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# Applied Mathematics Colloquium – Thomas P. Witelski (Duke University)

## November 15, 2023 @ 3:30 pm - 4:30 pm

**Coarsening dynamics of condensing fluid thin films**

**Abstract:** The behavior of thin layers of viscous fluids coating solid surfaces is of importance in many industrial and natural applications. Interfacial instabilities and pattern formation can occur in films on water-repellent surfaces. Thin films of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. Considered over long times, the volatility of the fluid can have a strong influence on the dynamics. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation. A reduced-order dynamical system is derived based on interactions between quasi-steady droplets in the weak condensation limit. Dynamics for arrays of identical drops and pairwise droplet interactions are investigated to provide insights into the coarsening dynamics of macroscopic systems. Weak condensation is shown to be a singular perturbation,

fundamentally changing the long-time coarsening dynamics compared to non-volatile mass-preserving fluids. This is joint work with Hangjie Ji (NCSU).

Applied Mathematics Colloquium

There will be a post-colloquium tea from 4:30p-5:00p in PH 330.