The evolution of particle size distributions due to aggregation between particles is described generally by incorporating an aggregation frequency into a population balance equation. The frequency is derived by analyzing the relative motion between particles culminating in their physical contact and aggregation. The usual approach, originating from the pioneering work of Smoluchowski (Smoluchowski, M. Sitzungber. Math., Astron., Phys., Meteriol. Mech. 1914,123, 2381), is to view the relative motion between two particles and their aggregation in isolation from the population balance. The procedure is predicated on the assumption that the spatial homogeneity of the population (over some length scale, say, L) is disturbed by relative motion only in a neighborhood of length scale 1 that is small compared to L; furthermore, relative motion is assumed to occur at a rate sufficiently higher than the rate at which the population of particles diminishes by aggregation. This paper presents a mathematical perspective on this approach, examines the circumstances of its validity, and provides a remedial procedure when it is inadmissible with potential applications. Thus, this work identifies circumstances that permit the use of an aggregation frequency, together with a procedure for its calculation.