Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows

  • Christopher Miles
  • Kristoffer G. van der ZeeEmail author
  • Matthew E. Hubbard
  • Roderick MacKenzie
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 132)


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.


Thin films Thermomechanical consistency Coleman–Noll procedure Phase-field model Thin-film rupture Dewetting Free-energy dissipation Rational mechanics 



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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Christopher Miles
    • 1
  • Kristoffer G. van der Zee
    • 1
    Email author
  • Matthew E. Hubbard
    • 1
  • Roderick MacKenzie
    • 2
  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamUK
  2. 2.Faculty of EngineeringUniversity of NottinghamNottinghamUK

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