Abstract
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.
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Acknowledgements
This work was funded by the Leverhulme Trust Modeling and Analytics for a Sustainable Society Grant. The contribution of the second author was partially supported by the Engineering and Physical Sciences Research Council (EPSRC) under grant EP/I036427/1.
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Miles, C., Zee, K.G.v.d., Hubbard, M.E., MacKenzie, R. (2020). Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-030-30705-9_11
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DOI: https://doi.org/10.1007/978-3-030-30705-9_11
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