Simulating capillary folding of thin elastic sheets with pinned contact lines

We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the elastic sheet and a droplet deposited on top of it. Firstly, we derive the equilibrium equations by minimizing the total energy of the system....

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Published inJournal of computational physics Vol. 511; p. 113124
Main Authors Li, Zhixuan, Ren, Weiqing
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.08.2024
Subjects
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ISSN0021-9991
1090-2716
DOI10.1016/j.jcp.2024.113124

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Abstract We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the elastic sheet and a droplet deposited on top of it. Firstly, we derive the equilibrium equations by minimizing the total energy of the system. This energy comprises the interfacial energies and the elastic energy, which is described by the nonlinear Koiter's model. Then we develop a time-splitting numerical scheme to solve the gradient flow dynamics. Following this dynamics, the system evolves towards the equilibrium state. At each time step, we first determine the droplet surface with a constant mean curvature by minimizing a squared area functional, subject to the boundary condition at the pinned contact line. The elastic sheet, discretized by the C1-conforming subdivision element method, is then evolved by taking into account the fluid pressure and the capillary force. We propose a novel remeshing strategy to avoid the need for interpolating the capillary force on the sheet boundary and to prevent simulations from breakdown due to distorted meshes. We perform numerical tests to demonstrate the accuracy of the numerical method, as well as its ability to predict folded structures for various types of sheets. •Introduced a 3D model for the capillary folding of thin elastic sheets.•Developed a time-splitting numerical scheme for the gradient flow dynamics.•Proposed a novel remeshing strategy to avoid distorted meshes.•Obtained numerical results in good agreements with experimental results.
AbstractList We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the elastic sheet and a droplet deposited on top of it. Firstly, we derive the equilibrium equations by minimizing the total energy of the system. This energy comprises the interfacial energies and the elastic energy, which is described by the nonlinear Koiter's model. Then we develop a time-splitting numerical scheme to solve the gradient flow dynamics. Following this dynamics, the system evolves towards the equilibrium state. At each time step, we first determine the droplet surface with a constant mean curvature by minimizing a squared area functional, subject to the boundary condition at the pinned contact line. The elastic sheet, discretized by the C1-conforming subdivision element method, is then evolved by taking into account the fluid pressure and the capillary force. We propose a novel remeshing strategy to avoid the need for interpolating the capillary force on the sheet boundary and to prevent simulations from breakdown due to distorted meshes. We perform numerical tests to demonstrate the accuracy of the numerical method, as well as its ability to predict folded structures for various types of sheets. •Introduced a 3D model for the capillary folding of thin elastic sheets.•Developed a time-splitting numerical scheme for the gradient flow dynamics.•Proposed a novel remeshing strategy to avoid distorted meshes.•Obtained numerical results in good agreements with experimental results.
ArticleNumber 113124
Author Li, Zhixuan
Ren, Weiqing
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Keywords Koiter's energy
Capillary folding
Elastic sheet
Subdivision element
Contact line
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Snippet We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the...
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StartPage 113124
SubjectTerms Capillary folding
Contact line
Elastic sheet
Koiter's energy
Subdivision element
Title Simulating capillary folding of thin elastic sheets with pinned contact lines
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