Experiments on Nonlocal Fluid-Flow Metamaterials.

Metamaterials for controlling fluid flow have recently attracted considerable attention as an emerging new direction in the field of metamaterials. Herein, nonlocal metamaterials composed of one-dimensionally periodic networks of standard microfluidic tubes and connectors are designed, comprising nearest-neighbor (local) and beyond-nearest-neighbor (nonlocal) connections of order N = 2,3,4. The relative importance of laminar water flow through the nonlocal and local tubes is controlled by introducing tailored constrictions into the local tubes that serve as water-flow resistors. Unusual alternating backward/forward laminar flows of water that depend on the metamaterial parameters and on the boundary conditions are observed. Qualitatively, the backward/forward flows can be seen with the naked human eye by following microparticles introduced into the water. Quantitatively, the backward/forward flows are characterized and mapped by digital image analysis of movies taken with a camera. The experimental findings agree well with finite-element calculations of the network's fluid streamlines that exhibit loop-like behavior as well with calculations of the evanescent zero-frequency Bloch eigenmodes of a simplified discrete periodic model, providing an intuitive understanding.