Abstract
Porous structures are naturally abundant and synthesized in the industry for their unique properties, offering specific features and benefits. Recently, these structures have been utilized as infill geometries in various applications, such as designing heat exchangers, chromatography, and catalysts to enhance their performance.
In chromatography, porous shapes are used as filters to facilitate the separation of fluid components in a mixture. The process involves flowing a mixture into a container filled with filters, where the components are separated through interaction with the filter surfaces. Porous structures are particularly advantageous as filters because they allow fluid to pass through without blockage while providing sufficient surface area for effective separation.
Manufacturing highly porous shapes remains a significant challenge. The advent of 3D printing has revolutionized the creation of these complex porous structures, enabling engineers to design and fabricate intricate infill geometries with diverse shapes and features tailored to specific applications. Among these 3D printable porous shapes, recently minimal surfaces have gained attention due to their periodic nature, which simplifies analysis by focusing on repeating atomic units. Performing calculations on these atomic units is sufficient to understand the structures formed by their extensions and predict their functionalities.
Despite the benefits of minimal surfaces, whether we can effectively modify and optimize these surfaces for specific chromatography applications and offer better filters remains to be seen. Traditional methods for representing minimal surfaces have limitations, such as mesh requirements and a lack of optimization parameters to provide adequate tunability.
This thesis investigates the challenge of fine-tuning minimal surfaces for the mentioned filters from two perspectives: (1) modifying a minimal surface-based shape on itself by imposing parameters on it to refine and enhance its characteristics, and (2) modifying a shape by interpolating it with other shapes to inherit features and characteristics from a group of shapes. For the purpose of modifying a shape on itself, this research developed a mathematical framework using geometric tools and medial axis graphs to formally represent minimal surface shapes. This representation provides an intuitive way to impose parameters on shapes by leveraging their skeletal graphs, which proved to offer both a greater number and more effective parameters for tuning minimal surface-based porous shapes. For the second perspective, we employed an AI-driven method to smoothly and compactly deform shapes between two or more shapes. This representation enables continuous deformation of shapes from one to another and beyond.
Since testing a large number of filters in practice is impractical to determine the most efficient designs, the performance of shapes in real chromatography applications is simulated. In each simulation, a porous filter with fine-tuned minimal surfaces was designed and tested in a digital test bed, which served as a digital twin of its industrial counterpart. Throughout the simulations, a constant mixture with the same characteristics as a real one was simulated to flow through the test bed for all filter shapes.
The simulations modeled the molecular behavior of fluid flow within the test bed, demonstrating how modified minimal surfaces in the filters could influence flow direction and enhance the separation of mixture components. By running these simulations with fine-tuned minimal surfaces, alternative optimized shapes were discovered.
The results highlighted that the representation method based on medial graphs provides an excellent alternative to traditional approaches for representing minimal surfaces. This method offers a robust framework for effectively fine-tuning shapes to improve performance in chromatography applications.
Additionally, the thesis analysis highlights the efficiency of neural networks in compactly representing shapes, with a single network capable of managing a group of shapes from a reduced embedding space. These shapes were found to inherit characteristics from various other shapes, combining advantageous features that make them highly suitable for engineering applications.
While we focused on chromatography applications for testing, the methods and solutions presented here are expected to apply to other engineering applications and computational simulation tasks, paving the way for developing and optimizing innovative minimal surface-based materials with application-specific advantages.