  Small particles advected in a fluid can collide (and therefore aggregate) due
to the stretching or shearing of fluid elements. This effect is usually
discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1,
16-30, (1956)]. We show that in complex or random flows the Saffman-Turner
theory for the collision rate describes only an initial transient (which we
evaluate exactly). We obtain precise expressions for the steady-state collision
rate for flows with small Kubo number, including the influence of fractal
clustering on the collision rate for compressible flows. For incompressible
turbulent flows, where the Kubo number is of order unity, the Saffman-Turner
theory is an upper bound.
