Statistical Analysis of Simulations of Coarsening Droplets Coating a Hydrophobic Surface

Abstract

Thin layers of slow-moving, viscous fluid which coat hydrophobic surfaces are shaped by the competing forces of disjoining pressure and surface tension. These forces form the fluid layer into an array of discrete droplets separated by an ultra thin layer. However, the droplet array is unstable, and the droplets will interact with one another. To determine the structure and properties of steady droplets, we use the Reynolds’ PDE in one dimension and phase-plane methods. We can then analyze the unstable droplet system by utilizing paired ODEs. Numerical solutions show how the droplets interact to produce movement and mass exchange, giving rise to coarsening events which reduce the number of droplets in the system. These events occur when a droplet collapses into the ultra thin layer or when two droplets collide, and thus, merge. Using numerical simulations and analysis of their results, we aim to gain a better understanding of the dynamics of this system including the factors that influence coarsening events such as system parameters and initial conditions.