Programming flow anisotropy in hydrodynamic metamaterials via series-parallel equivalent fluidic networks.

Abstract

Precise microflow control underpins microfluidic technologies in precision medicine, yet conventional approaches rely on anisotropic materials or external fields, limiting fabrication simplicity and scalability. Unlike transformation-based or data-driven approaches, we demonstrate that flow anisotropy can be programmed through the layered organization of locally homogeneous, isotropic media via a series-parallel equivalent fluidic network (SPEFN) realized as single-medium metamaterials (SMMs). SPEFN provides an analytically invertible mapping from network topology to the macroscopic effective-viscosity tensor, from which a connectivity-controlled anisotropy law and an exact non-disturbance condition emerge as direct analytical consequences. We experimentally realize three monolithic SMM devices: a spiral-layered director, an annular cloak, and a fan-shaped concentrator. Particle-tracking velocimetry confirms the predicted responses across all devices, including ≈30° streamline reorientation and a concentrator velocity ratio of 1.37 versus a predicted value of 1.38. The cloak exhibits higher apparent suppression than predicted; tracer retention or adhesion visible in Movie S1 may partly explain this difference. The system further shows robust performance under strongly non-uniform inflow and sub-percent fabrication tolerances.