Dynamics and Steady-states of Thin Film Droplets on Homogeneous and Heterogeneous Substrates

Abstract

In this dissertation, we study the dynamics and steady-states of thin liquid films on solid substrates using lubrication equations. Steady-states and bifurcation of thin films on chemically patterned substrates have been previously studied for thin films on infinite domains with periodic boundary conditions. Inspired by previous work, we study the steady-state thin film on a chemically heterogeneous 1-D domain of finite length, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the 1-D steady-state solutions that could exist on such substrates into six different branches and develop asymptotic approximation of steady-states on each branch. We show that using perturbation expansions, the leading order solutions provide a good prediction of steady-state thin film on a stepwise-patterned substrate. We also show that all of the analysis in 1-D can be easily extended to axisymmetric solutions in 2-D, which leads to qualitatively the same results. Subject to long-wave instability, thin films break up and form droplets. In presence of small fluxes, these droplets move and exchange mass. In 2002, Glasner and Witelski proposed a simplified model that predicts the pressure and position evolution of droplets in 1-D on homogeneous substrates when fluxes are small. While the model is capable of giving accurate prediction of the dynamics of droplets in presence of small fluxes, the model becomes less accurate as fluxes increase. We present a refined model that computes the pressure and position of a single droplet on a finite domain. Through numerical simulations, we show that the refined model captures single-droplet dynamics with higher accuracy than the previous model.