The effect of bulk fluid motion on aggregation of small particles subject to interaction forces of the DVLO type is investigated. In particular, the convection-diffusion equation for the probability of finding two particles at a given relative position is solved numerically for the case of an axisymmetrical linear flow field, which approximates a turbulent flow field. The effect of bulk motion is shown to be important particularly in the case of thick double layers, where a critical size exists above which aggregation exhibits a self-accelerating behavior, that is, the aggregation rate constant increases with particle size. On the other hand, systems with thin double layers appear to be almost unaffected by shear. An approximate criterion for distinguishing between these two cases is presented.