  The tendency for flows in microfluidic systems to behave linearly poses a
challenge for designing integrated flow control schemes to carry out complex
fluid processing tasks. This hindrance has led to 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. We suggest that these results, which are supported by fluid dynamical
simulations and theoretical modeling, have the potential to inspire development
of new built-in control capabilities, such as on-chip timing and synchronized
flow patterns.
