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Hydrodynamic interactions in suspensions with periodic boundary conditions

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  • Felderhof, B.U.

Abstract

We study hydrodynamic interactions in suspensions with periodic boundary conditions with the purpose of performing computer simulations with many particles per unit cell. The use of periodic boundary conditions minimizes surface effects. The formulation of the problem is complicated due to the long range nature of the hydrodynamic interactions. We show how macroscopic considerations may be used to arrive at a periodic solution of the flow equations. We derive expressions for the mobility tensors of freely moving particles, as well as for the friction tensor of a rigid array. Finally we discuss the high frequency effective viscosity of suspensions with periodic boundary conditions.

Suggested Citation

  • Felderhof, B.U., 1989. "Hydrodynamic interactions in suspensions with periodic boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 159(1), pages 1-18.
    • Handle: RePEc:eee:phsmap:v:159:y:1989:i:1:p:1-18
    DOI: 10.1016/0378-4371(89)90144-1
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    References listed on IDEAS

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    1. Smith, E.R. & Snook, I.K. & Van Megen, W., 1987. "Hydrodynamic interactions in Brownian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 143(3), pages 441-467.
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    Cited by:

    1. Wajnryb, E. & Szymczak, P. & Cichocki, B., 2004. "Brownian dynamics: divergence of mobility tensor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 339-358.

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    1. Snook, I.K. & Briggs, K.M. & Smith, E.R., 1997. "Hydrodynamic interactions and some new periodic structures in three particle sediments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(3), pages 547-559.
    2. Wajnryb, E. & Szymczak, P. & Cichocki, B., 2004. "Brownian dynamics: divergence of mobility tensor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 339-358.
    3. Cichocki, B. & Felderhof, B.U., 1989. "Periodic fundamental solution of the linear Navier-Stokes equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 159(1), pages 19-27.

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