Nested homogenization of xylem-inspired porous fluidic networks

Abstract

Xylem transport relies on a hierarchy of vessels, pits, and porous membranes that redistribute the flow across several length scales. Directly resolving this nested architecture is computationally prohibitive for network-scale studies, while existing reduced models often require prescribed inter-vessel hydraulic resistances. Here, we develop a nested homogenization framework for rigid porous membranes under single-phase viscous flow. The approach first replaces the pore-scale structure of a membrane by an effective stress-jump interface law, and then embeds this effective interface inside a second characteristic problem to obtain a conduit-scale closure for pit-mediated exchange. In this way, pore-scale geometry is systematically propagated to network-scale hydraulic response through effective tensors. The reduced model is compared against fully resolved simulations in simplified xylem-inspired vessel connections, showing that the homogenized description captures the pressure drop and flow redistribution. Finally, the resulting interface law is embedded within a xylem-like network with randomly disabled conducting elements, demonstrating that the model is suitable to describe the emergent hydraulic response from the coupling between local membrane-mediated transfer and network topology. The framework provides a tractable route for studying multiscale porous fluidic networks and forms a basis for extensions involving deformable structures and multiphase flows.