Hydrodynamic forces and velocities of spheroidal particles in a simple shear flow near a solid wall are calculated by a variant of the boundary integral equation method, combined with the use of the reciprocal theorem for Stokes flow equations. It is shown that the effect of the wall decreases with increasing particle nonsphericity (decreasing aspect ratio). For long slender particles the effective distance where the wall effect is significant is measured by several particle shorter axes. In the vicinity of the wall spheroids experience several interactions, which do not exist for spheres. These are the lift force component perpendicular to the wall and the corresponding rotational-translational coupling component of the resistance tensor. The data on particle hydrodynamic interactions are used to calculate the velocities of the inertialess spheroidal particles in a shear flow near a wall. The calculations reveal that the effect of the wall is to create a nonzero velocity component in the direction of the normal to the wall surface. This velocity is zero for spheroids in a free shear flow; near the wall it vanishes for spherical and, seemingly, for oblong particles. Therefore a spheroid moving in a shear flow near the wall will perform an oscillatory motion towards and away from the wall. The wall will retard the particle motion parallel to its surface, albeit in a lesser extent than for spheres. In addition, spheroidal particles will perform periodic rotational motion, as they do in an unbounded shear flow, however, with larger periods. For force components which act on spheres, as well as on nonspherical particles the wall effect is most pronounced for particles whose shape is close to spherical. Several correlation formulae are proposed for the forces and torques acting on spheroids, as well as for their friction tensor coefficients.
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Acknowledgements--This work was in part supported by the Israel Ministry of Sciences and Humanities and by the fund for the promotion of research at the Technion.
- Hydrodynamic resistance tensor
- Lift and retardation velocities
- Rotational period
- Spheroidal particles
- Wall effect