Motion of Small Solid Particles in a Viscous Fluid Enclosed in a Cavity

The motion of a solid particle embedded in a viscous fluid in a closed container requires a precise account of wall effects when in creeping flow. The boundary integral method, which amounts to solving a Fredholm integral equation for the stress on the particle and walls, is used here. The accuracy...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences 2011, Vol.73 (2), p.137-169
Main Authors: Hedhili, L, Sellier, A, Elasmi, L, Feuillebois, F
Format: Article
Language:English
Subjects:
Boundary integral method
Containers
Fredholm equations
Holes
Integral equations
Mathematical analysis
Mathematical models
Parallelepipeds
Particle shape
Settling
Viscosity
Viscous fluids
Wall effects
Walls
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Summary:The motion of a solid particle embedded in a viscous fluid in a closed container requires a precise account of wall effects when in creeping flow. The boundary integral method, which amounts to solving a Fredholm integral equation for the stress on the particle and walls, is used here. The accuracy of the method is improved by using curvilinear six-node triangular boundary elements, the size of which is specially adapted to the particle shape and position with respect to walls. The method is applied to resolve the case of a moving particle in a parallelepiped container. It is validated by comparing with earlier analytical results for a sphere interacting with two parallel or perpendicular walls and with numerical results for a sphere in the center of a cubic container. Results are then provided for a spherical and an ellipsoidal particle, both either with imposed motion or settling in a cubic container.
ISSN:1526-1492
1526-1506
DOI:10.3970/cmes.2011.073.137