Complex dewetting of thin liquid films

Significance 

Recent technological advances have led to broad applications of thin films, characterized by a small ratio of film thickness to typical lateral length, from the nanoscale to the microscale. To be more specific, lately, immense interest has emerged regarding the instabilities of thin films on the nanoscale, in particular for polymeric films, nematic liquid crystal (NLC) films and molten metal films. As such, most published works have concentrated on the developed instabilities being complicated by the interplay of a number of different physical effects. In the nanoscale range, such instabilities are often mediated by fluid/solid interaction, regularly modelled by incorporating in the governing equations a “disjoining pressure” term that plays an important role in determining the film stability. For NLC films, such effective disjoining pressure is often called a structural disjoining pressure, since it includes the elastic forces that arise due to interactions of the rod-like molecules, which affect the local structure of the director field.

To date, the long-wave theory framework has proven to be very useful in simplifying the otherwise extremely intricate free surface problems involved in such complex thin film flows. Various instability mechanisms relevant to thin films have been discussed in the literature; however, detailed and systematic studies of instabilities of fluid films of nanoscale thickness, where the disjoining pressure takes a complex form, and which catalogue precisely the conditions under which such films are unstable, metastable, and absolutely stable (depending on the mean film thickness), are lacking.

Motivated by their studies of NLC films, and by this perceived gap in the literature, New Jersey Institute of Technology researchers: Michael-Angelo Lam (PhD candidate), Professor Linda J. Cummings and Professor Lou Kondic conducted in-depth analysis of how changes in the mean film thickness can lead to different stability regimes, and the specific role that the disjoining pressure properties play in how instabilities are manifested. Furthermore, they carried out extensive numerical simulations of dewetting, and discussed the connection between instability mechanisms and the properties of the drop patterns that form during the final stages of instability development. They also discussed in detail the dynamics that result, both as a consequence of non-local infinitesimal perturbations, and of finite-size localized perturbations. Their work is currently published in Journal of Fluid Mechanics.

The research method employed commenced with the derivation of the governing equation in the context of NLC films where the differences between their model and those of other researchers were highlighted. Next, they discussed the spinodal instabilities, due to the presence of global (random) perturbations, intended to model the noise that is always present in physical experiments. Lastly, they assessed the influence of localized perturbations on the film stability where they applied the marginal stability criterion to help develop additional analytical insight regarding instability development.

The authors observed that, in the NLC context, novel elements included dynamic relaxation of the free surface polar anchoring, as a function of film thickness. Additionally, the researchers were also able to highlight the differences and similarities between the presented model, and others discussed in the literature. They also noted that their model exhibited a range of film thickness, such that the film was linearly unstable, which emerged to be analogous to the so-called ‘forbidden range’ discussed in the literature.

To sum it up, New Jersey Institute of Technology scientists presented results that were relevant to a much wider class of problems involving thin films on substrates, such that the fluid-solid interaction involving a relatively complex form of effective disjoining pressure. Generally, an extensive statistical analysis of the computational results obtained, combined with novel analytical results based on the marginal stability criterion, allowed them to identify a variety of instability mechanisms. Altogether, it is anticipated that their work will act as a stepping stone for future experimental and analytical investigations, which may provide additional insight into the phenomena presented.

About the author

Michael-Angelo Y.-H. Lam recently graduated with a D. Phil. in Mathematics at the New Jersey Institute of Technology where he has previously received his BA and MS degrees. His research focuses on computational mathematics and modeling of fluid mechanical systems such as thin liquid films and crystal growth in colloid suspensions.

He will continue his career at the U.S. Army Corps of Engineers’ Coastal and Hydraulics Laboratory where he will be working on nearshore processes and high-performance computing.

About the author

Linda Cummings is a Professor of Mathematics and an Associate Dean at the New Jersey Institute of Technology. She earned her BA and D.Phil. in Mathematics at the University of Oxford. Her research covers a range of applications of low-Reynolds number fluid dynamics, including industrial and biomedical applications.

Current research projects include flows of nematic liquid crystals, mathematical modeling of membrane filtration, and mathematical modeling of tissue engineering, as well as more theoretical investigations of the use of complex analysis in 2D slow viscous flow.

About the author

Lou Kondic is a Professor of Mathematics at the New Jersey Institute of Technology. He earned his BS degree at University of Zagreb, and his PhD degree at the City University of New York.

His research interests include scientific computing and modeling of complex systems including thin fluid films including non-Newtonian rheology, thermal and phase change effects. He also works extensively on developing new mathematical approaches to analysis of particulate-based systems.

Reference

Michael-Angelo Y.-H. Lam, Linda J. Cummings and Lou Kondic. Stability of thin fluid films characterized by a complex form of effective disjoining pressure. Journal of Fluid Mechanics (2018), volume 841, page 925–961.

Go To  Journal of Fluid Mechanics

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