UCLA

Microfluidics, fluid dynamics on the micro-scale, has been an active area of research due to its applications - separating particles, mixing fluids, and generating microdroplets. This thesis presents a mathematical model and analysis of two microfluidic technologies. The first is the use of micro-particles to form uniform microdroplets. We build a model using surface tension energy minimization to prove that the uniform distribution of droplets is an energy minimum distribution. Additionally, we use a random pairwise interaction model to understand the amount of mixing needed to achieve the uniform distribution. Based on this mathematical model we show that adding larger particles reduces the amount of mixing required and suggests an improved particle design.

The second is the focusing of particles flowing through a duct. Depending on both the size and shape of the particle and duct, the focusing can happen on different positions in the duct cross-section or not happen at all. Understanding the particle dynamics of the cross-section is important for the development of related technologies. We develop a simplified approximate model that combines the drag force due to Dean flow and the lift force with a single parameter that characterizes the relative strength between the two. The cross-sectional dynamics of this model preserve that of the full model. The simplified model exhibits three distinct dynamics as the single parameter changes. We analyze the three cross-sectional dynamics and the bifurcations between them.