Figure 1

Flocs in homogenous isotropic turbulence. (a) Instantaneous flow field with flocs of case S1 at later stage, with a zoomed in view within a sphere of radius 2 at the domain center. The green iso-surfaces are turbulent coherent structures visualized by the \(\lambda 2\) method⁴⁸, showing the region of vortices. Particles are colored with their vertical velocity. (b, c) The zoom-in view shows flocs at a later stage for case S1 and S2. Small and compact flocs are generated, while larger flocs are more elongated in case S1 (b). In S2 (c), with greater particle stickiness, much larger flocs consisting of hundreds of particles are generated. Smaller flocs show irregular structures, while larger ones are much more compact. (d, e) Floc size distribution \({N}_{{n}_{f}}\) based on primary particle number \({n}_{f}\) and floc size \({L}_{f}\) at equilibrium. Distribution with peak around Kolmogorov length scale is observed for S1 with lower \(Co\) in (e). Power-law size distribution is observed for case S2 with higher \(Co\) in (d). (f) Normalized fractal dimension of flocs with different \({n}_{f}\) for case S1 and S2, \(\widetilde{{d}_{0}}={d}_{0}/{d}_{0,max}\) (see Methods). \(\widetilde{{d}_{0}}\) close to 1 indicates compact floc structure. Floc structure becomes increasingly irregular and fragile as they grow in case S1. Although flocs in case S2 are more irregular in general, larger flocs show relatively compact structure and have similar fractal dimension. (g) Zingg’s shape classification⁴⁹ (Supplementary Table S2) for flocs within different \(n_{f}\) ranges for case S1 (\(n_{f,SM} = 10 - 25, n_{f,ME} = 26 - 35\), \(n_{f,LG} = 35 - 70\)) and case S2 (\(n _{f,SM} = 10 - 30, n_{f,ME} = 31 - 70\), \(n_{f,LG} = 71 - 200\)). Smaller flocs in case S1 are likely to have equant shape while those in S2 have a larger portion of prolate and oblate shapes. Large fractions of larger flocs in S1 tends to have prolate shape while large flocs in case S2 are more equant.