Figure 3

Effects of floc properties on the breakup process. Both floc size and floc structure can affect breakup, including the breakup rate and breakage distribution function. (a) Breakup rate \({r}_{bk}\) for flocs consisting of different number of primary particles in case S1 and S2. Power-law relation between \({n}_{f}\) and \({r}_{bk}\) is found for case S2, suggesting the independence of breakup rate on floc structure based on the empirical function \({r}_{bk}\propto {V}^{1/3}\) (which only considers the effect of floc size). \({r}_{bk}\) grows exponentially with \({n}_{f}\), as larger flocs in S1 becomes increasingly fragile. (b) Breakup rate \({r}_{bk}\) changes with floc structure characterized by the normalized fractal dimension \(\widetilde{{d}_{0}}\). \(r\) is the correlation coefficient. \({r}_{bk}\) is negatively correlated with the floc fractal dimension in case S1, while opposite relation is found in case S2, again showing the effect of structure on \({r}_{bk}\) for case S1 with lower \(Co\). (c) The mean floc breakup mode for flocs of different sizes quantified by the largest fragment ratio \(LFR\) (Methods) averaged over flocs of given \({n}_{f}\), denoted as \(\overline{LFR}\). Both cases show the dominance of erosion (\(\overline{LFR}\)>0.75) at specific size range. (d) Relations between the mean floc breakup mode (\(\overline{LFR}\)) and the floc structure (\(\widetilde{{d}_{0}}\)), where larger marker size indicates larger floc size. Breakup mode is correlated with the floc structure in case S1, while it is independent of floc structure in case S2. (e, f) Breakage distribution function for S1 and S2. Fragment sizes are normalized by the corresponding size of the breaking floc, \({n}_{frag}/{n}_{f}\). Only data of flocs that break into two fragments are included. For \({n}_{f}=40\) and \(50\) in case S1, the breakage distributions are fitted by a normal distribution in (e).