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.
Type
Honors thesisDepartment
MathematicsPermalink
https://hdl.handle.net/10161/2258Citation
Semko, Jeremy (2010). Statistical Analysis of Simulations of Coarsening Droplets Coating a Hydrophobic Surface.
Honors thesis, Duke University. Retrieved from https://hdl.handle.net/10161/2258.Collections
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