Figure 4

The effects of floc properties and turbulent modulation on the aggregation efficiency. (a, b) Dependence of aggregation efficiency (\({E}_{c}\)) on the pre-collision floc size ratio (\({n}_{1}/{n}_{2}<1\)) for all aggregation resulting in given \({n}_{f}\). The resultant floc size over the Kolmogorov length scale (\(\overline{{L}_{f}} /\eta\)) is indicated by the color bar. For flocs of \({n}_{f}\le 24\) or \(\overline{{L}_{f}}<1.5\eta\) in case S1 (see a) and all flocs in case S2 (see b), \({E}_{c}\) is independent of to the floc size ratio before aggregation. For large flocs of \(\overline{{L}_{f}}>1.5\eta\) in case S1 (see a), \({E}_{c}\) is high when two flocs of very different size (\({n}_{1}/{n}_{2}\sim 0\)) collide, while \({E}_{c}\) is low for the collision of two equal-sized flocs (\({n}_{1}/{n}_{2}\sim 1\)). (c) Relation between the aggregation efficiency \({E}_{c}\) and the resultant normalized floc size (\(\overline{{L}_{f}}/\eta\)) of equal-sized collision with \({n}_{1}/{n}_{2}\sim 1\). \({E}_{c}\) decreases when the post-collision floc size \(\overline{{L}_{f}}>1.5\eta\). (d, e) Relation between aggregation efficiency \({E}_{c}\) and the pre- and post-collision floc structures (characterized by the normalized fractal dimension \(\widetilde{{d}_{0}}\)), when two flocs with equal \({n}_{f}\) collide. For aggregation generates flocs smaller than \(1.5\eta\) (hollow markers), \({E}_{c}\) is high for both cases and is independent of both the pre- and post-collision floc structures. For aggregation that results in flocs larger than \(1.5\eta\) (see d, filled markers), \({E}_{c}\) decreases as pre-collision flocs become larger and compact in case S1, while as pre-collision flocs becomes larger and irregular in case S2. When two equal-sized flocs of increasingly compact structure aggregate in S1 (see d, filled blue circle), the resultant larger flocs become increasingly irregular with decreasing fractal dimension(see e, filled blue circle). When two equal-sized flocs of more irregular structure aggregate in case S2 (see d, filled red triangle), the resultant larger floc is more compact with increasing fractal dimension (see e, filled red triangle).