Nested homogenization of xylem-inspired porous fluidic networks

Abstract

Fluidic networks may contain hierarchical porous structures in which transport across macroscopic interfaces is controlled by geometrical features at multiple nested length scales. Direct resolution of all these scales rapidly becomes computationally prohibitive for network-scale studies, while reduced descriptions require a priori effective hydraulic properties. Here, we develop a nested homogenization framework for rigid porous interfaces under single-phase viscous flow. The pore-scale structure is first replaced by an effective stress-jump interface law, which is then embedded as an internal interface condition within a second characteristic problem at the intermediate scale. This successive upscaling propagates the pore-scale geometry through effective tensors to obtain a closure for flow across the whole porous structure. The approach is validated against fully resolved simulations at the mesoscopic and macroscopic scales, for two xylem-inspired channel configurations, and accurately captures pressure drops and flow redistribution while strongly reducing computational cost. The framework provides a tractable bottom-up description of a network composed of nested porous membranes and a basis for extensions to deformable structures and multiphase flows.