Migration of a solid and arbitrarily-shaped particle near a plane slipping wall

This work is concerned with the rigid-body migration of a solid and arbitrary-shaped particle immersed in a Newtonian liquid in vicinity of a plane, motionless and impermeable wall where a Navier slip condition [1] holds. The net hydrodynamic force and torque exerted on the moving particle are obtained by appealing to a new boundary elements approach which makes use of a specific Green tensor recently determined elsewhere [2]. The advocated technique results in the treatment of a Fredholm boundary-integral equation of the first kind on the particle surface and, by contrast to earlier works in this field, makes it possible to cope with non-spherical particles. The proposed numerical implementation is benchmarked against results obtained for a sphere by using the bipolar coordinates. Preliminary new results for the friction coefficients of an non-spheroidal ellipsoid are also reported and compared with those for a volume-equivalent sphere. The variations of the friction coefficients with the slip length are analogous for both particles.