An analytical solution in 2D for the motion of rigid elliptical particles with a slipping interface under a general deformation

A mathematical model for rigid inclusions with a slipping interface immersed in a general 2D homogeneous deformation is developed. Under bulk pure shear inclusions are expected to rapidly approach the stretching axis when compared to the behaviour of inclusions with no slip at the interface. The derived model predicts synthetic and antithetic motion into a stable orientation under simple shear, and thereafter the inclusion makes an antithetic angle with the shear direction. Under simple shear rotation rates can be higher or lower than those of no-slip inclusions, depending on orientation. A direct relationship between object inclination to the shear direction and the vorticity of the bulk flow is predicted. The model compares well with published analogue and numerical experiments.