We interpret the Taylor–Green cellular vortex model in terms of the Kolmogorov length and velocity scales, in order to study the balance between aggregation and breakup of cohesive sediment in fine-scale turbulence. One-way coupled numerical simulations, which capture the effects of cohesive, lubrication and direct contact forces on the flocculation process, reproduce the non-monotonic relationship between the equilibrium floc size and shear rate observed in previous experiments. The one-way coupled results are confirmed by select two-way coupled simulations. Intermediate shear gives rise to the largest flocs, as it promotes preferential concentration of the primary particles without generating sufficiently strong turbulent stresses to break up the emerging aggregates. We find that the optimal intermediate shear rate increases for stronger cohesion and smaller particle-to-fluid density ratios, and we propose a simple model for the equilibrium floc size that agrees well with experimental data reported in the literature.
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Flocculation of suspended cohesive particles in homogeneous isotropic turbulence
We investigate the dynamics of cohesive particles in homogeneous isotropic turbulence, based on one-way coupled simulations that include Stokes drag, lubrication, cohesive and direct contact forces. We observe a transient flocculation phase, followed by a statistically steady equilibrium phase. We analyse the temporal evolution of floc size and shape due to aggregation, breakage and deformation. Larger turbulent shear and weaker cohesive forces yield smaller elongated flocs. Flocculation proceeds most rapidly when the fluid and particle time scales are balanced and a suitably defined Stokes number is $O(1)$ . During the transient stage, cohesive forces of intermediate strength produce flocs of the largest size, as they are strong enough to cause aggregation, but not so strong as to pull the floc into a compact shape. Small Stokes numbers and weak turbulence delay the onset of the equilibrium stage. During equilibrium, stronger cohesive forces yield flocs of larger size. The equilibrium floc size distribution exhibits a preferred size that depends on the cohesive number. We observe that flocs are generally elongated by turbulent stresses before breakage. Flocs of size close to the Kolmogorov length scale preferentially align themselves with the intermediate strain direction and the vorticity vector. Flocs of smaller size tend to align themselves with the extensional strain direction. More generally, flocs are aligned with the strongest Lagrangian stretching direction. The Kolmogorov scale is seen to limit floc growth. We propose a new flocculation model with a variable fractal dimension that predicts the temporal evolution of the floc size and shape.
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- Award ID(s):
- 1924532
- NSF-PAR ID:
- 10289153
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 921
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We propose a one-way coupled model that tracks individual primary particles in a conceptually simple cellular flow set-up to predict flocculation in turbulence. This computationally efficient model accounts for Stokes drag, lubrication, cohesive and direct contact forces on the primary spherical particles, and allows for a systematic simulation campaign that yields the transient mean floc size as a function of the governing dimensionless parameters. The simulations reproduce the growth of the cohesive flocs with time, and the emergence of a log-normal equilibrium distribution governed by the balance of aggregation and breakage. Flocculation proceeds most rapidly when the Stokes number of the primary particles is $O(1)$ . Results from this simple computational model are consistent with experimental observations, thus allowing us to propose a new analytical flocculation model that yields improved agreement with experimental data, especially during the transient stages.more » « less
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We develop a physical and computational model for performing fully coupled, grain-resolved direct numerical simulations of cohesive sediment, based on the immersed boundary method. The model distributes the cohesive forces over a thin shell surrounding each particle, thereby allowing for the spatial and temporal resolution of the cohesive forces during particle–particle interactions. The influence of the cohesive forces is captured by a single dimensionless parameter in the form of a cohesion number, which represents the ratio of cohesive and gravitational forces acting on a particle. We test and validate the cohesive force model for binary particle interactions in the drafting–kissing–tumbling (DKT) configuration. Cohesive sediment grains can remain attached to each other during the tumbling phase following the initial collision, thereby giving rise to the formation of flocs. The DKT simulations demonstrate that cohesive particle pairs settle in a preferred orientation, with particles