Skip to main content
Journal cover image

Steady states of thin film droplets on chemically heterogeneous substrates

Publication ,  Journal Article
Liu, W; Witelski, TP
Published in: IMA Journal of Applied Mathematics
November 25, 2020

We study steady-state thin films on chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the 1D steady-state solutions that exist on such substrates into six different branches and develop asymptotic estimates for the steady states on each branch. Using perturbation expansions, we show that leading-order solutions provide good predictions of the steady-state thin films on stepwise-patterned substrates. We show how the analysis in one dimension can be extended to axisymmetric solutions. We also examine the influence of the wettability contrast of the substrate pattern on the linear stability of droplets and the time evolution for dewetting on small domains. Results are also applied to describe 2D droplets on hydrophilic square patches and striped regions used in microfluidic applications.

Duke Scholars

Published In

IMA Journal of Applied Mathematics

DOI

EISSN

1464-3634

ISSN

0272-4960

Publication Date

November 25, 2020

Volume

85

Issue

6

Start / End Page

980 / 1020

Publisher

Oxford University Press (OUP)

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0199 Other Mathematical Sciences
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Liu, W., & Witelski, T. P. (2020). Steady states of thin film droplets on chemically heterogeneous substrates. IMA Journal of Applied Mathematics, 85(6), 980–1020. https://doi.org/10.1093/imamat/hxaa036
Liu, Weifan, and Thomas P. Witelski. “Steady states of thin film droplets on chemically heterogeneous substrates.” IMA Journal of Applied Mathematics 85, no. 6 (November 25, 2020): 980–1020. https://doi.org/10.1093/imamat/hxaa036.
Liu W, Witelski TP. Steady states of thin film droplets on chemically heterogeneous substrates. IMA Journal of Applied Mathematics. 2020 Nov 25;85(6):980–1020.
Liu, Weifan, and Thomas P. Witelski. “Steady states of thin film droplets on chemically heterogeneous substrates.” IMA Journal of Applied Mathematics, vol. 85, no. 6, Oxford University Press (OUP), Nov. 2020, pp. 980–1020. Manual, doi:10.1093/imamat/hxaa036.
Liu W, Witelski TP. Steady states of thin film droplets on chemically heterogeneous substrates. IMA Journal of Applied Mathematics. Oxford University Press (OUP); 2020 Nov 25;85(6):980–1020.
Journal cover image

Published In

IMA Journal of Applied Mathematics

DOI

EISSN

1464-3634

ISSN

0272-4960

Publication Date

November 25, 2020

Volume

85

Issue

6

Start / End Page

980 / 1020

Publisher

Oxford University Press (OUP)

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0199 Other Mathematical Sciences
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics