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Large-scale calculation of hydrodynamic transport properties for random suspensions of hard-sphere particles

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Abstract

A numerical method based on fast multipole summation scheme is used to calculate hydrodynamic interactions in random suspensions of non-colloidal hard-sphere particles. The calculation is carried out for suspensions of 1,024 particles randomly placed in periodic unit cell to determine hydrodynamic transport properties such as permeability of a viscous flow through porous medium, effective viscosity of suspension, and sedimentation velocity of the suspended particles. The particle volume fraction ø ranges from 0.01 to 0.25. Effect of particle number N on the transport properties was examined through the numerical calculations with N=64-1,024. It is shown that sedimentation velocity increases with N approaching an estimate for infinite N, and the finite N effect is negligible in effective viscosity and permeability problems. The present scheme is quite useful for obtaining a statistically-averaged quantity for random suspensions. As an example, ensemble-averaged velocity when position of one particle is fixed is numerically obtained in sedimentation problem. The numerical results are shown to be in excellent agreement with theoretical prediction.

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Authors and Affiliations

  1. Department of Chemical Engineering and Materials Science, Sangmyung University, Seoul, 03016, Korea

    Sangkyun Koo

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  1. Sangkyun Koo
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Correspondence to Sangkyun Koo.

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Koo, S. Large-scale calculation of hydrodynamic transport properties for random suspensions of hard-sphere particles. Korean J. Chem. Eng. 33, 2298–2307 (2016). https://doi.org/10.1007/s11814-016-0111-9

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  • DOI: https://doi.org/10.1007/s11814-016-0111-9

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