of very different sizes preferentially aligning themselves in the vertical direction, so that the smaller particle is drafted in the wake of the larger one. This preferred orientation of cohesive particle pairs is found to remain influential for systems of higher complexity. To this end, we perform large simulations of 1261 polydisperse settling particles starting from rest. These simulations reproduce several earlier experimental observations by other authors, such as the accelerated settling of sand and silt particles due to particle bonding, the stratification of cohesive sediment deposits, and the consolidation process of the deposit. They identify three characteristic phases of the polydisperse settling process, viz. (i) initial stir-up phase with limited flocculation, (ii) enhanced settling phase characterized by increased flocculation, and (iii) consolidation phase. The simulations demonstrate that cohesive forces accelerate the overall settling process primarily because smaller grains attach to larger ones and settle in their wakes. For the present cohesive number values, we observe that settling can be accelerated by up to 29 %. We propose physically based parametrization of classical hindered settling functions introduced by earlier authors, in order to account for cohesive forces. An investigation of the energy budget shows that, even though the work of the collision forces is much smaller than that of the hydrodynamic drag forces, it can substantially modify the relevant energy conversion processes.more » « less
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Abstract Due to the flocculation process, suspended mud aggregates carried by rivers to the coastal ocean are thought to undergo changes in size and shape in response to environmental drivers such as turbulence, sediment concentration, organic matter (OM), and salinity. Some have assumed that salt is necessary for floc formation, and that mud, therefore, reaches the estuary unflocculated. Yet mud flocs exist in freshwater systems long before the estuarine zone, likely due to the presence of OM acting as a floc‐promoting binder. Therefore, it is important to consider how salinity affects flocculation, if at all, in the presence of OM. Here, we used experiments to examine the flocculation of a natural mud with and without OM. Results showed that the rate of floc growth and equilibrium size both increase with salinity regardless of the presence or absence of OM. However, the response of both to salinity was stronger when OM was present. In deionized water, natural sediment with OM was seen to produce large flocs. However, the size distribution of the suspension tended to be bimodal. With the addition of salt, increasing amounts of unflocculated material became bound within flocs, producing a more unimodal size distribution. Here, the enhancing effects of salt were noticeable at even 0.5 ppt, and increases in salinity past 3–5 ppt only marginally increased the floc growth rate and final size. Data from the experiment were used to develop a salinity‐dependent model to account for changes in floc growth rate and equilibrium size.
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null (Ed.)Biophysical cohesive particles in aquatic systems, such as extracellular polymeric substances (EPS) and clay minerals, play an important role in determining the transport of spilled oil contamination and its eventual fate, particularly given that suspended sediment and microbial activities are often prevalent and diverse in natural environments. A series of stirring jar tests have been conducted to understand the multiple structures characteristics of the oil-mineral aggregates (OMAs) and EPS-oil-mineral aggregates (EPS-OMAs). OMAs and EPS-OMAs have been successfully generated in the laboratory within artificial seawater using: Texas crude oil (Dynamic viscosity: 7.27 × 10 –3 Pa⋅s at 20°C), two natural clay minerals (Bentonite and Kaolin clay), and Xanthan gum powder (a proxy of natural EPS). A magnetic stirrer produced a homogeneous turbulent flow with a high turbulence level similar to that under natural breaking waves. High-resolution microscopy results show that EPS, kaolinite, and bentonite lead to distinguished oil floc structures because of the different stickiness character of EPS and mineral clay particles. With relatively low stickiness, kaolinite particles tend to attach to an oil droplets surface (droplet OMAs) and become dominant in small-sized flocs in the mixture sample. In contrast, the more cohesive bentonite particles stickiness could adsorb with oil droplets and are thus dominated by larger sized flocs. Biological EPS, with the highest stickiness, demonstrated that it could bond multiple small oil droplets and form a web structure trapping oil and minerals. Generally, adding EPS leads to flake/solid OMAs formation, and individual oil droplets are rarely observed. The inclusion of ESP within the matrix, also reduced the dependence of settling velocity on floc size and mineral type.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.487
