Drag on eccentrically positioned spheres translating and rotating in tubes

The steady motion of an eccentrically positioned sphere in a circular cylindrical tube filled with viscous fluid is considered as a regular perturbation of the axisymmetric problem. A sequence of boundary-value problems is formulated involving Stokes equations and some linear boundary conditions. Solutions of the first- and second-order problems yield the leading terms in the perturbation series of the additional drag and the torque on the spheres. The results are found to be in good agreement with the previous off-axis solutions.