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Slow motion of a non-spherical solid body immersed in a fluid near a plane slip wall
Published online by Cambridge University Press: 28 October 2025
Abstract
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 
$\lambda$ small compared with the wall–particle gap 
$d$ a ‘recipe’ connecting, at 
$O((\lambda /d)^2),$ the results for the slip wall and another no-slip wall with gap 
$d+\lambda$ is established. A numerical analysis is performed for a family of inclined non-spheroidal ellipsoids, having the volume of a sphere with radius 
$a,$ to quantity the particle behaviour sensitivity to the normalised wall slip length 
$\overline {\lambda }=\lambda /a,$ the normalised wall–particle gap 
${\overline {d}}=d/a$ and the particle shape and orientation (here one angle 
$\beta ).$ The friction coefficients for the resistance problem exhibit quite different behaviours versus the particle shape and 
$({\overline {d}}, \overline {\lambda },\beta ).$ Some coefficients increase in magnitude with the wall slip. The migration of the freely suspended particle can also strongly depend on 
$({\overline {d}}, \overline {\lambda },\beta )$ and in a non-trivial way. For sufficiently small 
$\overline {d}$ 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.
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