A two-level, discrete particle approach for large-scale simulation of colloidal aggregates

Most numerical techniques employed for aggregation simulation are based on equilibrium growth assumption and Smoluchowski theory. We present a new two-level discrete particle model, which can be employed in simulating large colloidal clusters in highly nonequilibrium physical conditions. We consider the system of colloidal particles (CP) interacting via conservative CP-CP repulsive-attractive two-body forces, which is initially mixed in a dissipative solvent. In order to obtain a high-resolution picture of colloidal dynamics, we employ around 20 million particles consisting of two kinds of particles. For bridging the spatio-temporal scales between nanoscale colloidal and the solvent particles (SP), the solvent is modeled by dissipative particle dynamics (DPD) fluid. We focus on the systems size for which the CP-SP interactions can also be described by the DPD forces. Unlike previous numerical techniques, the two-level particle model can display much more realistic physics, thus allowing for the simulation of aggregation for various types of colloids and solvent liquids in a broad range of conditions. We show that not only large and static clusters but also the initial stages of aggregation evolution can be better scrutinized. The large-scale simulation results obtained in two-dimensions show that the mean cluster size grows with time t according to the power law t^κ. Because of the time-dependence of growth mechanism, the value of κ necessarily must change. We have first κ = 1 with a value of 1 achieved asymptotically with time. We can also discern intermediate-scale structures. We emphasize that the method developed here can be easily extended to algorithms dealing with multi-level hierarchy and multiphase fluid dynamics.