(In)Compressibility and parameter identification in phase field models for capillary flows

M. Dehsara, H. Fu, S. Dj Mesarović, D. P. Sekulić, M. Krivilyov

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Phase field (diffuse interface) models accommodate diffusive triple line motion with variable contact angle, thus allowing for the no-slip boundary condition without the stress singularities. We consider two commonly used classes of phase field models: the compositionally compressible (CC) model with compressibility limited to the fluid mix within the diffuse interface, and the incompressible (IC) model. First, we show that the CC model applied to fluids with dissimilar mass densities exhibits the computational instability leading to the breakup of the triple line. We provide a qualitative physical explanation of this instability and argue that the compositional compressibility within the diffuse interface is inconsistent with the global incompressible flow. Second, we derive the IC model as a systematic approximation to the CC model, based on a suitable choice of continuum velocity field. Third, we benchmark the IC model against sharp interface theory and experimental kinetics. The triple line kinetics is well represented by the triple line mobility parameter. Finally, we investigate the effects of the bulk phase field diffusional mobility parameter on the kinetics of the wetting process and find that within a wide range of magnitudes the bulk mobility does not affect the flow.

Original languageEnglish
Pages (from-to)189-214
Number of pages26
JournalTheoretical and Applied Mechanics
Volume44
Issue number2
DOIs
StatePublished - 2017

Bibliographical note

Funding Information:
This work was supported by through US NSF Grants CBET #1234581 and CBET #1235759 and NASA grants NNX16AG57G and NNX17AB52G. DPS acknowledges the support through the Distinguished 1000 Plan Foreign Professorship at the Harbin Institute of Technology, China. MK acknowledges financial support from Ministry of High Education and Research, Russia, under Grant No. 2049 and RFBR under Grant No. 14-29-10282.

Funding Information:
Acknowledgements. This work was supported by through US NSF Grants CBET #1234581 and CBET #1235759 and NASA grants NNX16AG57G and NNX17AB52G. DPS acknowledges the support through the Distinguished 1000 Plan Foreign Professorship at the Harbin Institute of Technology, China. MK acknowledges financial support from Ministry of High Education and Research, Russia, under Grant No. 2049 and RFBR under Grant No. 14-29-10282.

Keywords

  • Computational instabilities
  • Diffusive triple line motion
  • No-slip boundary condition
  • Quasicompressibility

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering
  • Applied Mathematics

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