(19e) Predictive MODEL for Aggregation RATE of Nanoparticles in Porous MEDIA

The transport of nanoparticles (NPs) in porous media holds significant importance due to the adverse effects of NPs on the environment and human health. Aggregation of nanoparticles has been proven to be one of the most critical phenomena affecting NP mobility, as the formation of large aggregates can lead to ripening, straining, and clogging mechanisms. This study investigates how the rate of diffusion-limited aggregation of NPs is affected by pore velocity, particle size, and NP concentration as they move through porous media. The movement and aggregation of cerium dioxide (CeO₂) nanoparticles suspended in 0.2 M potassium chloride (KCl) are simulated by incorporating the Lattice Boltzmann method [1] and Lagrangian particle tracking method [2], which consider interactions among particles. The flow fields of KCl solutions through the pore space between randomly packed spheres at different velocities are solved using the Lattice Boltzmann method, while the motion and agglomeration of NPs are conducted by applying the Lagrangian particle tracking based on a force balance approach (LPT/FB). At each fluid velocity, multiple LPT runs with different particle sizes and concentrations are performed. The LPT/FB employs Newton's second law of motion, where the movement of each particle at each timestep results from six major forces exerted on each particle, including gravity, buoyancy, drag, random, electrostatics, and Van der Waals forces. Consequently, the velocities and positions of particles are tracked as time progresses. Two particles are considered to be in the same aggregate if the separation distance between them is smaller than the primary minimum; thus, at each timestep, the number and size of aggregates can be determined. The rate of aggregation is discovered to correlate linearly with time. Moreover, the slope of this line is influenced by a power function involving particle concentration, Reynolds (Re), and Schmidt (Sc) numbers [3]. Notably, the exponent for the Sc number is three times that of the Re number, suggesting that the impact of the random movement of particles dominates over that of convection in the diffusion-limited regime.

REFERENCES

(1) Papavassiliou, D. V.; Pham, N. H.; Kadri, O. E.; Voronov, R. S. Lattice Boltzmann Methods for Bioengineering Applications. In Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes; Elsevier, 2018; pp 415–429. https://doi.org/10.1016/B978-0-12-811718-7.00023-X.

(2) Nguyen, V. T.; Pham, N. H.; Papavassiliou, D. V. Aggregation of Nanoparticles and Morphology of Aggregates in Porous Media with Computations. J. Colloid Interface Sci. 2023, 650 (PA), 381–395. https://doi.org/10.1016/j.jcis.2023.06.045.

(3) Nguyen, V. T.; Pham, N. H.; Papavassiliou, D. V. Prediction of the Aggregation Rate of Nanoparticles in Porous Media in the Diffusion-Controlled Regime. Sci. Rep. 2024, 14 (1), 1–14. https://doi.org/10.1038/s41598-023-50643-x.