Estimating the Rate of Nanopartice Aggregation in Porous Media*

The diffusivity of nanoparticles (NPs) in porous media is strongly affected by aggregation among particles, a poorly understood phenomenon due to the challenges of conducting experiments in complex porous media and simulating interaction forces responsible for agglomeration. Our aim was to build a Lagrangian particle tracking method based on the force balance approach to simulate the movement, interaction, and aggregation of cerium dioxide (CeO₂) NPs suspended in 0.2 M potassium chloride (KCl) when they moved through randomly packed spheres.¹ The movement of each particle at each timestep was generated by six major forces including gravity, buoyance, random, drag, Van der Walls, and electrostatic forces. The distances among particles were calculated at each step, and two particles would be in the same cluster if the separation distance between them was less than the primary minimum. Thus, the number of aggregates and their sizes were tracked in time and space. We also set up a model to examine the effects of fluid velocity, particle size, and particle concentration on the aggregation rate of CeO₂.² Different simulations of NPs with different particle sizes and concentrations moving through porous media at different velocities were performed. The aggregation rate of CeO₂ NPs in the diffusion-limited aggregation was found to be linearly dependent on time (in pore volume units), and the slope of the line was a power function of Reynolds number, Schmidt number, and particle concentration.³ Moreover, the exponent of the Sc number is three times larger than that of the Re number, suggesting that the dominance of random particle movement surpasses convection.

REFERENCES

1. Nguyen, V. T.; Pham, N. H.; Papavassiliou, D. V. J. Colloid Interface Sci. 2023, 650 (PA), 381–395.
   
   Nguyen, V. T.; Pham, N. H.; Papavassiliou, D. V. Sci. Rep. 2024, 14 (1), 1–14.