Programmable flow in nonlinear bistable channels.

Flow in a channel at low Reynolds numbers typically exhibits a linear relationship between pressure drop and flow rate due to the dominance of viscous forces. Here, we demonstrate that introducing an anchored, deformable fiber into a microfluidic channel disrupts this linearity, resulting in nonlinear flow behaviors, including bistability and hysteresis. We show that beyond a critical flow rate, the fiber undergoes a sudden snap-through transition. This behavior generates a hysteresis loop, analogous to those observed in mechanical metamaterials. The topology of these hysteresis loops can be modulated by varying the channel geometry and fiber properties. Leveraging this bistability, we propose the concept of fluidic metamaterials that are capable of programmable flow control and memory-like responses, thereby opening new avenues for applications in microfluidics and soft robotics.