# Coarsening of Thin Fluid Films

The ensemble model takes the form of an integro-differential equation for the distribution function, much like the model of Ostwald ripening proposed by Lifshitz and Slyozov. A convenient choice of scaling yields an intermediate asymptotic self-similar solution. This solution is compared to numerical simulations of the ensemble model and histograms of drop masses from the CDS model. The early-time dynamics before similarity are explored by varying the initial distribution of drop sizes. Interesting far-from-similarity ``stairstep'' behavior is observed in the coarsening rate when the initial distribution has a very small variance. A well-chosen initial condition with a fractal-like structure is shown to replicate the stairstep behavior.

At very long times, the mean drop size grows large, requiring the inclusion of gravity in the model. The CDS model parameters are modified as a result of the dependence of drop shapes on both size and gravity. The new dynamical system predicts the coarsening rate slowing from a power law to an inverse logarithmic rate. The energy liberated by each coarsening event is shown to approach a gravity-dependent constant as the mean drop mass increases. This suggests a reason for the coarsening slow-down.

Advisor:Witelski, Thomas P.

School:Duke University

School Location:USA - North Carolina

Source Type:Master's Thesis

Keywords:mathematics coarsening thin films stairstep dynamical system

ISBN:

Date of Publication:04/15/2008