Mobility functions of a spheroidal particle near a planar elastic membrane

Using an analytical theory, we compute the leading order corrections to the translational, rotational and translation-rotation coupling mobilities of a prolate spheroid immersed in a Newtonian fluid and moving nearby an elastic cell membrane. The corrections are expressed in terms of the spheroid-to-membrane distance, spheroid orientation and the characteristic frequencies associated with membrane shearing and bending. We find that the corrections to the translation-rotation coupling mobility are primarily determined by bending resistance whereas shearing elasticity manifests itself in a more pronounced way in the rotational mobility. We further demonstrate the validity of the analytical approximation by close comparison with boundary integral simulations of a truly extended spheroidal particle. The analytical calculations are found to be in a good agreement with the numerical simulations over the whole range of the applied frequencies.