Sectional and discrete representations of floc breakage in agitated suspensions

The destruction of large aggregates plays several important roles in the sea, yet a rigorous method for incorporating this process into commonly applied models of aggregate dynamics has not been available. To fill this void the statistical, population-balance approach to modelling floc breakage developed most formally and completely by Pandya and Spielman (Journal of Colloid and Interface Science, 90(2) (1982) 517–531) is cast into geometric sectional and discrete forms popular for modelling the effect of aggregation on particle-size distributions. Two breakup mechanisms are considered. Floc erosion occurs when small particles are removed from the surface of larger flocs. Floc splitting is the rupture of flocs into roughly equal-sized daughter fragments. The rate of change of mass in a size class due to these mechanisms is best represented by six terms: loss due to diminution by erosion of fines, loss due to erosion of fines, gain from diminution of larger flocs, gain from production of erosion fines, loss due to splitting and gain from splitting. Comparisons of the sectional and discrete equations are made with inputs that are consistent with observations of flocs in the marine environment. A simple, new model of particle-disaggregation rate that emphasizes the importance of dissipative eddies in disrupting flocs is proposed. It suggests that splitting dominates the breakup of flocs of all sizes.