| Summary: | One of the most significant challenges in materials science and engineering is to create materials with tailored surface properties that can be controlled and optimized for specific applications. A common problem in this application is the creation of surfaces of minimal area, since many processes such as surface tension and reactivity create an energy penalty for a surface having unnecessary area. Many processes exist to calculate these surfaces for various scenarios, but the goal of this work is to create a simulation for calculating surfaces that not only try to minimize their area, but also try to adhere to a specific curvature, as surfaces which naturally curve are common in nature, especially biomaterials. In fact, any surface treatment process which leaves one side of an interface with a different compressive force than the other side (thermal tempering of glass, cell membrane formation, thin film vapor deposition) can be a suitable target for simulation using this method.
The examples displayed in this work all focus on the evolution of the shape of a soap film between two rings, which in the case of minimal area forms a catenoid. It is important to note, however, that the algorithm developed is not constrained to this problem, and any starting mesh of a surface can be input to calculate upon; as many variables as possible have been left entirely generic to create a multipurpose tool that can calculate ideal curved surfaces for thin film materials. The performance of the system lacks what would be required for processing larger models such as foam surfaces, but this work also details methods by which one could further optimize the system for dealing with larger models in a timely fashion.
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