Flow rate variations in microfluidic circuits with free surfaces

We investigate analytically and experimentally the flow rate through a biochip in a circuit involving a peristaltic pump and reservoirs with liquid/air interfaces. Peristaltic pumps are a convenient way to achieve recirculation in microfluidic circuits. We consider different cases: reservoirs in contact with ambient air, tight reservoirs, and imperfect tightness leading to air or liquid leaks. We demonstrate that if changes in hydraulic resistance are slow enough, i.e., if cells do not proliferate too fast, the system may reach an equilibrium, with a difference in liquid height between inlet and outlet reservoir compensating the pressure drop in the biochip. We compute the flow rate through the biochip in the transient regime as well as the characteristic time. We also show that depending on the circuit dimensions, this equilibrium may never be reached. We provide guidelines to design tubings and reservoirs to avoid this situation and ensure a smooth recirculation at a desired flow rate, which is a necessary condition for dynamic cell culture.