Flocs Restructuring during Aggregation: Experimental Evidence and Numerical Simulation
01 Nov 2001-Vol. 243, Iss: 1, pp 171-182
TL;DR: In this paper, different collision frequency kernel calculation schemes were evaluated to simulate experimentally determined latex particle aggregation kinetics, and the intermediate collision scheme proposed by Veerepanneni and Wiesner (J. Colloid Interface Sci. 177, 45-57 (1996)) is in agreement with experimental aggregation kinetic if considered along with experimentally derived fractal dimension evolution.
Abstract: Aggregate structure, i.e., fractal dimension, has a coupled geometric and hydrodynamic impact on the aggregate collision frequencies. In this work, we evaluated different collision frequency kernel calculation schemes to simulate experimentally determined latex particle aggregation kinetics. Light scattering was used to simultaneously measure aggregate size and fractal dimension throughout the latex aggregation experiments. The intermediate collision scheme proposed by Veerepanneni and Wiesner ( J. Colloid Interface Sci. 177, 45–57 (1996)) is in agreement with experimental aggregation kinetics if considered along with experimentally determined fractal dimension evolution. Aggregate restructuring was found to be an important mechanism in explaining aggregation kinetics.
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TL;DR: A new concept of environmental fate modeling for ENPs with process descriptions based on the specific properties of ENPs, which demonstrates the importance of both the SPM properties (concentration, size, density) as well as the affinity of TiO(2) NPs and SPM, characterized by the attachment efficiency, α(het-agg), on the transport potential of ENP in a surface water system.
Abstract: For a proactive risk assessment of engineered nanoparticles (ENPs) it is imperative to derive predicted environmental concentration (PEC) values for ENPs in different environmental compartments; PECs can then be compared to effect thresholds. From the basis of established multimedia environmental fate models for organic pollutants, we develop a new concept of environmental fate modeling for ENPs with process descriptions based on the specific properties of ENPs. Our new fate modeling framework is highly flexible and can be adjusted to different ENPs and various environmental settings. As a first case study, the fate and transport of TiO2 NPs in the Rhine River is investigated. Predicted TiO2 NP concentrations lie in the ng/L range in the water compartment and mg/kg in the sediment, which represents the main reservoir for the nanoparticles. We also find that a significant downstream transport of ENPs is possible. A fundamental process, the heteroaggregation between TiO2 NPs and suspended particulate matter...
275 citations
TL;DR: A novel method for determining α hetero values is presented by using a combination of laser diffraction measurements and aggregation modeling based on the Smoluchowski equation for heteroaggregation of engineered nanoparticles with natural colloids.
Abstract: The heteroaggregation of engineered nanoparticles (ENPs) with natural colloids (NCs), which are ubiquitous in natural surface waters, is a crucial process affecting the environmental transport and fate of ENPs. Attachment efficiencies for heteroaggregation, αhetero, are required as input parameters in environmental fate models to predict ENP concentrations and contribute to ENP risk assessment. Here, we present a novel method for determining αhetero values by using a combination of laser diffraction measurements and aggregation modeling based on the Smoluchowski equation. Titanium dioxide nanoparticles (TiO2 NPs, 15 nm) were used to demonstrate this new approach together with larger silicon dioxide particles (SiO2, 0.5 ?m) representing NCs. Heteroaggregation experiments were performed at different environmentally relevant solution conditions. At pH 5 the TiO2 NPs and the SiO2 particles are of opposite charge, resulting in αhetero values close to 1. At pH 8, where all particles are negatively charged, αhetero was strongly affected by the solution conditions, with αhetero ranging from <0.001 at low ionic strength to 1 at conditions with high NaCl or CaCl2 concentrations. The presence of humic acid stabilized the system against heteroaggregation.
162 citations
TL;DR: Assessment of the heteroaggregation of TiO2 nanoparticles with a smectite clay as analogues for natural colloids shows that, at a relevant concentration, nanoparticle behavior is mainly driven by heterOaggregation with colloids, while homoagggregation remains negligible.
Abstract: To better understand and predict the fate of engineered nanoparticles in the water column, we assessed the heteroaggregation of TiO2 nanoparticles with a smectite clay as analogues for natural colloids. Heteroaggregation was evaluated as a function of water salinity (10(-3) and 10(-1) M NaCl), pH (5 and 8), and selected nanoparticle concentration (0-4 mg/L). Time-resolved laser diffraction was used, coupled to an aggregation model, to identify the key mechanisms and variables that drive the heteroaggregation of the nanoparticles with colloids. Our data show that, at a relevant concentration, nanoparticle behavior is mainly driven by heteroaggregation with colloids, while homoaggregation remains negligible. The affinity of TiO2 nanoparticles for clay is driven by electrostatic interactions. Opposite surface charges and/or high ionic strength favored the formation of primary heteroaggregates via the attachment of nanoparticles to the clay. The initial shape and dispersion state of the clay as well as the nanoparticle/clay concentration ratio also affected the nature of the heteroaggregation mechanism. With dispersed clay platelets (10(-3) M NaCl), secondary heteroaggregation driven by bridging nanoparticles occurred at a nanoparticle/clay number ratio of greater than 0.5. In 10(-1) M NaCl, the clay was preaggregated into larger and more spherical units. This favored secondary heteroaggregation at lower nanoparticle concentration that correlated to the nanoparticle/clay surface area ratio. In this latter case, a nanoparticle to clay sticking efficiency could be determined.
122 citations
TL;DR: In this paper, the capacity dimension of fractal flocs has been investigated in terms of a population balance equation that implements a novel description of floc geometry, and a comparison of experimental floc size distributions from settling column test with computed distributions for two hypotheses of capacity dimension (i.e., constant and variable) and two hypotheses for flocculation reactions (e.g., semi-stochastic and deterministic) are shown.
120 citations
TL;DR: In this paper, the fractal dimensions of flocs formed under different flocculation mechanisms were calculated using small-angle laser light scattering (SALLS) and image analysis.
118 citations
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2,773 citations
TL;DR: A family of explicit Runge-Kutta formulas that contains imbedded formulas of all orders 1 through 4 is derived, which is very efficient for problems with smooth solution as well as problems having rapidly varying solutions.
Abstract: Explicit Runge-Kutta methods (RKMs) are among the most popular classes of formulas for the approximate numerical integration of nonstiff, initial value problems. However, high-order Runge-Kutta methods require more function evaluations per integration step than, for example, Adams methods used in PECE mode, and so, with RKMs, it is expecially important to avoid rejected steps. Steps are often rejected when certain derivatives of the solutions are very large for part of the region of integration. This corresponds, for example, to regions where the solution has a sharp front or, in the limit, some derivative of the solution is discontinuous. In these circumstances the assumption that the local truncation error is changing slowly is invalid, and so any step-choosing algorithm is likely to produce an unacceptable step. In this paper we derive a family of explicit Runge-Kutta formulas. Each formula is very efficient for problems with smooth solution as well as problems having rapidly varying solutions. Each member of this family consists of a fifty-order formula that contains imbedded formulas of all orders 1 through 4. By computing solutions at several different orders, it is possible to detect sharp fronts or discontinuities before all the function evaluations defining the full Runge-Kutta step have been computed. We can then either accpet a lower order solution or abort the step, depending on which course of action seems appropriate. The efficiency of the new algorithm is demonstrated on the DETEST test set as well as on some difficult test problems with sharp fronts or discontinuities.
673 citations
TL;DR: In this article, a review of recent developments in this area is discussed with reference to the classical analytical expression of Smoluchowski defining collision frequency and originally published in 1917, with the key models that have been developed to address specific limitations discussed in detail.
434 citations