Flows in fluid-walled conduits driven by Laplace pressure

In conventional microfluidic devices, fluids are often confined behind solid plastic walls that restrict access and trap gas bubbles; in open microfluidics some solid walls are replaced by fluid ones (i.e. interfaces with immiscible fluids). In both cases, flows are usually driven by external pumps or gravity. An innovative open technology has been developed in which two-dimensional patterns of cell-culture medium in standard Petri dishes are confined by fluid walls made of an immiscible and bio-inert fluorocarbon (FC40). To provide refreshing media flows to cells in such circuits, an established pumping system that exploits differences in Laplace pressure across open interfaces has been applied to drive flow without using external pumps: a source drop autonomously empties through a straight conduit into the rest of the dish (the sink). Whereas conduits with solid walls have unchanging boundaries and flows within them are well understood, the challenge is to predict flows in circuits where fluid walls morph as pressures change. Numerical and semi-analytical equations enabling the prediction of changing flows are developed, and predictions validated experimentally.