(550e) Lattice Kinetic Monte Carlo Simulations of Convectively-Driven Particle Aggregation

Flamm, M. H., University of Pennsylvania
Sinno, T. R., University of Pennsylvania
Diamond, S. L., University of Pennsylvania

The aggregation of particles entrained in a fluid in response to flow is an important and ubiquitous phenomenon in systems such as channel or tube fouling, aerosol aggregation, and platelet aggregation in blood. The temporal and spatial distribution of particle size can strongly affect the performance in these systems, e.g. the efficiency of a fouling reactor or the possibility of vessel occlusion in platelet aggregation. Classically, the isotropic population balance equation (PBE) has been used to model and control the size distribution. However, the PBE requires knowledge of the aggregation kernel (the rate of collisions), collision efficiency (probability of aggregation during a collision), and the particle morphologies. Although aggregation kernels have been derived for the simple cases of Brownian motion and constant shear rate, more complex flows and particle interactions require the use of a more direct simulation technique. Mesoscale simulations such as lattice Boltzmann (LB) [1], dissipative particle dynamics (DPD) [2], and kinetic Monte Carlo (KMC) provide a bridge between molecular simulations such as molecular dynamics and continuum models such as the PBE. LB and DPD both consider ?packets' of fluid and solid material, capturing the hydrodynamic effects between particles. KMC, in general, does not directly capture the hydrodynamics, but appropriate coarse-graining in KMC does allow the study of large scale aggregation phenomena.

The aim of this talk is to present a new KMC method for simulation of particulate aggregation in flow. The main input into KMC is a rate database for all possible events in the system. To constrain the number of possible events, space is discretized to obtain a variant of KMC known as lattice kinetic Monte Carlo (LKMC). First, a method for including convective motion in LKMC is shown to accurately capture the motion of tracer particles in a fluid [3]. This method is compared to results from Taylor-Aris dispersion in parallel plate flow and is shown to be accurate over a large range of Peclet number. The LKMC technique is then applied to aggregating systems with both ideal and non-ideal collision efficiencies. For non-ideal collisions, a new method is introduced to account for the hydrodynamically-determined particle-particle interaction time [4]. The results are compared to the PBE for simple shear flow and shown to be in excellent agreement. Open systems with isotropic and non-isotropic shear rates are compared to closed systems (i.e. with periodic boundary conditions). Furthermore, complex geometries that introduce flow recirculation are considered.

1. A. J. C. Ladd and R. Verberg. Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys., 104:1191-1251, 2001.

2. P. J. Hoogerbrugge and J. M. V. A. Koelman. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 19:155, 1992.

3. M. H. Flamm, S. L. Diamond, and T. Sinno. Lattice kinetic Monte Carlo simulations of convective-diffusive systems. J. Chem. Phys. 130:094904, 2009.

4. R. S. J. Manley and S. G. Mason. Particle motions in sheared suspensions. II. Collisions of uniform spheres. J. Colloid Sci. 7:354-369, 1952.