Modeling steady-state particle size spectra

Fractal dimensions of marine aggregates are often estimated from the measured slopes of particle size spectra. One technique uses dimensional analysis to determine the dependence of the spectrum's slope with fractal dimension. In this paper, we use numerical simulations to examine the assumptions underlying the dimensional analysis approach to particle size spectra. We find that the slopes of numerically computed steady-state particle size spectra disagree with those predicted by dimensional analysis. The assumptions underlying the dimensional analysis approach that are responsible for the disagreement are as follows: only one coagulation mechanism operates in each particular particle size range, particle loss through sedimentation occurs at particle sizes larger than those for which differential sedimentation dominates, particles only interact with like-sized particles. Including disaggregation steepens the slope of the particle size spectrum for both large and small particles and changes the shape of the spectrum. These results indicate that one should exercise caution when using the measured slopes of particle size spectra to estimate aggregate fractal dimension.