Geometry-Induced Capillary Rise and Directional Flow in Porous Lattice Structures

Precise control of capillary-driven liquid transport in porous media underpins numerous interfacial processes in microfluidics, water harvesting, and biomimetic systems. Conventional random porous materials exhibit structural heterogeneity that yields stochastic and irreproducible flow behavior. It was hypothesized that three-dimensional ordered lattices with well-defined geometry, particularly body-centered-cubic (BCC) lattices, could realize deterministic and tunable capillary rise by regulating structural parameters such as the strut diameter, aspect ratio, and unit-cell configuration. To validate this hypothesis, BCC lattices with systematically varied structural parameters were produced by using an additive-manufacturing approach, and capillary rise behavior was examined across geometries. Visualization techniques, including optical- and X-ray-based methods, were used to elucidate the progression of liquid fronts and meniscus evolution. A force-balance model was developed to predict the maximum rise height by incorporating adhesive and gravitational effects within the lattice. Geometric periodicity and asymmetry were found to strongly govern the interfacial transport behavior. Larger strut diameters and denser lattice arrays enhance the capillary height by increasing Laplace pressure and extended liquid-solid contact perimeter. Multicell configurations promoted cooperative meniscus coalescence and triangular wetting fronts, yielding predictable and anisotropic fluid propagation. Moreover, gradient-configured lattices with asymmetric strut distributions yield passive yet directional liquid transport, driven by spatial variations in hydraulic resistance. These findings extend classical capillary theory to ordered three-dimensional porous networks, unveiling geometry as a powerful design parameter for programmable, energy-efficient fluidic, and interfacial systems.