The effects of fluid turbulence on the coagulation of aerosols are studied quantitatively and qualitatively. Direct numerical simulation data is used to isolate the effect of the small or subgrid-scale (SGS) particle-particle interactions on nanoparticle coagulation in three-dimensional flows. The rate of particle growth is decomposed into the contribution of the large-scales and small-scales interactions. The contribution of the small-scale interactions is presented as a function of time, space, flow dynamics, and coagulation Damköhler number. Results show that small-scale interactions act to both increase and decrease particle growth. The probability density functions (PDFs) of the SGS growth rate exhibit a negative bias, which increases with time and coagulation Damköhler number. Additionally, PDFs conditioned on the Q-criterion suggest that the contribution of the small-scale interactions primarily act to reduce particle growth in regions characterized by fluid rotation.