Large-scale calculation of hydrodynamic transport properties for random suspensions of hard-sphere particles |
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Authors: | Sangkyun Koo |
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Affiliation: | 1.Department of Chemical Engineering and Materials Science,Sangmyung University,Seoul,Korea |
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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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