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Zbl 0899.76118
Dassios, G.; Hadjinicolaou, M.; Coutelieris, F.A.; Payatakes, A.C.
Stokes flow in spheroidal particle-in-cell models with Happel and Kuwabara boundary conditions. (English)
[J] Int. J. Eng. Sci. 33, No.10, 1465-1490 (1995). ISSN 0020-7225

Summary: Particle-in-cell models are useful in the development of simple but reliable analytical expressions for heat and mass transfer in swarms of particles. Most such models consider spherical particles. Here the creeping flow through a swarm and spheroidal particles, that move with constant uniform velocity in the axial direction through an otherwise quiescent Newtonian fluid, is analyzed with a spheroid-in-cell model. The solid internal spheroid represents a particle of the warm. The external spheroid contains the spheroidal particle and the amount of fluid required to match the fluid volume fraction of the swarm. The boundary conditions on the (conceptual) external spheroidal surface are similar to those of the sphere-in-cell Happel model, namely, nil normal velocity component and shear stress. The stream function is obtained in series form using the recently developed method of semiseparation of variables. It turns out that the first term of the series is sufficient for most engineering applications, so long as the aspect ratio of the spheroids remains within moderate bounds, say $\sim 1/5< a_3<\sim 5$. Analytical expressions for the streamfunction, the velocity components, the vorticity, the drag force acting on each particle, and the permeability of the swarm are obtained. Representative results are presented in graph form and they are compared with those obtained using Kuwabara-type boundary conditions. The Happel formulation is slightly superior because it leads to a particle-in-cell that is self sufficient in mechanical energy.

MSC 2000:: *76D07 Stokes flows

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Zentralblatt MATH Berlin [Germany]