Hydrodynamics in a minimal nanocomposite system: theoretical description and computational simulation

In this thesis, we introduce the concept of a minimal nanocomposite system and use it to explore the wetting and dewetting behaviour that is observed during the fabrication of nanocomposite materials, and the shear-induced migration of a nanoparticle across the interface between two liquid polymer phases. Having described the relevant equilibrium thermodynamics of polymer blends, and the dynamics of phase separation when a polymer blend is near its critical point, we present a theoretical framework for understanding the motion of out-of-equilibrium, inhomogeneous liquids in the presence of a solid surface. This framework is consistent with known results in colloidal science, and with Onsager's formalism for non-equilibrium thermodynamics, and is derived by applying variational principles to a generic Gibbs free energy functional for a system in which there is a composition gradient, and an interaction potential between the inhomogeneous liquid and the solid surface. Within this framework, we construct a physical model of the minimal nanocomposite system. The model is grounded in continuum fluid dynamics, and uses the fluid particle dynamics method to manage the boundary conditions in a multi-phase system. One benefit of this approach is that a non-zero slip length, of monomer length scale, naturally emerges when the system is described in the correct physical terms. The result is a pair of coupled equations for the velocity field and the order parameter (concentration) field, which we solve numerically. Thus, our model can represent the effects of both hydrodynamic flows and diffusion in the minimal nanocomposite system. We apply our model to systems with various degrees of entanglement, and various degrees of segregation between the two liquid polymer phases. At higher degrees of entanglement, we observe slower wetting and dewetting dynamics, and greater difficulty in inducing the particle to migrate from one liquid phase to the other when the system is sheared. With weaker segregation between the liquid polymer phases, we observe a wider range of steady states when the system is sheared, and less predictability in the final steady state. A simple geometrical model of dewetting under shear, combined with a small dose of physical realism, is found to predict the dewetting simulation results with fair accuracy. Our model is grounded in the physics of continuum fluid dynamics and non-equilibrium thermodynamics and, suitably adapted, has the potential to describe the behaviour of more complex systems, including those that contain many nanoparticles.