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Capillary-induced deformations of a thin elastic sheet.
1Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA nbrubaker@math.arizona.edu.
Summary
We present a 3D model for capillary origami, simulating the initial folding of a finite-thickness plate during droplet encapsulation. This model offers insights into the mechanics of capillary-driven self-assembly processes.
Area of Science:
- Physics
- Materials Science
- Fluid Dynamics
Background:
- Capillary origami utilizes surface tension for self-assembly.
- Modeling droplet-plate interactions is crucial for micro-device fabrication.
Purpose of the Study:
- To develop a three-dimensional model for capillary origami systems.
- To analyze the initial folding phase of a finite-thickness rectangular plate during droplet encapsulation.
- To provide a solvable two-dimensional model for comparison and a full three-dimensional model for numerical simulation.
Main Methods:
- Development of a three-dimensional model for capillary origami with a finite-thickness, stretchable, and slightly deflecting rectangular plate.
- Simplification to a two-dimensional model for an infinite aspect ratio plate, allowing for exact solutions.
- Numerical simulations of the full three-dimensional model under small drop volume conditions.
Main Results:
- The two-dimensional model provides an exactly solvable expression, comparable to existing inextensible plate models.
- Numerical simulations demonstrate the deformation of the plate and droplet due to capillary forces in the three-dimensional model.
- The study characterizes the initial folding dynamics of the capillary origami system.
Conclusions:
- The developed three-dimensional model accurately captures the initial folding dynamics of capillary origami systems.
- The study validates the model through comparison with two-dimensional analogs and numerical simulations.
- This work provides a foundation for understanding and designing capillary-driven self-assembly processes.
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