(4e) Multi-Order Combinatorial Lattices for Spatial Control of Transport Phenomena

Additive manufacturing advances have spawned numerous applications across chemical engineering domains, spanning separations, engineered living systems, biomedical devices, and process intensification. These applications frequently leverage additive-only lattice structures as novel substrates to control the relevant transport phenomena through tunable geometric features and functional material properties. However, the potential to use these systems for precise spatial control of phenomena is hindered by choices often made to streamline the design process. In particular, lattice designs tend to use homogeneous parameters and a cubic grid system in which a unit cell is simply stacked along the primary Cartesian axes. Here we present a framework for multi-order combinatorial lattices that facilitates local tunability and inherently complements multi-material additive manufacturing. We report the range of fluid dynamic behavior in lattice columns composed of one-, two-, and three-dimensional alternating combinations of various unit cells with cell-based length scales ranging from 1-5 millimeters. Furthermore, for unit cells like simple cubic and Kelvin, which can be described with characteristic features either at the core or perimeter of the repeat unit, we examine column performance and as-printed dimensional fidelity as a function of standard or alternative unit cell design. In comparing the types of combinatorial structures produced via vat photopolymerization on a Carbon M1, we find results that are consistent with previous reports, and depending on unit cell selection, 2D combinations can achieve lower pressure gradients than 1D or 3D combinations. Furthermore, we find that alternative unit cell designs show nearly identical pressure gradients as standard homogeneous columns, but in combinatorial form with complementary unit cells, there is a statistically significant performance difference between alternative and standard combinations. Finally, we discuss the implications of these findings for structures deviating from cubic grid systems, and we highlight the compatibility of this framework with our previous developments in lattice generation and designs exhibiting directionally dependent flow behavior. Together, these advances capitalize on the design flexibility of additive-only structures to create spatially distributed, dynamic, and responsive phenomena, enhancing the potential of current technologies and enabling new approaches and applications throughout the discipline.