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

thesis

posted on 22.05.2021, 11:24 by Salina AktarIn 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.