particles which are immobilized by external forces and is a consequence of the absorption of fluid momentum at the particle surfaces. In this respect such porous media are fundamentally different from suspensions of freely moving particles which merely scatter the momentum flow.
  8. J. Rotne and S. Prager, J. Chem. Phys. 50, 4831 (1969).
  9. B. R. A. Nijboer and F. W. de Wette, Physica 23, 309 (1957).
  10. For a related application see R. Kapral and D. Bedeaux, Physica A 91, 590 (1978).
  11. To evaluate this integral, write [integral]<sub>0</sub><sup>[infinity]</sup> dr r2 sinkr erf(xir) = −([partial-derivative]2/[partial-derivative]k2) ×[integral]<sub>0</sub><sup>[infinity]</sup> dr sinkr erf(xir), where [integral]<sub>0</sub><sup>[infinity]</sup> dr sinkrerf(xir). = [integral]<sub>0</sub><sup>[infinity]</sup>dr sin kr[integral]<sub>0</sub><sup>[infinity]</sup> dr sinkrerf(xir) = k−1k−1{1−exp(−1/4xi−2k2)}.
  12. B. U. Felderhof, Physica A 89, 373 (1977).
  13. C. W. J. Beenakker and P. Mazur, Phys. Lett. A 91, 290 (1982).
  14. C. W. J. Beenakker and P. Mazur, Physica A 126, 349 (1984).
  15. C. W. J. Beenakker, Physica A 128, 48 (1984).

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