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PROJECTION METHOD FOR DROPLET DYNAMICS ON GROOVE-TEXTURED SURFACE WITH MERGING AND SPLITTING

Publication ,  Journal Article
Gao, Y; Liu, JG
Published in: SIAM Journal on Scientific Computing
January 1, 2022

The geometric motion of small droplets placed on an impermeable textured substrate is mainly driven by the capillary effect, the competition among surface tensions of three phases at the moving contact lines, and the impermeable substrate obstacle. After introducing an infinite dimensional manifold with an admissible tangent space on the boundary of the manifold, by Onsager's principle for an obstacle problem, we derive the associated parabolic variational inequalities. These variational inequalities can be used to compute the contact line dynamics with unavoidable merging and splitting of droplets due to the impermeable obstacle. To efficiently solve the parabolic variational inequality, we propose an unconditional stable explicit boundary updating scheme coupled with a projection method. The explicit boundary updating efficiently decouples the computation of the motion by mean curvature of the capillary surface and the moving contact lines. Meanwhile, the projection step efficiently splits the difficulties brought by the obstacle and the motion by mean curvature of the capillary surface. Furthermore, we prove the unconditional stability of the scheme and present an accuracy check. Convergence of the proposed scheme is also proved using a nonlinear Trotter-Kato product formula under the pinning contact line assumption. After incorporating the phase transition information at splitting points, several challenging examples including splitting and merging of droplets are demonstrated.

Duke Scholars

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Published In

SIAM Journal on Scientific Computing

DOI

EISSN

1095-7197

ISSN

1064-8275

Publication Date

January 1, 2022

Volume

44

Issue

2

Start / End Page

B310 / B338

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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ICMJE
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Gao, Y., & Liu, J. G. (2022). PROJECTION METHOD FOR DROPLET DYNAMICS ON GROOVE-TEXTURED SURFACE WITH MERGING AND SPLITTING. SIAM Journal on Scientific Computing, 44(2), B310–B338. https://doi.org/10.1137/20M1338563
Gao, Y., and J. G. Liu. “PROJECTION METHOD FOR DROPLET DYNAMICS ON GROOVE-TEXTURED SURFACE WITH MERGING AND SPLITTING.” SIAM Journal on Scientific Computing 44, no. 2 (January 1, 2022): B310–38. https://doi.org/10.1137/20M1338563.
Gao Y, Liu JG. PROJECTION METHOD FOR DROPLET DYNAMICS ON GROOVE-TEXTURED SURFACE WITH MERGING AND SPLITTING. SIAM Journal on Scientific Computing. 2022 Jan 1;44(2):B310–38.
Gao, Y., and J. G. Liu. “PROJECTION METHOD FOR DROPLET DYNAMICS ON GROOVE-TEXTURED SURFACE WITH MERGING AND SPLITTING.” SIAM Journal on Scientific Computing, vol. 44, no. 2, Jan. 2022, pp. B310–38. Scopus, doi:10.1137/20M1338563.
Gao Y, Liu JG. PROJECTION METHOD FOR DROPLET DYNAMICS ON GROOVE-TEXTURED SURFACE WITH MERGING AND SPLITTING. SIAM Journal on Scientific Computing. 2022 Jan 1;44(2):B310–B338.

Published In

SIAM Journal on Scientific Computing

DOI

EISSN

1095-7197

ISSN

1064-8275

Publication Date

January 1, 2022

Volume

44

Issue

2

Start / End Page

B310 / B338

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics