Stable diffusion gradients in microfluidic conduits bounded by fluid walls

Assays mimicking in vitro the concentration gradients triggering biological responses like those involved in fighting infections and blood clotting are essential for biomedical research. Microfluidic assays prove especially attractive as they allow precise control of gradient shape allied to a reduction in scale. Conventional microfluidic devices are fabricated using solid plastics that prevent direct access to responding cells. Fluid-walled microfluidics allows the manufacture of circuits on standard Petri dishes in seconds, coupled to simple operating methods; cell-culture medium sitting in a standard dish is confined to circuits by fluid walls made of an immiscible fluorocarbon. We develop and experimentally validate an analytical model of diffusion between two or more aqueous streams flowing at different rates into a fluid-walled conduit with the cross-section of a circular segment. Unlike solid walls, fluid walls morph during flows as pressures fall, with wall shape changing down the conduit. The model is validated experimentally for Fourier numbers