  Microfluidic systems are now being designed with precision to execute
increasingly complex tasks. However, their operation often requires numerous
external control devices due to the typically linear nature of microscale
flows, which has hampered the development of integrated control mechanisms. We
address this difficulty by designing microfluidic networks that exhibit a
nonlinear relation between applied pressure and flow rate, which can be
harnessed to switch the direction of internal flows solely by manipulating
input and/or output pressures. We show that these networks exhibit an
experimentally-supported fluid analog of Braess's paradox, in which closing an
intermediate channel results in a higher, rather than lower, total flow rate.
The harnessed behavior is scalable and can be used to implement flow routing
with multiple switches. These findings have the potential to advance
development of built-in control mechanisms in microfluidic networks, thereby
facilitating the creation of portable systems that may one day be as
controllable as microelectronic circuits.
