Sphere in a uniform straining Stokes flow

Let the ambient velocity be $\mathbf{Ex}$, with $\mathbf{E}$ symmetric and trace free, and centre a rigid sphere of radius $a$ at the origin. It is force-free and torque-free, with zero translation and rotation. Its disturbance isThe total velocity vanishes at $r=a$, and the leading disturbance is a stresslet. Harmonic dipole and quadrupole potentials in the Papkovich–Neuber representation give the complete field.