Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows

Zee, Kristoffer G.van der; Zee, Kristoffer G. van der; Miles, Christopher; van der Zee, Kristoffer George; Hubbard, Matthew E.; MacKenzie, Roderick

Abstract

© Springer Nature Switzerland AG 2020. We use phase-field techniques coupled with a Coleman–Noll type procedure to derive a family of thermomechanically consistent models for predicting the evolution of a non-volatile thin liquid film on a flat substrate starting from mass conservation laws and the second law of thermodynamics, and provide constraints which must be met when modeling the dependent variables within a constitutive class to ensure dissipation of the free energy. We show that existing models derived using different techniques and starting points fit within this family. We regularise a classical model derived using asymptotic techniques to obtain a model which better handles film rupture, and perform numerical simulations in 2 and 3 dimensions using linear finite elements in space and a convex splitting method in time to investigate the evolution of a flat thin film undergoing rupture and dewetting on a flat solid substrate.

Citation

Zee, K. G. D., Zee, K. G. V. D., Miles, C., van der Zee, K. G., Hubbard, M. E., & MacKenzie, R. (2020). Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows. In H. van Brummelen, A. Corsini, S. Perotto, & G. Rozza (Eds.), Numerical methods for flows: FEF 2017 selected contributions (121-129). Springer Verlag. https://doi.org/10.1007/978-3-030-30705-9_11

• Acceptance Date: Jun 25, 2018
• Online Publication Date: Feb 23, 2020
• Publication Date: Jan 1, 2020
• Deposit Date: Jul 24, 2018
• Publicly Available Date: Jan 2, 2021
• Publisher: Springer Verlag
• Pages: 121-129
• Series Title: Lecture Notes in Computational Science and Engineering
• Series Number: 132
• Series ISSN: 1439-7358
• Book Title: Numerical methods for flows: FEF 2017 selected contributions
• ISBN: 9783030307042
• DOI: https://doi.org/10.1007/978-3-030-30705-9_11
• Public URL: https://nottingham-repository.worktribe.com/output/941690
• Publisher URL: https://link.springer.com/chapter/10.1007%2F978-3-030-30705-9_11
• Additional Information: First Online: 23 February 2020