  Two identical particles driven by the same steady force through a viscous
fluid may move relative to one another due to hydrodynamic interactions. The
presence or absence of this relative translation has a profound effect on the
dynamics of a driven suspension consisting of many particles. We consider a
pair of particles which, to linear order in the force, do not interact
hydrodynamically. If the system possesses an intrinsic property (such as the
shape of the particles, their position with respect to a boundary, or the shape
of the boundary) which is affected by the external forcing, hydrodynamic
interactions that depend nonlinearly on the force may emerge. We study the
general properties of such nonlinear response. Analysis of the symmetries under
particle exchange and under force reversal leads to general conclusions
concerning the appearance of relative translation and the motion's
time-reversibility. We demonstrate the applicability of the conclusions in
three specific examples: (a) two spheres driven parallel to a wall; (b) two
deformable objects driven parallel to their connecting line; and (c) two
spheres driven along a curved path. The breaking of time-reversibility suggests
a possible use of nonlinear hydrodynamic interactions to disperse or assemble
particles by an alternating force.
