UC Merced

This thesis aims to characterize the behavior of reactive gas mixtures and aggregate dynamics at small scales. Since at scales ranging from nanometers to micrometers fluids are discrete systems made of individual particles, the full characterization of their dynamics requires modeling approaches capable of capturing both the mean behavior of the fluid and the impacts of thermal fluctuations due to random molecular motion. Here I present three different approaches to model fluid systems at small scales in a physically-accurate, mathematically-sound and computationally-efficient manner.

First, I discuss how to model the dynamics of reactive gas mixtures at the mesoscopic scale in a thermodynamically consistent manner. To this end, I incorporate a chemical Langevin equation approach into the framework of fluctuating hydrodynamics (continuum stochastic approach). I find that in order to obtain physically accurate results, one needs to fully characterize the temperature dependence of the rate constants of a chemical reaction. I validate this formulation by simulating a reversible dimerization reaction and characterize the spectrum of fluctuations at thermodynamic equilibrium.

Secondly, I discuss a Brownian dynamics formulation (particle-based approach) to model the formation of aggregates. I incorporate rotational effects, size-dependent diffusivities and settling under gravity into the well-established framework of Diffusion-Limited Cluster Aggregation. I characterize how the inclusion of rotational effects and settling lowers the fractal dimension typically found in aggregates, while size-dependent diffusivities slow down their growth rate.

Finally, I discuss a boundary integral formulation to solve the Stokes Equations (continuum deterministic approach) to characterize the internal and external stresses felt by different types of marine aggregates settling under gravity or exposed to some laminar shear flow. I find that the internal stresses induced by gravity distribute differently in aggregates compared to those induced by a shear flow, leading to different breakup distributions. Furthermore, I find that the largest stress felt by aggregates exposed to a shear background flow shows a quadratic dependence on the aggregate's radius, indicating that the contribution of extensional effects on the stresses is dominant over rotational effects.