Modelling particle size distribution dynamics in marine waters

Numerical simulations were carried out to determine the particle size distribution (PSD) in marine waters by accounting for particle influx, coagulation, sedimentation and breakage. Instead of the conventional rectilinear model and Euclidean geometry, a curvilinear collision model and fractal scaling mathematics were used in the models. A steady-state PSD can be achieved after a period of simulation regardless of the initial conditions. The cumulative PSD in the steady state follows a power-law function, which has three linear regions after log–log transformation, with different slopes corresponding to the three collision mechanisms, Brownian motion, fluid shear and differential sedimentation. The PSD slope varies from −3.5 to −1.2 as a function of the size range and the fractal dimension of the particles concerned. The environmental conditions do not significantly alter the PSD slope, although they may change the position of the PSD and related particle concentrations. The simulation demonstrates a generality in the shape of the steady-state PSD in the ocean, which is in agreement with many field observations. Breakage does not affect the size distribution of small particles, while a strong shear may cause a notable change in the PSD for larger and fractal particles only. The simplified approach of previous works using dimensional analysis still offers valuable approximations for the PSD slopes, although the previous solutions do not always agree with the simulation results. The variation in the PSD slope observed in field investigations can be reproduced numerically. It is argued that non-steady-state conditions in natural waters could be the main reason for the deviation of PSD slopes. A change in the nature of the particles, such as stickiness, and environmental variables, such as particle input and shear intensity, could force the PSD to shift from one steady state to another. During such a transition, the PSD slope may vary to some extent with the particle population dynamics.