(390e) Model for Nanoparticle Aggregation in Confined Geometries

The use of nanoparticles (NPs) has been ever-increasing in various fields such as the energy industry, agriculture and so on. For instance, the injection of nanoparticles in combination with surfactants into hydrocarbon reservoirs can reduce the surface tension of oil-water or change the wettability of oil-rock interface, thereby increasing the recovery of trapped oil. However, the release of hazardous nanoparticles is harmful to the environment. For example, the discharge of nanoparticles from petroleum recovery projects or agricultural fertilizers into the subsurface may contaminate aquifers. Hence, understanding the mobility of nanoparticles can either improve desired effects or hinder the undesired ones; and the mobility of NPs is strongly affected by the aggregation of nanoparticles. Aggregation changes the size and shape of NPs during transportation. Carrying out experiments can be challenging, especially when the nanoparticles move in porous media. Our aim is to develop a computational model to simulate the aggregation process of particles as they propagate in the confined geometries of porous media. The aggregation of NPs is examined by a force balance approach, which is based on Newton’s second law of motion. The rate of change in momentum (product of mass and velocity) of a particle is proportional to the total force applied on the particle, which includes the Van der Waals attraction force, electrostatic force, gravity force, buoyancy force, random force and drag force. In this study, the particle movement is caused by these forces and the trajectories of particles are recorded at every single time step. When the separation distance between particles is less than the primary potential minimum, they are considered to form a permanent aggregate. The most challenging issue in this method is that the motion and aggregation process is a multiscale process [1]. One needs to determine an appropriate time step, given the difference in the range where these forces apply. The NP movement is governed by convection, diffusion and drag, but aggregation is governed by the electrostatic forces and the Van der Waals forces that apply in distances as short as nanometers. If the time step is too large, the particles will move and pass their nearest neighbors without agglomeration. However, if the time step is too small, it will take a prohibitively very long computational time to simulate the process. Therefore, it is critical to apply a dynamic time-step to ensure that the particles will not overlap or run through each other, and the simulation time is affordable. The presentation will focus on the development of a multiscale computational approach and on the validation of the results against experiments. The aggregation kinetics of CeO₂ nanoparticles in KCl and CaCl₂ solutions are used [2] for validation and the kinetics of the aggregation process compared to the Smoluchowski theory [3] will be presented.

REFERENCES

[1] N.H. Pham,and D.V. Papavassiliou, “Hydrodynamic effects on the aggregation of nanoparticles in porous media,” Int. J. Heat Mass Transf., Vol. 121, pp. 477-487, 2018, doi: 10.1016/j.ijheatmasstransfer.2017.12.150

[2] K. Li, W. Zhang, Y. Huang, and Y. Chen, “Aggregation kinetics of CeO 2 nanoparticles in KCl and CaCl 2 solutions: Measurements and modeling,” J. Nanoparticle Res., vol. 13, no. 12, pp. 6483–6491, 2011, doi: 10.1007/s11051-011-0548-z.

[3] M. Smoluchowski, Versuch einer mathematischen theorie der koagulationskinetik kolloider losungen, Z. Phys. Chem. (N. F.) Vol. 92, pp. 129–168, 1917.