Slow motion of a non-spherical solid body immersed in a fluid near a plane slip wall

Wall slip sensitivity and non-sphericity and orientation effects are investigated for a moving no-slip solid body immersed in a fluid above a plane slip wall with a Navier slip. The wall-particle interactions are examined for the body motion in a quiescent fluid (resistance problem) or when freely suspended in a prescribed 'linear' or quadratic ambient shear flow. This is achieved, assuming Stokes flows, by using a boundary method which reduces the task to the treatment of six boundary-integral equations on the body surface. For a wall slip length small compared with the wall-particle gap a 'recipe' connecting, at the results for the slip wall and another no-slip wall with gap is established. A numerical analysis is performed for a family of inclined non-spheroidal ellipsoids, having the volume of a sphere with radius to quantity the particle behaviour sensitivity to the normalised wall slip length the normalised wall-particle gap and the particle shape and orientation (here one angle The friction coefficients for the resistance problem exhibit quite different behaviours versus the particle shape and Some coefficients increase in magnitude with the wall slip. The migration of the freely suspended particle can also strongly depend on and in a non-trivial way. For sufficiently small a non-spherical particle can move faster than in the absence of a wall for a large enough wall slip for the ambient 'linear' shear flow and whatever the wall slip for the ambient quadratic shear flow.