Braess's paradox and programmable behaviour in microfluidic networks.

Microfluidic systems are now being designed with precision as miniaturized fluid manipulation devices that can execute increasingly complex tasks. However, their operation often requires numerous external control devices owing to the typically linear nature of microscale flows, which has hampered the development of integrated control mechanisms. Here we address this difficulty by designing microfluidic networks that exhibit a nonlinear relation between the applied pressure and the flow rate, which can be harnessed to switch the direction of internal flows solely by manipulating the input and/or output pressures. We show that these networks- implemented using rigid polymer channels carrying water-exhibit an experimentally supported fluid analogue of Braess's paradox, in which closing an intermediate channel results in a higher, rather than lower, total flow rate. The harnessed behaviour is scalable and can be used to implement flow routing with multiple switches. These findings have the potential to advance the development of built-in control mechanisms in microfluidic networks, thereby facilitating the creation of portable systems and enabling novel applications in areas ranging from wearable healthcare technologies to deployable space systems.

Levitation of heavy particles against gravity in asymptotically downward flows.

In the fluid transport of particles, it is generally expected that heavy particles carried by a laminar fluid flow moving downward will also move downward. We establish a theory to show, however, that particles can be dynamically levitated and lifted by interacting vortices in such flows, thereby moving against gravity and the asymptotic direction of the flow, even when they are orders of magnitude denser than the fluid. The particle levitation is rigorously demonstrated for potential flows and supported by simulations for viscous flows. We suggest that this counterintuitive effect has potential implications for the air-transport of water droplets and the lifting of sediments in water.

Heterogeneity-stabilized homogeneous states in driven media.

Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven systems, but there are many instances in which such instabilities are undesirable. Using parametric resonance as a model process, here we show that a range of states that would be destabilized by symmetry-breaking instabilities can be preserved and stabilized by the introduction of suitable system asymmetry. Because symmetric states are spatially homogeneous and asymmetric systems are spatially heterogeneous, we refer to this effect as heterogeneity-stabilized homogeneity. We illustrate this effect theoretically using driven pendulum array models and demonstrate it experimentally using Faraday wave instabilities. Our results have potential implications for the mitigation of instabilities in engineered systems and the emergence of homogeneous states in natural systems with inherent heterogeneities.

Spontaneous oscillations and negative-conductance transitions in microfluidic networks.

The tendency for flows in microfluidic systems to behave linearly poses challenges for designing integrated flow control schemes to carry out complex fluid processing tasks. This hindrance precipitated the use of numerous external control devices to manipulate flows, thereby thwarting the potential scalability and portability of lab-on-a-chip technology. Here, we devise a microfluidic network exhibiting nonlinear flow dynamics that enable new mechanisms for on-chip flow control. This network is shown to exhibit oscillatory output patterns, bistable flow states, hysteresis, signal amplification, and negative-conductance transitions, all without reliance on dedicated external control hardware, movable parts, flexible components, or oscillatory inputs. These dynamics arise from nonlinear fluid inertia effects in laminar flows that we amplify and harness through the design of the network geometry. These results, which are supported by theory and simulations, have the potential to inspire development of new built-in control capabilities, such as on-chip timing and synchronized flow patterns.