Abstract
A previously developed self-consistent field method is used to study an arbitrary finite set of identical spherical particles of arbitrary density moving in a uniform inviscid incompressible flow specified at infinity in the presence of a flat wall. For a given initial particle distribution in space, expressions for the particle and fluid velocities are derived taking into account the collective hydrodynamic interaction of the particles with each other and the wall. For a statistically uniform particle distribution in a semibounded inviscid fluid, analytical averaged particle and fluid velocity profiles are obtained in the first approximation with respect to the particle volume fraction in the suspension.
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This work was performed in the framework of the State assignment, state number registration AAAA-A19-119012290136-7.
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Translated by I. Ruzanova
APPENDIX
APPENDIX
The functions \({{q}_{p}}({{z}_{i}})\), \({{k}_{p}}({{z}_{i}})\), \({{q}_{f}}(z)\), and \({{k}_{f}}(z)\) involved in formulas (2.1) for the averaged particle and fluid velocities are given by
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Gus’kov, O.B. Inviscid Suspension Flow along a Flat Boundary. Comput. Math. and Math. Phys. 61, 470–479 (2021). https://doi.org/10.1134/S0965542521030088
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DOI: https://doi.org/10.1134/S0965542521030088