Hindered diffusion of nanoparticles

Abstract: Brownian theory provides us with a powerful tool which can be used to delve into a microscopic world of molecules, cells and nanoparticles, that was originally presumed to be beyond our reach. Consequently, modeling the inherent dynamics of a system through a Brownian transport equation is of relevance to several real-word problems that involve nanoparticles including, the transport and mitigation of particulate matter (PM) generated though fossil fuel combustion and nanocarrier mediated drug delivery. Experimentally forecasting these systems is challenging due to the simultaneous prevalence of disparate length and time scales in them. Correspondingly, an in-silico driven assessment at such nanoscales can complement existing experimental techniques. Hence, in this thesis, a novel multiphase direct numerical simulation (DNS) framework is proposed to address the transport at these nanoscales. A coupled Langevin-immersed boundary method ( LaIBM ), that solves the fluid as an Eulerian field and the particle in a Lagrangian basis, is developed in this thesis. This framework is unique in its capability to include the resolved instantaneous hydrodynamics around the Brownian nanoparticle (without the need for an a-priori determination of the relevant mobility tensors) into the particle (Langevin) equation of motion. The performance of this technique is established and validated using well-established theoretical bases including the well-known theories for unbounded and hindered diffusion (wherein hydrodynamic interactions mediated by the fluid such as particle-particle or particle-wall influence the governing dynamics) of Brownian particles in a liquid. Correspondingly, it is shown that directional variations in mean-squared displacements, velocity auto-correlation functions and diffusivities of the Brownian nanoparticle correspond well with these standard theoretical bases. Moreover, since the resolved flow around the particle is inherently available in the proposed DNS method, the nature of the hydrodynamic resistances (on the particle) including the inherent anisotropies and correlated inter-particle interactions (mediated by the fluid) are further identified and shown to influence particle mobility. Furthermore, this framework is also extended towards Brownian transport in a rarefied gas using first order models to account for the non-continuum effects. Thus, the utility of this novel method is established in both colloids and aerosols, thereby aiding in modeling the transport of a fractal shaped PM (in the latter) and a spherical nanocarrier in a micro-channel (in the former).