  Particles of low velocity, travelling without dissipation in a superfluid,
can interact and emit sound when they collide. We propose a minimal model in
which the equations of motion of the particles, including a short-range
repulsive force, are self-consistently coupled with the Gross-Pitaevskii
equation. We use this model to demonstrate the existence of an effective
superfluid-mediated attractive interaction between the particles; and we study
numerically the collisional dynamics of particles as a function of their
incident kinetic energy and the length-scale of the repulsive force. We find a
transition from almost elastic to completely inelastic (sticking) collisions as
the parameters are tuned. We find that aggregation and clustering result from
this sticking transition in multi-particle systems.
