Duke Math

Thin Film Dynamics Research

Dynamics of Evaporating Fluid Films

Keywords

Fluid dynamics, thin films, viscous fluids, partial differential equations, dynamical systems

Overview

Volatile liquids play fundamental roles in numerous settings spanning natural and biophysical systems to engineering and industrial processes such as printing and painting. Models for evaporation and condensation are crucial for many applications where such slow processes can shift systems into different operating conditions, as in evaporation of the tear film on the human eye for people with dry-eye syndrome or in engineering cooling systems. Whether the dynamics maintain the liquid as a uniform layer or drive break-up into many droplets can have major consequences.

This research will use numerical simulations and analytical approaches from applied mathematics to develop a better understanding of the long-time dynamics of evaporating layers of viscous liquids. A lubrication model with an evaporative flux will be used to describe the evolution of the height profile of thin films of viscous fluids. The governing equation is a fourth-order nonlinear parabolic partial differential equation generating phase separation between droplets and thin layers while fluid mass is lost or gained due to phase change from the surrounding vapor phase.

The presence of evaporation in the problem fundamentally changes key properties of the solutions of the model and necessitates the development of new extensions of previous methods or other novel approaches. The long-term goal of the project is to develop asymptotic models for the evolution of arrays of interacting volatile droplets.

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Grant Support

We are grateful for support from the following funding programs:

This material is based upon work supported by the National Science Foundation under Grant Number 2008255.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.