A novel Monte Carlo - Discrete Element Method approach for the micro-mechanics of colloidal suspensions

This thesis is focused on the development of a novel computational tool capable of predicting the behaviour of dilute colloidal suspensions. The work has been focused in particular on the investigation of the aggregation and breakup phenomena occurring under the effect of a spatially uniform shear flow. Aggregation and breakup phenomena have in fact significant effects on the size of the dispersed particles, their shape, their composition, the distribution of these quantities over the entire population of particles and, consequently, on the macroscopic properties of the suspension. Frequently, the investigation of colloidal suspensions is conducted resorting to Population Balance Equations (PBE); by this method it is possible to follow the dynamics of a colloidal suspension, or more in general of a disperse system, by simply imposing the conservation of mass throughout the process. However, several factors hinder the application of PBE to colloidal suspensions such as the lack of reliable models for aggregation and breakup, their inherent inability to fully take into account the disordered structure of colloidal aggregates and their integro-differential nature which asks for complex solution techniques. Discrete Element Methods (DEM) represent a valid alternative to study colloidal suspensions; DEM simulations assume colloidal clusters to be composed by a number of distinct elements, each one subject to the colloidal forces arising from the interaction with nearby elements and to the hydrodynamic forces due to the interaction with the dispersing medium. Introducing models for such forces, DEM simulations can track the motion of each individual particle of a cluster, providing valuable insight into the suspension dynamics. However, the applicability of DEM is hindered by the high computational cost, which so far has restricted its use to the study of single aggregates or at most of very small populations. In this work, in order to circumvent the high computational cost typically associated to pure DEM simulations and to deal with the uncertainty which affects the PBE approach, a novel method was developed: it is a mixed stochastic-deterministic numerical method which couples the mean-field approach of PBE (solved stochastically with a Monte Carlo (MC) algorithm) with detailed DEM simulations; the basic idea behind such a combination is that the dynamics of a dilute suspension is determined by a sequence of binary encounter events between the suspended particles, each of which can result into an aggregation, a breakage, a restructuring of the aggregates or into any combination of these phenomena. Therefore, the MC is used to sample a sequence of such events and the DEM is used to accurately simulate them; the advantage of such a combination is that the DEM is used to track the motion of just two clusters at a time. The developed MC-DEM was proven to be a flexible and reliable tool; it was used to investigate some typical phenomena occurring in colloidal suspensions, returning valuable insights both in the aggregation/breakup dynamics and in the morphology of colloidal clusters.