Theoretical predictions for the coagulation rate induced by turbulent shear have often been based on the hypothesis that the turbulent velocity gradient is persistent (Saffman & Turner 1956) and that hydrodynamic and interparticle interactions (van der Waals attraction and electrostatic double-layer repulsion) between colloidal particles can be neglected. In the present work we consider the effects of interparticle forces on the turbulent coagulation rate, and we explore the response of the coagulation rate to changes in the Lagrangian velocity gradient correlation time (i.e. the characteristic evolution time for the velocity gradient in a reference frame following the fluid motion). Stokes equations of motion apply to the relative motion of the particles whose radii are much smaller than the lengthscales of turbulence (i.e. small particle Reynolds numbers). We express the fluid motion in the vicinity of a pair of particles as a locally linear flow with a temporally varying velocity gradient. The fluctuating velocity gradient is assumed to be isotropic and Gaussian with statistics taken from published direct numerical simulations of turbulence (DNS). Numerical calculations of particle trajectories are used to determine the rate of turbulent coagulation in the presence and absence of particle interactions. Results from the numerical simulations correctly reproduce calculated coagulation rates for the asymptotic limits of small and large total strain where total strain is a term used to describe the product of the characteristic strain rate and its correlation time. Recent DNS indicate that the correlation times for the fluctuating strain and rotation rate are of the same order as the Kolmogorov time (Pope 1990), suggesting theories that assume either small or large total strain may poorly approximate the turbulent coagulation rate. Indeed, simulations for isotropic random flows with intermediate total strain indicate that the coagulation rate in turbulence is significantly different from the analytical limits for large and small total strain. The turbulent coagulation rate constant for non-interacting monodisperse particles scaled with the Kolmogorov time and the particle radius is 8.62±0.02, whereas the commonly used model of Saffman & Turner (1956) predicts a value of 10.35 for non-rotational flows in the limit of persistent turbulent velocity gradients. Additional simulations incorporating hydrodynamic interactions and van der Waals attraction were used to estimate the actual rate of particle coagulation. For typical values of these parameters, particle interactions reduced the coagulation rate constant by at least 50%. In general, the collision efficiency (the ratio of coagulation with particle interactions to that without) decreased with increasing particle size and Kolmogorov shear rate.

Estuaries have been reported to be sinks for hydrophobic pollutants, and sorption has been commonly attributed to be an important mechanism responsible for the observed pollutant trapping. The sorption enhancement caused by “salt effects” and dissolved organic matter (DOM) coatings were both measured and modeled, and the results were used to probe the extent to which equilibrium sorption could explain estuarine pollutant trapping. The polycyclic aromatic compound phenanthrene, an extracellular polymer from a soil bacterial isolate, and a low organic carbon kaolinite were used as models for the hydrophobic pollutant, DOM, and suspended sediment, respectively. Sorptive interactions between phenanthrene, extracellular polymer, and kaolinite were measured at pH 8 as a function of salinity. The experimentally determined binary distribution coefficients were combined using a three-component sorption model to calculate the overall sorption coefficient for phenanthrene, K O. Increasing the ionic strength to seawater levels increased the overall sorption coefficient by 55% as compared to the freshwater value while the presence of polymer coatings increased K O by 9% at all salinities. The three-component model simulation of sorption in the estuary showed that only 0.1% of available phenanthrene would be sorbed to suspended sediment given reasonable estimates of the DOM and particulate concentrations. Order of magnitude analyses carried out with other combinations of estuarine DOM and sediments also fell short of levels required to explain observed estuarine pollutant trapping. These experiments and model simulations lead to the conclu sion that equilibrium sorption of phenanthrene cannot explain the full extent of pollutant trapping in estuaries.

Diffusion and coagulation are investigated in a random, isotropic flow in the presence of hydrodynamic interactions, interparticle forces, and Brownian diffusion. Different strain and rotation rate time scales characterize the velocity field and the particles are assumed small compared with the characteristic length of the flow, so that the velocity field is linear in the vicinity of the particles. The pair probability equation for the relative motion of two particles is written in terms of a diffusion tensor and a drift velocity. This technique is valid in the limit of small strain, i.e., when the product of the characteristic velocity gradient and time scale of the fluctuating velocity gradient is small. A consequence of the drift velocity is that, at steady state in a noncoagulating system, the pair probability distribution is nonuniform when hydrodynamic interactions are included, and there is a higher probability of particle pairs at close proximity. The pair probability conservation equation is used to determine the coagulation rate both without and with consideration of interparticle interactions. The stability factor, W, is the ratio of the coagulation rate in the absence and presence of interparticle forces, and W is calculated numerically for different size particles influenced by van der Waals attraction, electrostatic repulsion, hydrodynamic interactions, and Brownian motion. A semi-analytical expression is derived that is valid for large particles that are not influenced by Brownian motion and that experience weak van der Waals attraction. The analysis shows that colloidal stability increases with increasing particle size and shear rate as a result of the hydrodynamic resistance to particle-particle collision. Double layer repulsion can lead to stable colloidal suspensions, but increasing the fluid shear can reduce this effect. Colloid stability for the randomly varying flow considered here is comparable to that obtained for steady linear flows, such as simple shear when only van der Waals attraction is considered. Compared with the steady linear flows, double layer repulsion imparts additional resistance to aggregation in the randomly varying flow. The relevance of applying this analysis to coagulation in isotropic turbulent flows is discussed.

Turbulent-shear-induced coagulation of monodisperse particles was examined experimentally in the nearly isotropic, spatially decaying turbulence generated by an oscillating grid. The 3.9 μm polystyrene microspheres used in the experiments were made neutrally buoyant and unstable by suspending them in a density-matched saline solution. In this way, particle settling, double-layer repulsion and particle inertia were negligible and the effect of turbulent shear was isolated. The coagulation rate was measured by monitoring the loss of singlet particles as a function of time and reactor turbulence intensity. By restricting consideration to experimental conditions where the singlet concentration was in excess, the effect of higher-order aggregate (i.e. triplet) formation was negligible and nonlinear regression using an integral rate expression that included terms for doublet formation and breakup was used to obtain the turbulent coagulation rate constant. The strength of the van der Waals attractions was characterized with the Hamaker constant obtained from Brownian coagulation experiments. Since particle bulk mixing was fast compared to the coagulation rate, the observed coagulation rate constants were averages over the local coagulation rates within the grid-stirred reactor. Knowledge of the spatial variation of turbulence within the reactor was necessary for quantitative prediction of the experiments because model predictions for the coagulation rate are nonlinear functions of shear rate. The investigation was conducted with particles smaller than the length scales of turbulence and since the smallest turbulent length scales, the Kolmogorov scales, have the highest shear rate they controlled the rate of particle aggregation. The distribution of the Kolmogorov shear rate at various grid oscillation frequencies was obtained by measuring the turbulent kinetic energy (E) using acoustic Doppler velocimetry and relating E to the Kolmogorov shear rate using scaling arguments. The experimentally measured turbulent coagulation rate constants were significantly lower than theoretical predictions that neglect interparticle interactions; however, simulations that included particle interactions showed excellent agreement with the experimental results. The favourable comparison provides evidence that the computer simulations capture the important physics of turbulent coagulation. That is, particle transport on length scales comparable to the particle radius controls the rate of turbulent shear coagulation and particle interactions are significant.

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