  We study the properties and symmetries governing the hydrodynamic interaction
between two identical, arbitrarily shaped objects, driven through a viscous
fluid. We treat analytically the leading (dipolar) terms of the pair-mobility
matrix, affecting the instantaneous relative linear and angular velocities of
the two objects at large separation. We prove that the instantaneous
hydrodynamic interaction linearly degrades the alignment of asymmetric objects
by an external time-dependent drive [Moths and Witten, Phys. Rev. Lett. 110,
028301 (2013)]. The time-dependent effects of hydrodynamic interactions are
explicitly demonstrated through numerically calculated trajectories of model
alignable objects composed of four stokeslets. In addition to the orientational
effect, we find that the two objects usually repel each other. In this case the
mutual degradation weakens as the two objects move away from each other, and
full alignment is restored at long times.
