  An analytical method is proposed for computing the low-Reynolds-number
hydrodynamic mobility function of a small colloidal particle asymmetrically
moving inside a large spherical elastic cavity, the membrane of which is
endowed with resistance toward shear and bending. In conjunction with the
results obtained in the first part [Daddi-Moussa-Ider, L\"{o}wen, and Gekle,
Eur. Phys. J. E 41, 104 (2018)], in which the axisymmetric motion normal to the
surface of an elastic cavity is investigated, the general motion for an
arbitrary force direction can be addressed. The elastohydrodynamic problem is
formulated and solved using the classic method of images through expressing the
hydrodynamic flow fields as a multipole expansion involving higher-order
derivatives of the free-space Green's function. In the quasi-steady limit, we
demonstrate that the particle self-mobility function of a particle moving
tangent to the surface of the cavity is larger than that predicted inside a
rigid stationary cavity of equal size. This difference is justified by the fact
that a stationary rigid cavity introduces additional hindrance to the
translational motion of the encapsulated particle, resulting in a reduction of
its hydrodynamic mobility. Furthermore, the motion of the cavity is
investigated, revealing that the translational pair (composite) mobility, which
linearly couples the velocity of the elastic cavity to the force exerted on the
solid particle, is solely determined by membrane shear properties. Our
analytical predictions are favorably compared with fully-resolved computer
simulations based on a completed-double-layer boundary integral method.
