Finite system approximation in colloidal systems with aggregation and break-up

Abstract

In this Thesis, reactive multiparticle collision dynamics (RMPC) is used to simulate red blood cell cluster concentration profiles in the presence of aggregation, as well as when aggregation and break-up are present together. RMPC dynamics involves local collisions, reactions and free-streaming of particles. Reactive mechanisms are used to model the aggregation and break-up of particles. This analogy is motivated by a system of ODES called the Smoluchowski differential equations that have been used to model aggregating systems in the well-mixed case. Exact solutions for the (infinite) systems of ODEs for the Smoluchowski equation are compared to a numerical ODE system solution where the maximum cluster size is N (finite) rather than infinite as assumed in the Smoluchowski equation. The numerical ODE solution is compared to the exact solution in the infinite system when the maximum cluster size is 20 or less. Stochastic RMPC simulations are performed when the maximum cluster size N = 3, and the simulation domain is a cubic volume subject to periodic boundary conditions. Constant and equal aggregation and break-up rates are considered, as well as much smaller aggregation rates compared to break-up rates and vice-versa. Two different initial conditions are considered: monomer-only, as well as non-zero initial concentrations for clusters of all sizes. The simulation for the RMPC (finite), numerical ODE (finite) and exact (infinite) can be shown to have good agreement in the equilibrium concentrations of the chemical species in the system in some cases, although agreement is poor in other cases. This work is an important stepping stone that can be expanded to incorporate flow conditions into the particle dynamics in future work, so as to more accurately investigate pathological conditions including atherosclerotic plaque formation.