Imbibition Theory and Design for Multiscale Micropillar Random Arrays

Efficient liquid transport in micrometer-scale confined spaces is crucial for phase-change thermal management systems, like heat pipes (HPs). While multiscale micropillar random arrays (MMRAs) demonstrate enhanced imbibition performance, their structural randomness has hindered the development of a concise predictive theory. The imbibition dynamics of MMRAs can be effectively modeled using an equivalent square micropillar array approach, where liquid transport is primarily governed by the continuous interpillar spacing. Representative MMRAs, copper forest arrays (CFAs), were fabricated via electrodeposition with gradient current density. Key parameters, average porosity (ε), total covered area fraction (ϕ), and effective pillar radius (re), were characterized. A predictive model linking the ratio of permeability K to effective capillary radius Rc (i.e., K/Rc) to these microstructural parameters was developed and validated with imbibition experiments. The parameters ε, ϕ, and re are the dominant factors controlling K/Rc. High K/Rc was achieved in CFAs by synergistically enhancing ε and re at low ϕ. The model enables direct K/Rc prediction from structural parameters without imbibition experiments. Furthermore, a generalized dimensionless resistance coefficient (Cf) is introduced, quantifying the fundamental Rc-K trade-off in porous media and extending the theory's utility to the design of advanced materials for thermal management.