Forced air oscillations - pneumatic capacitance in microfluidic oscillators produces non-linear responses and emergent behaviors.

Pneumatic control mechanisms have long been integral to microfluidic systems, primarily using solenoid valves, pressurized gases, and vacuums to direct liquid flow. Despite advancements in liquid-driven self-regulated microfluidic circuits, gas-driven systems leveraging fluid compressibility remain underexplored. This study presents a mathematical and experimental investigation of gas-driven microfluidic circuits, focusing on forced-air oscillators. We derive and validate a first-principles model of microfluidic circuit elements operated under positive pressurization, using a 'molecular packets' analogy to elucidate compressibility effects. Our findings reveal that gas compressibility impacts circuit behavior, by acting similar to a large capacitor in the system, which inherently results in longer oscillation periods. As the syringe evacuates, the capacitance decreases, which in turn reduces the oscillation period. Experimental validation of our system demonstrates persistent behavior when using forced air to drive the microfluidic oscillators, this includes assessing devices with various PDMS membrane thicknesses, as well as evaluating device performance under different flow rates and syringe sizes. The forced air oscillators exhibited decreasing periods and capacitance over time, aligning with our theoretical predictions.