Dynamics of Evaporating Fluids Films

Duke University, Durham NC

Investigators

Abstract

This research project addresses the needs to develop more comprehensive understanding of models that can predict the behaviors of layers of evaporating fluids. 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. Whether the dynamics maintain the liquid as a uniform layer or drive break-up into many droplets can have major consequences. Volatile liquid films can be used in cooling systems for high-power electrical or mechanical equipment. Heat transfer through uniform fluid layers is known to be less efficient than transfer through comparable arrays of droplets. Hence, optimizing the performance of such systems involves reliably controlling the behavior of the fluid film. While there have been extensive studies of evaporation leading to simple models for the drying of uniform liquid layers and shrinking of individual droplets in many contexts, there are gaps in applying the models uniformly to broader settings. This work seeks to build a systematic understanding of the dynamics that can result from the interaction of evaporation competing with wetting effects for fluids on solid surfaces. In addition to presenting results from this project in journals targeting broader audiences in fluid dynamics and engineering, the PI will use the project to incorporate new techniques into training in applied mathematics. Parts of the project will be used in the PI's courses on mathematical modeling and fluid dynamics. The project will also serve as the focus for the PI's continuing track record in the training of graduate students and providing research experiences for undergraduates. 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 describing wetting effects generating phase separation (sometimes called de-wetting instabilities) between droplets and thin layers while fluid mass is lost or gained due to phase change from the surrounding vapor phase. Recent results have shown that there is a critical range of parameters where the influence of substrate properties can dramatically change the course of the dynamics between the two long-time attracting behaviors: evaporation of droplets down to a minimal adsorbed film or condensation yielding growing thicker layers. Mathematical analyses for many aspects of the study of mass-conserving unstable thin film models have been well-developed using techniques from partial differential equations, nonlinear dynamics, and related models in materials science. However, introducing evaporation into 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. Obtaining this kind of coarsening model will involve new challenges as the quasi-steady framework underpinning the mass-conserving model no longer directly applies. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.